Author: Richard B. Langley

Innovation: GNSS Antennas and Humans

A Study of Their Interactions

By Jared B. Bancroft, Valérie Renaudin, Aiden Morrison, and Gérard Lachapelle

INNOVATION INSIGHTS by Richard Langley

GPS IS VIRTUALLY UBIQUITOUS with more than 400 million units estimated to be in use in the United States alone. Some of these units are standalone devices such as those used in surveying and timing applications and those used for vehicle navigation or tracking with permanent or temporary mountings. However, the majority of the units are integrated into cellular telephones, tablet computers, personal digital assistants, watches, cameras, and other devices, which are designed to be operated in close contact with the human body. We even now have GPS shoes!

It is well known that the performance of the antenna of a radio receiver can be affected when it is used in close proximity to the human body. We only have to touch the whip antenna of a portable AM/FM or scanner radio to convince ourselves of the effect. So, when we use a handheld GPS receiver or wear a GPS watch, or put a GPS-equipped cellular telephone up to our ear, are there any effects on the operation of the receiver?

It turns out that there are four major effects that can change the performance of a GPS (or other GNSS) receiver antenna when placed near or on the human body. The impedance of the antenna may be changed causing a drop in power transfer to the receiver front end. The center frequency and bandwidth of the antenna may be changed again resulting in a loss of received power. The gain pattern of the antenna may be changed. However, the change may be favorable, improving reception for a given satellite azimuth and elevation angle. And lastly, there will be close-range multipath between the antenna and the body skin.

All of these factors need to be taken into consideration when a manufacturer is designing a GPS unit to be operated in close proximity to a human body. Trade-offs might be possible and certain designs may make the antenna less likely to interact with its surroundings.

But how does one go about assessing the antenna’s performance in a repeatable and quantifiable way?

In this month’s column, a team of researchers from The University of Calgary report on tests conducted on two different types of GPS antennas operated in the vicinity of a human phantom — an artificial body with similar electromagnetic properties as that of a real human.

“Innovation” features discussions about advances in GPS technology, its applications, and the fundamentals of GPS positioning. The column is coordinated by Richard Langley, Department of Geodesy and Geomatics Engineering, University of New Brunswick. To contact him with topic ideas, email him at lang @ unb.ca.

GNSS-based navigation is the foundation of many pedestrian navigation systems. The use and benefit of GNSS receivers to locate people has increased dramatically over the past few years. Pedestrian navigation applications include mobile phone users, first responders, health and activity monitoring, consensual tracking (such as offender management), recreational use, and tracking of military personnel. GNSS navigation systems are commonly available in watches and personal entertainment devices. Some applications contain GNSS receivers and antennas in shoes, glasses, and jackets. Since each application using a GNSS receiver to locate people requires an antenna, the optimal type, size, and location on the body is becoming increasingly important.

This article addresses adverse antenna effects when the antenna is placed near or on the human body, specifically in the reactive near field at the GPS L1 frequency. Using real data collected on a human phantom over prolonged periods, the changes within the antenna are observed as a function of distance from the body. Thus, a performance profile can be generated to quantify the power loss incurred by loading the antenna. The study applies equally well to all GNSS operating at or near the GPS L1 frequency.

The researchers have theoretically addressed performance of GPS antennas in close proximity to a human body. Using simulations to provide analysis of antenna detuning effects, one research group showed a 24.4-MHz shift in the resonance frequency of the antenna when placed 10–40 millimeters from a simulated human chest. The resonance shift was common at all distances, although the return loss decreased as the antenna was moved further away from the chest.

A few studies have developed antennas to be located in protective (or otherwise) garments for specific applications. Our team previously analyzed the impact of antenna location on the human body by comparing the solution of eight identical and simultaneous navigation solutions.

Antenna-Body Interaction

Antenna detuning refers to the consequence of the electrical interaction between an antenna and an adjacent object, the body of a user in this context, which causes the center frequency of the antenna to deviate from the desired center frequency. More generally, there are several effects that serve to degrade antenna performance that arise when an antenna operates near the body of a user.

The first of these effects is a change in the impedance of the antenna, as shown in FIGURE 1. (See online sidebar for antenna and electromagnetic radiation term definitions.) The change results in the impedance of the antenna no longer properly matching that of the network that it is expected to drive, therefore causing incomplete power transfer between the antenna element and the subsequent radio-frequency (RF) stages.

Selected Antenna and Electromagnetic Radiation Terms

Axial ratio. A measure of the polarization ellipticity of an antenna designed to receive circularly polarized signals. An axial ratio of unity, or 0 dB, implies a perfectly circularly polarized antenna.

Bandwidth. The range of frequencies over which an antenna is designed to operate efficiently. The bandwidth limits are typically determined by a particular reduction in gain compared to that at the antenna’s center frequency; for example, 3 dB or 10 dB.

Conductivity. A measure of a material’s ability to conduct an electric current. The reciprocal of resistivity. Units are mhos per meter.

Dielectric. A material in which there are no free charges that can move through it under the influence of an electric field. An insulator. However, minute displacements of positive and negative charges in opposite directions are possible. A dielectric in which this charge displacement has taken place is said to be polarized.

Far field. The area sufficiently far from an antenna where the gain pattern is essentially independent of distance. In the far field, the power of an electromagnetic wave traveling in free space drops off as the square of the distance from the transmitting antenna.

Fresnel reflection coefficient. A measure of the degree of reflection of an electromagnetic wave at the interface between two media. Dependent on the properties of the media, the polarization of the wave, and the angle of incidence.

Gain. For a transmitting antenna, the ratio of the radiation intensity in a given direction to the radiation that would be obtained if the power accepted by the antenna was radiated isotropically. For a receiving antenna, it is the ratio of the power delivered by the antenna in response to a signal arriving from a given direction compared to that delivered by a hypothetical isotropic reference antenna.

Gain (amplitude) pattern. The spatial variation of an antenna’s gain.

Human phantoms. Models of parts of the human body used in engineering, science, and medical studies designed to mimic a particular physical, chemical, or electrical behavior.

Impedance. The complex ratio of the voltage to the current in an alternating current circuit. Sometimes called complex resistance in which case the absolute value of the complex resistance is called the impedance. Units are ohms.

Lossy material. A material in which a significant amount of the energy of a propagating electromagnetic wave is absorbed (dissipated) per unit distance traveled by the wave.

Near field. The region around an antenna within a few wavelengths where there are strong inductive and capacitive effects from the currents and charges in an antenna that cause electromagnetic components not to behave like far-field radiation. Within the radiating part of the near field, the gain pattern is dependent on the distance from the antenna.

Polarization. The sense of vibration of electromagnetic radiation. There are two main types of polarization: linear, in which the radiating wave’s electric field vector is confined to a particular direction (typically vertical or horizontal); and circular, where the electric field vector rotates as the wave propagates through space. Depending on the sense of rotation, a signal’s waves may be left-hand or, as with GPS signals, right-hand circularly polarized. For maximum response, the polarization of a receiving antenna should match the polarization of the signals.

(Absolute) Permittivity. A measure of how an electric field affects, and is affected by, a dielectric material. In a sense, it describes a material’s ability to transmit (or “permit”) an electric field. Since the response of most materials to external fields generally depends on the frequency of the field, permittivity is expressed as a complex quantity with real and imaginary components as a function of frequency. Units are farads per meter.

Relative permittivity. The ratio of the permittivity of a material to that of free space or a vacuum. Also called the dielectric constant. Unitless.

Return loss. A measure of the effectiveness of power delivery from a transmission line to a load such as an antenna or vice versa. If the power incident on an antenna is Pin and the power reflected back to the source is Pref, the degree of mismatch between the incident and reflected power in the traveling waves is given by the ratio Pin/Pref. Units are dB. Functionally related to the Fresnel reflection coefficients and VSWR.

Voltage standing wave ratio (VSWR). A measure of the size of the reflected waves in a transmission line due to impedance mismatches between the line and a connected antenna. The ratio of the maximum voltage along the line to the minimum voltage along the line. Ideally, an antenna should have a VSWR value of unity.

FIGURE 1. Change in the reactive portion of the impedance of a patch antenna versus separation distance between the antenna element and imitation human skin (Courtesy, Buckley et al., 2010; see Further Reading).

The figure provides an example of the impedance for a patch antenna plotted against the separation distance of a simulated human wrist. When mounted directly on the user’s skin surface, this specific antenna gains significant reactive impedance that results in a large voltage standing wave ratio (VSWR) with the network.

A second effect of antenna proximity to human skin is the alteration of the center frequency, as well as the alteration of the antenna bandwidth. Depending on the bandwidth of the signal of interest, the bandwidth of the antenna element, and the degree of center-frequency shifting and bandwidth loss experienced, these factors can contribute to significant loss of received power.

Thirdly, it is important to note that in some configurations, a “lossy” medium adjacent to an antenna may improve the apparent performance of the antenna due to changes in its gain pattern that result in better receive or transmit performance for a given azimuth and elevation angle.

For any application in which the antenna may be either in free space or directly adjacent to a lossy medium such as a human body, the use of balanced antennas is recommended. The image current of a balanced antenna is contained within complementary structures of the antenna itself, not within the casing or adjacent material of the antenna, therefore making the antenna much less likely to interact with surrounding media.

Fourth, the close proximity of a reflective material increases close-range multipath. If the distance between the reflector (that is, skin) and the antenna is close to half a wavelength, giving a 180º phase shift of the carrier, deconstructive interference can occur. There are several factors that contribute to this including the back lobe of the antenna gain pattern, reflection coefficient of the skin beneath the antenna, and the incident angle of the incoming ray. Approximation via simple ray tracing becomes dauntingly complex due to the variation of the antenna properties listed above, resulting from detuning. Therefore, observation of the effect becomes easier than modeling an incoming ray and its multipath counterparts.

Phantom Body Simulation

To conduct an assessment of the impact of the human body on the radiation patterns of diverse antennas in the context of tracking GNSS signals, a human body phantom has been designed for collecting the experimental data. Variations of the locations and orientations of the antenna rigidly mounted on a human shoulder, head, or any other locations would render the repeatability and comparison of the collected data hardly feasible. Furthermore, the distance that separates the antenna from the human body surface could only be precisely controlled using an artificial modeling of the human body. Therefore, a human body phantom is required for productive analysis.

Because the human body is mainly composed of water, the presence of human tissue in the vicinity of the antenna introduces an absorption and reflective effect that alters the performance of the antenna. Different mathematical models have been developed for representing the different component combinations of a human body. Based on the study of numerous women and men of different ages and sizes, a classic model predicting the fat-free mass of a person has been developed and assumes that 73 percent of a human body consists of water. Looking at the elemental composition in the human body, it can be found that a concentration of 7 grams of salt per liter of water provides an acceptable modeling of the human tissues. Complex shapes of the human body are used for modeling more precisely the layered structure of the human tissues using either a more realistic human phantom or a more detailed model comprising the extensive data on the dielectric properties of each layer constituting the human tissues of interest. For context of this study, the phantom was kept simple and was made of a large plastic container filled with a 7 percent concentration of a saline solution.

The radiative transfer of the human body phantom on the reception of GNSS signals can be evaluated through the understanding of the dielectric permittivity of the solution. Different models, including the Wagner, Debye, Cole & Cole, or Fricke, are commonly used for studying the dielectric behavior of biological tissues. The Debye model gives the permittivity of an aqueous saline solution of salinity, S, at a fixed temperature, t, as

(1)

where

is the angular frequency (Hz),

ε_i equals 8.8419 ×10^-12 (farads per meter),

τ is the relaxation time (seconds),

σ is the ionic conductivity of the dissolved salts (mhos per meter), and

ε₀ and ε∞ are the static and high frequency dielectric constants.

Equation (1) gives the dielectric proprieties of the human phantom solution for a specific temperature, saline concentration, and temperature. The experiments we conducted and report on in this article lasted several days and were conducted outside, which unfortunately resulted in temperature fluctuations. Consequently, the 7 percent saline solution over the temperature range of 11º to 31º C for L1 (1575.42 MHz) results in a 9 percent variation of permittivity. As shown in FIGURE 2, the dielectric constant over the experimental temperature range is in the interval [74.6, 81.9]. Because the variation is small, the permittivity value can be closely approximated to a mean value of 78.

FIGURE 2. Real part of the permittivity of the human body phantom as a function of temperature for the GPS L1 frequency.

Reflection Coefficient of the Phantom Body

The Fresnel reflection coefficients for a smooth flat surface depend on frequency, the incident angle, polarization, and ground characteristics. Since the container is full of salted water it can also be considered a reflective surface.

The relative permittivity of the saline solution given in Equation (1) can be reformatted as

(2)

The reflection coefficients with vertical and horizontal polarizations, respectively, of the electromagnetic wave on the surface of the saline water are given by the following Fresnel equations:

(3)

(4)

where R_v and R_h are the vertical and horizontal polarized reflection coefficients, respectively, and θ is the incident angle.

Assuming that the water surface is flat and infinite, Equations (3) and (4) are plotted against the incident angle in FIGURE 3. The reflection coefficients were estimated using a mean temperature of 21°C, a salt concentration of 7 percent and at the L1 frequency.

FIGURE 3. Fresnel coefficient for L1 considering a flat surface of salted water.

While the saline solution of the human phantom has an angle of incidence and direction of polarization dependent on reflectivity, the fact that the GPS carrier is circularly polarized must be considered. Due to the circular polarization of the carrier and that of most antenna elements intended for GPS use, the received signal strength of the reflected wave will always appear to be equal to or higher than that of the reflected portion of the horizontal polarization.

Test Setup

To evaluate the change in gain pattern as function of distance from the phantom, we collected 24-hour data segments. These segments allowed the receiver to observe all satellites. A high-performance GPS L1 receiver module evaluation kit was used with two antennas. The first was a patch antenna while the second was a quadrifilar helix antenna. FIGURE 4 shows both antennas without their coverings. Each antenna has a built-in low noise amplifier (LNA). The antenna specifications are listed in TABLE 1.

FIGURE 4. Patch (above) and quadrifilar (below) antennas used in the tests.

TABLE 1. Antenna specifications.

A water container holding the saline solution was placed on the roof of a building as shown in FIGURE 5. The container had a slight inclination to move a small air pocket to the corner of the container away from the antenna. After a successful 24-hour data collection period, the antenna was supported by a small plastic box and oriented in the same direction. Six vertical distances were selected, namely 0, 11, 22, 30, 41, and 52 millimeters.

FIGURE 5. Data collection with patch antenna fixed to phantom body.

The gain pattern as measured by the C/N₀ values of the path antenna is shown in FIGURE 6. In general, the largest effect is seen near the zenith where the power decreased by 10–15 dB when the antenna was 22 millimeters from the phantom body. It is also observed that the effect is maximized at 22 millimeters, and then reverts back to near normal operation at 52 millimeters. Additionally, at lower elevation angles (< 30º), the gain behaves more linearly, where the largest distance has the least gain, while the smallest distance has the most gain. The effect of the phantom body appears to flatten the gain pattern.

The pattern shown in Figure 6 shows the effect of the proximity to the phantom body over all elevation angles. However, a prominent pattern emerges for measurements made at elevation angles of 45º and 85º. In the case of a 22-millimeter antenna distance from the body, a significant power decrease occurs. For satellites with an 85º elevation angle, nearly 8 dB is lost compared to 5 dB loss at a 45º elevation angle.

FIGURE 6. Gain pattern of the patch antenna as measured by the measured C/N0 at all elevation angles as a function of antenna distance from body. Elevation angles [0º, 90º] have azimuths [180º, 360º], while elevation angles [90º, 180º] have azimuths [0º, 180º].
FIGURE 7 provides the trend as a function of distance from the body. The trend of the power loss at 22 millimeters is common on all measurements, albeit more significant for higher-elevation-angle satellites. For satellite measurements made at an 85º elevation angle, the power varies by 12 dB. When all measurements are considered, which includes more frequent lower-elevation-angle satellite measurements and the fact that the gain pattern deviates significantly at higher elevation angles (as shown in Figure 6), the fluctuation is less prominent.

FIGURE 7. Mean C/N0 measurements of the patch antenna from all measurements and those only at 45º and 85º elevation angles as a function of antenna distance from the body.

To assess the cause of the impact, we removed the phantom and replaced it with a flat aluminum reflector placed beneath the antenna. The antenna was then placed at the same distances above the reflector as previously. Since the gain pattern had been established and this test was to observe the effect of the reflector, only 60 seconds of data was collected at each distance.

FIGURE 8 provides the change in C/N₀ for two tests, which has a comparable trend to that of Figure 7. From the corroboration of the two tests, it appears that the salt water provides similar multipath effects to that of the aluminum sheet. The power loss is then attributed to destructive interference.

FIGURE 8. Mean C/N0 measurements (over 60 seconds) of satellite PRN 8 with 85º elevation angle when placed above an aluminum reflector.

Similar data collections were conducted with the quadrifilar helix in order to assess its ability to perform close to the human phantom. The quadrifilar antenna has the LNA circuitry vertically below the antenna and therefore was placed horizontally on the water container. FIGURE 9 shows its gain pattern. The overall C/N₀is lower but is subject to less variation compared to that of the patch antenna. In general, we noticed lower C/N₀ values with the quadrifilar antenna, regardless of the environment and despite the LNA having 5 dB more amplification. Some moderate variations of up to 10 dB appear on the east side of the antenna (zenith angle [0º, 90º]), but overall the pattern appears to be more regular.

FIGURE 9. Gain pattern of the quadrifilar antenna as measured by the C/N0 of all measurements as a function of antenna distance from body. Elevation angles [0º, 90º] have azimuths [180º, 360º], while elevation angles [90º, 180º] have azimuths [0º, 180º].
The overall power variation was assessed in a similar method. FIGURE 10 shows cubic-like functions with 3-dB variations. There is also no consistent downward power loss trend at 22 millimeters as observed with the patch antenna. As expected, due to the balanced nature of the quadrifilar antenna, the degree of apparent power loss caused by adjacent material is substantially lower compared to the patch antenna. While the peak level of power received is not as high as that experienced with the patch antenna, the consistency of the received power level is better.

FIGURE 10. Mean C/N0 measurements of the quadrifilar antenna from all measurements and those only at 45º and 85º elevation angles as a function of antenna distance from the body.

Conclusions

We have investigated the impact of the proximity of the human body on received signal power associated with operation of L1 GPS antennas through experimental tests. GPS signals have been collected using two different antenna types (a patch antenna and a quadrifilar helix antenna), placed on a human body phantom with different separation distances. A strong relationship between these distances and the averaged received signal power has been observed for both antennas with overall lower C/N₀ values for the quadrifilar antenna. The largest attenuation is not observed when the antenna is directly adjacent to the user body but when it is about 22 millimeters above it. We found that the attenuation mainly results from destructive interference due to multipath. These results suggest that body-mounted GPS antennas should be directly in contact with the user’s body for achieving better tracking performance. Our future research will include theoretically assessing the experimental results for better understanding of the underlying effects.

Acknowledgments

This article is based on the paper “GNSS Antenna-Human Body Interaction” presented at ION GNSS 2011, the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 19–23, 2011. The authors would like to thank Prof. Ron Johnston, Dept. of Electrical and Computer Engineering, The University of Calgary, for his insight and consultation in preparing that paper. We thank John Buckley, Tyndall National Institute, Ireland, and his co-authors for permission to use Figure 1, a version of which appears in “The Detuning Effects of a Wrist-Worn Antenna and Design of a Custom Antenna Measurement System” (see Further Reading).

Manufacturers

The tests discussed in this article used a u-blox AG EVK-6T evaluation kit using a LEA-6T L1 GPS module, an Allis Communication Co. Ltd. M827B active L1 patch antenna, and a Sarantel Ltd. SL1206 active L1 quadrifilar helix antenna.

Jared B. Bancroft is a senior research engineer in the Position, Location And Navigation (PLAN) Group in the Department of Geomatics Engineering at The University of Calgary in Calgary, Alberta, Canada. He received his Ph.D. in geomatics engineering in 2010 and has worked in the area of navigation since 2004. Dr. Bancroft’s research interests include pedestrian and vehicular navigation through data fusion of sensors and satellite navigation data.

Valérie Renaudin is a senior research associate in the PLAN Group. She received an M.S. in geomatics engineering from the Ecole Supérieure des Géomètres et Topographes, France, in 1999 and a doctorate in geomatics engineering from the Ecole Polytechnique Fédérale de Lausanne, in 2009. She was previously the technical director at Swissat AG. Her research interests include low-cost sensors, hybridization techniques, magnetometers, and indoor navigation.

Aiden Morrison is a senior research associate in the PLAN Group. He received his B.Eng. in electrical engineering from Ryerson University, Canada, in 2006 and a Ph.D. in geomatics engineering from The University of Calgary in 2010. His research interests include development of integrated navigation systems.

Gérard Lachapelle holds a Canada Research Chair in Wireless Location in the Department of Geomatics Engineering at The University of Calgary, where he has been a professor since 1988 and heads the PLAN Group. He has been involved in a multitude of GNSS R&D projects since 1980, ranging from RTK positioning to indoor location and GNSS signal processing enhancements.

Further Reading

• Previous Work by Authors
“GPS Observability and Availability for Various Antenna Locations on the Human Body” by J.B. Bancroft, G. Lachapelle, T. Williams, and J. Garrett in Proceedings of ION GNSS 2010, the 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 21–24, 2010, pp. 2941–2951.

• GNSS Antennas
“Mobile-Phone GPS Antennas: Can They be Better?” by T. Haddrell, M. Phocas, and N. Ricquier in GPS World, Vol. 21, No. 2, February 2010, pp. 29–35.

“GNSS Antennas: An Introduction to Bandwidth, Gain Pattern, Polarization, and All That” by G.J.K. Moernaut and D. Orban in GPS World, Vol. 20, No. 2, February 2009, pp. 42–48.

“A Primer on GPS Antennas” by R.B. Langley in GPS World, Vol. 9, No. 7, July 1998, pp. 73–77.

• Interaction between Receiving Antennas and Human Body Parts
“The Detuning Effects of a Wrist-Worn Antenna and Design of a Custom Antenna Measurement System” by J. Buckley, K.G. McCarthy, B. O’Flynn, and C. O’Mathuna in Proceedings of the 40th European Microwave Conference, Paris, France, 28–30 September 2010, pp. 1738-1741.

“One-Layer GPS Antennas Perform Well Near a Human Body” by T. Kellomaki, J. Heikkinen, and M. Kivikoski in Proceedings of EuCAP 2007, the Second European Conference on Antennas and Propagation, Edinburgh, Scotland, November 11–16, 2007, 6 pp.

“Effects of Human Body Interference on the Performance of a GPS Antenna” by M. Ur Rehman, Y. Gao, X. Chen, C.G. Parini, and Z. Ying in Proceedings of EuCAP 2007, the Second European Conference on Antennas and Propagation, Edinburgh, Scotland, November 11–16, 2007, 4 pp.

• Wearable Antennas
“Design of a Protective Garment GPS Antenna” by L. Vallozzi, W. Vadendriessche, H. Rogier, C. Hertleer, and M.L. Scarpello in Microwave and Optical Technology Letters, Vol. 51, No. 6, June 2009, pp. 1504–1508, doi: 10.1002/mop.24372.

“Wearable Antennas in the Vicinity of Human Body” by P. Salonen, Y. Rahmat-Samii, and M. Kivikoski in Proceedings of the IEEE Antennas and Propagation Society International Symposium, Monterey, California, June 20–26, 2004, pp. 467–470, doi: 10.1109/APS.2004.1329675.

“A Small Planar Inverted-F Antenna for Wearable Applications” by P. Salonen, L. Sydänheimo, M. Keskilammi, and M. Kivikoski in Digest of Papers, the Third International Symposium on Wearable Computers, San Francisco, California, October 18–19, 1999, pp. 95–100, doi: 10.1109/ISWC.1999.806679.

• Dielectric Properties of Human Tissue and Sea Water
“New Permittivity Measurements of Seawater” by W. Ellison, A. Balana, G. Delbos, K. Lamkaouchi, L. Ey, C. Guillou, and C. Prigent in Radio Science, Vol. 33, No. 3, 1998, pp. 639–648, doi: 10.1029/97RS02223.

Compilation of the Dielectric Properties of Body Tissues at RF and Microwave Frequencies by C. Gabriel, Final Technical Report, AL/OE-TR-1996-0004, Radio Frequency Radiation Division, Occupational and Environmental Health Directorate, Brooks Air Force Base, Texas, January 1996.

“Studies on Body Composition. III. The Body Water and Chemically Combined Nitrogen Content in Relation to Fat Content” by N. Pacen and E.N. Rathurn in Journal of Biological Chemistry, Vol. 158, 1945, pp. 685–691.

• Human Phantoms
“Solid Phantoms for Evaluation of Interactions Between the Human Body and Antennas” by K. Ito and H. Kawai in Proceedings of IWAT 2005, the 2005 IEEE International Workshop on Antenna Technology: Small Antennas and Novel Metamaterials, Singapore, March 7–9, 2005, pp. 41–44, doi: 10.1109/IWAT.2005.1460993.

“A High-Precision Real Human Phantom for EM Evaluation of Handheld Terminals in a Talk Situation” by K. Ogawa, T. Matsuyoshi, H. Iwai, and N. Hatakenaka in 2001 Digest, IEEE Antennas and Propagation Society International Symposium, Boston, Massachusetts, July 8–13, 2001, Vol. 2, pp. 68–71, doi: 10.1109/APS.2001.959623.

February 1, 2012
Innovation: Know Your Enemy

Signal Characteristics of Civil GPS Jammers

By Ryan H. Mitch, Ryan C. Dougherty, Mark L. Psiaki, Steven P. Powell, Brady W. O’Hanlon, Jahshan A. Bhatti, and Todd E. Humphreys

GPS jamming is a continuing threat. A detailed understanding of how the available jammers work is necessary to judge their effectiveness and limitations. A team of researchers from Cornell University and the University of Texas at Austin reports on their analyses of the signal properties of 18 commercially available GPS jammers.

INNOVATION INSIGHTS by Richard Langley

GPS IS AT WAR. It is a major asset for United States and allied military forces in a number of operating theaters around the world in both declared and undeclared conflicts. But GPS is at war on the domestic front, too — at war against a proliferation of jamming equipment being marketed to cause deliberate interference to GPS signals to prevent GPS receivers from computing positions to be locally stored or relayed via tracking networks.

There have been many notable examples of deliberate jamming of GPS receivers. Many more likely go undetected each day. In 2009, outages of a Federal Aviation Administration reference receiver at Newark Liberty International Airport close to the New Jersey Turnpike were traced to a $33, 200 milliwatt GPS jammer in a truck that passed the airport each day. The driver was reportedly arrested and charged. In July 2010, two truck thieves in Britain were jailed for 16 years. They used GPS jammers to prevent the trucks from being tracked after the thefts. And in Germany, some truck drivers have been using jammers to evade the country’s GPS-based road-toll system.

The U.S. and some foreign governments have enacted laws to prohibit the importation, marketing, sale or operation of these so-called personal privacy devices. Nevertheless, a certain number of jammers are in the hands of individuals around the world and they continue to be available from manufacturers and suppliers in certain countries. So, GPS jamming is a continuing threat both at home and abroad and a detailed understanding of how the available jammers work is necessary to judge their effectiveness and limitations. This information will also help in developing countermeasures that could be incorporated into GPS receivers to limit the impact of jammers.

Jammers constitute an enemy force, and as the Chinese General Sun Tzu stated in the Art of War more than 2,000 years ago, battles will be won by knowing your enemy. In the last verse of Chapter Three, he states:

So it is said that if you know your enemies and know yourself, you can win a hundred battles without a single loss.

If you only know yourself, but not your opponent, you may win or may lose.

If you know neither yourself nor your enemy, you will always endanger yourself.

In this month’s column, a team of researchers from Cornell University and the University of Texas at Austin reports on their analyses of the signal properties of 18 commercially available GPS jammers. The enemy has been exposed.

The Global Positioning System has become increasingly incorporated into civilian infrastructure. The increase in GPS-integrated systems has caused a proportional increase in the vulnerability of these systems to jamming and interference. The interests of individuals or groups willing to break the law may be served by interfering with the normal operation of GPS-enabled systems. As a result, in recent years many GPS jamming devices have become available for purchase over the Internet. These relatively cheap devices, some costing less than an inexpensive GPS receiver, pose a significant risk to the normal operation of many systems reliant on GPS.

Many types of intentional radio frequency (RF) interference exist, including tones, swept waveforms, pulses, narrowband noise, and broadband noise. There are a number of methods for mitigating the effects of jamming and interference, and additional methods exist to locate the sources of the interference. Mitigation and location methods can be improved by use of a priori information about the interference source. This article provides such a priori information for a set of jammers and assesses their threats. Its results are based on two tests. The first test records raw RF data from a selection of jammers and analyzes it using fast Fourier transform (FFT) spectral methods. The second test evaluates the effective range of a subset of the GPS jammers using a commercial off-the-shelf (COTS) receiver.

The article presents results based on 18 civil GPS jammers. There are other types of GPS jammers for sale that were not tested. Furthermore, civil jammer behavior and design is likely to evolve over time. In this article, we draw conclusions based on only the jammers that we tested.

Overview of Civil GPS Jammers

Devices that claim to jam or “block” GPS signals are widely available through a number of websites and online entities. The cost of these devices ranges from a few tens of dollars to several hundred. Their price does not seem to correlate with the claims made by the purveyors of these devices regarding the features and effectiveness of the product in question. Effective ranges from a few meters to several tens of meters are advertised, but the actual effective ranges are significantly greater. Claimed and true power consumptions range from a fraction of a watt to several watts.

We grouped the GPS jammers we examined in this article into three categories based on morphology. The first is a group of jammers designed to plug into an automotive 12-volt auxiliary power supply outlet (cigarette lighter socket); this class of jammer is referred to in the remainder of this article as Group 1. The second category contains those jammers that are both powered by an internal rechargeable battery and that have an external antenna connected via an SMA connector; these jammers are referred to as Group 2. The jammers in Group 3 are disguised as cell phones; they have batteries but no external antennas. Figure 1 shows an example of a device from each of Groups 1–3.

Figure 1. Three jammers are depicted, from left to right Jammers 1, 5, and 15 from Groups 1, 2, and 3, respectively.

All 18 jammers broadcast power at or near the L1 carrier frequency, six broadcast power at or near the L2 carrier frequency, and none broadcast power at or near the L5 carrier frequency. Some of the jammers also broadcast power at frequencies outside of the GPS bands, typically cellular phone or Wi-Fi bands, but those frequencies are outside the scope of this article. Results in this article are for the current power levels broadcast in the GPS L1 and L2 bands, but examination of power levels in non-GPS bands indicate that many of these devices could be easily modified to broadcast much more power in the GPS bands.

The jammer antennas have been removed in most of the testing for this article, but their use in a real-world scenario will modify the jammer behavior. The antennas used by Group 1 and Group 2 jammers are loaded monopole antennas, while those used by the Group 3 jammers are electrically short helical antennas that have approximately the same gain pattern as the loaded monopoles. These antennas broadcast linearly polarized radiation, as opposed to the right-hand circular polarization of GPS signals. The polarization mismatch will cause some loss in received power at a right-hand circularly polarized GPS receiver antenna.

Jammer Signal Characteristics Test

The goal of the first set of tests was to record complex samples of the jamming signals and to derive the jammer characteristics from these data. A two-step procedure was used to collect useful data. The first step used a spectrum analyzer to find the frequency range of the jamming signal near L1 and L2. The second step used this frequency information to set the center frequency of a general-purpose RF digitization and signal storage device with a 12-drive RAID storage array. Offline analyses were then conducted on the recorded data.

The test procedure was as follows. For the first two groups, the jammer was placed inside an RF-shielded test enclosure shown in Figure 2, to prevent any signal leakage, and its SMA signal output port was connected to the relevant data collection device using a shielded coaxial cable. The signal had to pass from the inside to the outside of the RF enclosure using the built-in coaxial feed-through. Note, therefore, that no jammer signal radiation occurred for Group 1 and 2 jammers even inside the RF enclosure. The enclosure was used primarily as a precaution.

Figure 2. RF-shielded test enclosure. Jammers were operated inside the enclosure to prevent emission of their RF signals.

None of the Group 3 jammers had external antennas. Therefore, they were allowed to radiate in the RF enclosure using their internal antennas. To capture the signal, a receiving patch antenna with active amplification was placed in the RF enclosure, and the antenna output was connected to the relevant RF recording device via the enclosure’s coaxial feed-through. The jammer and receiving antenna were separated by about 14 centimeters. The patch antenna field-of-view center was pointed directly at the jammer. The jammer was oriented such that the axis of its helical antenna was pointing perpendicular to the line from the receiving antenna to the jammer.

Jammer Signal Characteristics Test Results

Although 18 jammers were tested, only a representative subset is discussed here. The signals were analyzed using FFT spectral methods and measurements of in-band power. Figure 3 displays the results of this analysis for a typical jammer from Group 1.

The top plot of Figure 3 graphs frequency on the vertical scale versus time on the horizontal scale. The bottom plot graphs power on the vertical scale versus time on the horizontal scale. Each vertical slice of the recorded RF data plot is a single FFT frequency spectrum. It covers 62.5 MHz centered on the L1 band and has a resolution of approximately 1 MHz. The relative power spectral density of each slice is indicated by color. The time axes of both plots span 80 microseconds.

Figure 3. Jammer 4 power spectral density versus time, with color indicating relative power (top plot) and power versus time in a 62.5-MHz band centered at the L1 carrier frequency (bottom plot).

The upper plot of Figure 3 is clearly that of a linear frequency modulation interspersed with rapid resets — a series of linear chirps. Each sweep takes nine microseconds and spans a range of about 14 MHz. This range includes the civil L1 GPS band. The center frequency is depicted by the horizontal red line in the top plot. The power is about 20 milliwatts and remains fairly constant over the sweep.

Three of the Group 1 jammers appeared to be of the same model and one was slightly different. All of them broadcast power only at L1. Despite their similarities in external appearance, the three jammers of the same model exhibited markedly different signal properties. These differences will be presented later in terms of tabulated frequency modulation characteristics and in-band power levels.

One of the Group 2 jammers was unusual in two respects, as illustrated in Figure 4. This figure plots the L2 spectrum whose center is indicated by the horizontal red line in the top plot. The first obvious difference from Figure 3 is that the frequency modulation in time is a triangular wave instead of a sawtooth. Additionally, the modulation frequency is very high in comparison to all the other jammers; its period is only about 1 microsecond. Note that the horizontal scale of this figure spans only 8 microseconds, that is, 10 times less than in Figure 3.

The other Group 2 jammers tended to broadcast sawtooth frequency modulations as in Figure 3. They all broadcast jamming power at L1. Of course, the jammer depicted in Figure 4 broadcast power at L2 as well. Only one other Group 2 jammer had L2 jamming capability. Two of the jammers suffered from poor design of their L1 frequency modulation schemes: they placed no jamming power closer than 4.6 MHz away from the nominal L1 carrier frequency.

Figure 4. Jammer 10 power spectral density versus time (top plot), with resolution of about 3 MHz and color indicating relative power, and power versus time (bottom plot) in a 62.5-MHz band centered at the L2 carrier frequency.

Another unusual frequency modulation was encountered in a Group 3 jammer. The L1 results for this jammer are depicted in Figure 5. It seems to show a linear-type frequency modulation distorted by sudden frequency jumps, as seen in the upper plot of the figure. Despite its irregular nature, this waveform maintains its jamming efficacy.

Figure 5. Jammer 15 power spectral density versus time, with color indicating relative power (top plot) and power versus time in a 62.5-MHz band centered at the L1 carrier frequency (bottom plot). Note the additional frequency jumps in the sweep pattern.

All four jammers in Group 3 broadcast power at L1, L2, and additional frequency bands. Three of the jammers appeared to be of the same model, while a fourth was different. Jammers in this group normally use a standard sawtooth frequency modulation. Figure 5 represents the exception.

Additional types of distortion from the nominal sawtooth frequency modulation have been observed in some of the jammers. Discussion of each additional variation has been omitted here for the sake of brevity. See the authors’ companion conference paper, listed in the Further Reading sidebar for more details.

Frequency Modulation Periods and Ranges. The frequency modulation characteristics of all 18 jammers are listed in Table 1. The first two columns identify each jammer by group number and jammer number. The sweep period and frequency range for the L1 sweep are shown in the third and fourth columns. The two numbers in the fourth column are the upper and lower bounds of the jamming tone sweep range in megahertz above and below the L1 carrier frequency. For instance, the period between resets of the linear frequency modulation of Jammer 1 is 26 microseconds and the tone sweeps from 25.4 MHz below L1 to 31.3 MHz above L1. The fifth and sixth columns are analogous to the third and fourth columns, but for jamming in the L2 band, with entries only for those jammers that broadcast in this band.

The sweep periods were calculated using four contiguous sweeps from near the beginning of each data set and another four sweeps 30 seconds later. The sweep periods exhibited standard deviations of less than 1 microsecond. The reported sweep ranges are the minimum and maximum frequency observed in the same data used to calculate sweep periods. The sweep ranges changed by as much as 2.5 MHz between sweeps.

One can make a number of observations based on Table 1. First, as mentioned previously, jammers which appeared to be of the same model exhibited significant variations in sweep behavior. For instance, Jammers 1, 3, and 4 appeared to be of the same models, yet Jammer 1 has a sweep period nearly three times as long as Jammers 3 and 4. It also has a sweep range four times as wide. Second, some individual jammers were exceptional. For example, Jammer 10 has a sweep period nearly 10 times shorter than any other jammer, and its L1 sweep range exceeded the 62.5 MHz bandwidth recorded by the RF sampling equipment. The sweep range of Jammer 16 also exceeded the sampled bandwidth, though its sweep period was not exceptional. Jammers 12 and 13 do not sweep through the L1 carrier frequency, as indicated by the negative signs in the fourth column of Table 1. Jammer 17 suffered from the same problem, but for both L1 and L2.

Table 1. Frequency characteristics of GPS jammers.

In-Band Jammer Power Levels. The GPS signal is spread over several megahertz by the pseudorandom noise (PRN) codes that modulate the L1 or L2 carrier waves. Different GPS receivers exploit this spreading by processing more or less of the full bandwidth. The RF power of the GPS jamming signal within different bands centered at L1 is an important concern because different receiver RF front-end bandwidths may allow different total amounts of jammer power to pass through them. For example, a C/A-code receiver with a 2-MHz RF front-end bandwidth will pass 10 dB less jammer power than will a 20-MHz bandwidth RF front end of a P(Y)-code receiver if the jammer in question spreads its power evenly over the 20-MHz band centered at the L1 carrier frequency. If the jammer power is concentrated in a 2-MHz range, however, then both receiver front ends will pass equal total jammer power.

To determine the power in different bandwidths, the raw data were filtered to pass only the bandwidths of interest. The data were digitally filtered using a finite input response (FIR) equiripple band-pass filter, providing 60 dB of attenuation at 2 MHz past the roll-off frequency. Note that a real GPS receiver will probably not have analog filter frequency roll offs as sharp as those used in our work.

Table 2 presents the results of this study. It reports power measurements averaged over 15 milliseconds in three different bandwidths: 2, 20, and 50 MHz, all centered at the nominal L1 or L2 carrier frequency. The table also indicates whether each jammer broadcasts power at frequencies other than the GPS frequencies. No power data is given for the non-GPS frequencies because they are not the focus of this article.

A number of observations can be drawn from Table 2. First, there is a large variation in broadcast power among jammers, with Group 2 jammers being on average more powerful. Specifically, Jammer 11 is the most powerful, broadcasting more than a watt in the GPS bands! Second, jammers of the same model broadcast roughly the same amount of power despite the differences in sweep behavior mentioned above. For instance, Jammers 1, 3, and 4 broadcast roughly the same amount of power, and Jammers 15, 17, and 18 do so as well. Third, the poor frequency plans of Jammers 12, 13, and 17 are apparent in the power measurements. These jammers did not sweep a tone through L1 or L2, and effectively no power was measured in the 2-MHz band centered on the L1 or L2 carrier frequencies.

Table 2. Jammer power levels in frequency bands of interest.

Although not shown in the tables, Jammers 12, 13, and 14 exhibited periodic variations in broadcast power. Their peak-to-peak power varies as a sawtooth wave with period approximately 15 milliseconds and amplitude on the order of 10 percent of the total broadcast power.

The measured power values in Table 2 for jammers of Groups 1 and 2 were derived using direct cable connections. Thus, they report the total power into the transmitting antenna. The power received at a GPS receiver’s RF front end will be affected by any antenna inefficiency, the antenna gain pattern, and the space loss, among other effects.

In contrast, the power reported for Group 3 jammers includes all of those effects for the given test configuration. Specifically, the receiving antenna picked up only a fraction of the radiated power because the receiving antenna subtended only a fraction of the 4π steradians around the transmitting antenna. Also, the power that was received was boosted by the receiving antenna’s active low-noise amplifier. Finally, the radiation environment inside the RF enclosure is uncertain, and the enclosure constrains the separation of the antennas to be on the order of one wavelength, thereby giving rise to near-field effects. Therefore, the indicated power levels for the Group 3 jammers do not constitute measures of absolute power. The tabulated power levels for Group 3 jammers are included primarily for purposes of comparison within the group.

Maximum Effective Range Test

The goal of the second set of tests was to determine the effective ranges of the GPS jammers when interfering with a COTS receiver. A constraint on this test was that it could not broadcast harmful radiation to the environment. Ideally, the jammers and a receiver would be taken outside and tested with all antennas attached. However, this type of test would possibly interfere with other equipment and is illegal in the United States. A close approximation to this scenario can be constructed using a high-fidelity simulated GPS signal, a commercial GPS receiver, a GPS jammer in an RF enclosure, and a set of attenuators to simulate various distances. The setup for the second test is shown in the block diagram of Figure 6.

Figure 6. Block diagram of the test procedure and equipment used to determine the GPS jammers’ effective ranges.

Each range test involved running a GPS jammer inside the RF enclosure, passing its signal through the enclosure’s coaxial feed-through, and electrically combining that signal with a GPS simulator signal. The combined signal was then input to the antenna connector of the COTS GPS receiver. Attenuators were inserted in-line with the GPS jammer before it arrived at the combiner. Using this setup, two tests were conducted. The first test determined the jamming signal attenuation level necessary for continuous tacking. The second test determined the attenuation level necessary to allow the receiver to acquire the simulator signal within five minutes from a cold start. As will be shown in the next section, the resulting attenuation values can be converted into effective ranges of the jammers if one makes certain reasonable assumptions about transmitting and receiving antenna gains and path losses.

The simulator power level was set so that the power into the receiver matched that which it would receive from the actual GPS constellation through a typical roof-mounted passive patch antenna. This power level was checked by comparing the resulting C/N0 for all of the visible satellites when using the simulator against typical C/N₀ values when using the roof-mounted antenna. Typical levels reported by the receiver were C/N₀ = 43 dB-Hz.

Maximum Effective Range Results

The jamming signal attenuation levels resulting from the two tests are presented in Table 3. These tests were conducted on one jammer from Group 1 and three jammers from Group 2. No jammers from Group 3 were included because of the broadcast power uncertainties discussed in connection with Table 2.

The attenuation values by themselves are not very useful, but they can be converted into distance measurements with a number of assumptions. The ratio of received power to transmitted power can be expressed as

where G_t is the transmitting antenna gain, G_r is the receiving antenna gain, and the term (λ/(4πr))² is the path loss for radiation of wavelength λ over the distance r. This equation can be solved for the range, r:

The quantity in this formula that equates to the total electrical jammer attenuation produced in each bench-top test is the product of the antenna gains and the ratio of transmitted to received power: G_t G_r(P_t ⁄P_r).

To convert the results in Table 3 into effective ranges, the transmitting and receiving antennas can be assumed to be perfect, lossless, isotropic radiators. In this case, the gain terms, G_t and G_r, are unity. Each measured attenuation value can be converted to the unitless ratio, P_t ⁄P_r , and substituted into the equation for r. Use of this equation at the L1 carrier frequency yields the ranges in Table 4. If the range between the jammer and receiver is less than that listed in the third column of the table, then the jammer will prevent the receiver from tracking and acquiring. If the range is less than that listed in the last column but more than that listed in the third column, the receiver will continue to track but be unable to acquire. The effective ranges are at least an order of magnitude greater than the claims of the jammers’ purveyors.

Table 3. Jammer attenuation levels needed to allow COTS GPS receiver acquisition and tracking.

Table 4. Ranges of jammer effectiveness against COTS GPS receiver when using lossless isotropic antennas.

Distinct scenarios with different antennas can be approximately tested using Table 3 and the range equation. For example, a patch antenna that is oriented perfectly skyward might have 10 dB of attenuation at very low elevation angles, and the jammer might have an additional 3 dB loss due to polarization mismatch. In this scenario, the effective jamming range would be factored down by 10^-13/20 = 0.22. In this case, Jammer 11’s tracking interference range would be reduced from 6.1 kilometers to 1.4 kilometers. Additional jammer signal attenuation might occur if the emissions passed through the reduced RF aperture of a vehicle’s body and windows. Such an effect could be incorporated into the range equation to determine a revised effective range.

Due to the ignored losses in the real system, it would likely be safe to assume that the effective ranges of the GPS jammers would be no greater than those listed in Table 4. The ranges could potentially be greater if a high-gain receiving antenna were aimed directly at the jamming source, or if the jamming source used a high-gain transmitting antenna aimed at the receiver. None of the jammers tested employed such an antenna.

Summary and Conclusions

This article has presented the signal properties of 18 commercially available GPS jammers as determined from two types of live experimental tests. The first test examined the frequency structures and power levels of the jammer signals. It showed that all of the jammers used some sort of swept tone method to generate broadband interference. The majority of the jammers used linear chirp signals, all jammed L1, only six jammed L2, and none jammed L5. The sweep period of the jammers is about 9 microseconds on average, and they tend to sweep a range of less than 20 MHz. Some of the jammers’ sweep ranges failed to encompass the target L1 or L2 carrier frequencies.

The second test provided an estimate of four of the jammers’ effective ranges when deployed against a typical commercial receiver. An upper bound on the effective ranges was calculated for idealized, lossless, isotropic radiating and receiving antennas with matched polarizations. The weakest of the four jammers affected tracking at a range of about 300 meters and acquisition at about 600 meters, while the strongest affected tracking at a range of about 6 kilometers and acquisition at about 8.5 kilometers.

Acknowledgments

The authors thank the U.S. Department of Homeland Security for providing interference devices for testing. This article is based on the paper “Signal Characteristics of Civil GPS Jammers” presented at ION GNSS 2011, the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 19–23, 2011, where it received a best-presentation-in-session award.

Manufacturers

The tests discussed in this article used an Agilent Technologies (www.home.agilent.com) model N1996A spectrum analyzer, a National Instruments PXI-5663 RF vector signal analyzer, a Ramsey Electronics model STE3000B RF shielded test enclosure, an Antcom (www.antcom.com) model 53G1215A-XT-1 patch antenna, and a NovAtel ProPakII-RT2 GPS receiver.

Ryan H. Mitch is a graduate student in the Sibley School of Mechanical and Aerospace Engineering at Cornell University, Ithaca, New York. He received his B.S. degree in mechanical engineering from the University of Pittsburgh.

Ryan C. Dougherty is a graduate student in the Sibley School. He holds a B.S. degree in aerospace engineering from the University of Southern California.

Mark L. Psiaki is a professor in the Sibley School. He received a B.A. degree in physics and M.A. and Ph.D. degrees in mechanical and aerospace engineering from Princeton University.

Steven P. Powell is a senior engineer with the GPS and Ionospheric Studies Research Group in the Department of Electrical and Computer Engineering at Cornell University. He has M.S. and B.S. degrees in electrical engineering from Cornell University.

Brady W. O’Hanlon is a graduate student in the School of Electrical and Computer Engineering at Cornell University. He received a B.S. degree in electrical and computer engineering from Cornell University.

Jahshan A. Bhatti is pursuing a Ph.D. degree in the Department of Aerospace Engineering and Engineering Mechanics at the University of Texas (UT) at Austin, where he also received his M.S. and B.S. degrees. He is a member of the UT Radionavigation Laboratory.

Todd E. Humphreys is an assistant professor in the Department of Aerospace Engineering and Engineering Mechanics at UT Austin and Director of the UT Radionavigation Laboratory. He received B.S. and M.S. degrees in electrical and computer engineering from Utah State University and a Ph.D. degree in aerospace engineering from Cornell University.

Further Reading

• Authors’ Conference Paper

“Signal Characteristics of Civil GPS Jammers” by R.H. Mitch, R.C. Dougherty, M.L. Psiaki, S.P. Powell, B.W. O’Hanlon, J.A. Bhatti, and T.E. Humphreys in Proceedings of ION GNSS 2011, the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation, Portland, Oregon, September 19–23, 2011, pp. 1907–1919.

• Vulnerability of GPS

Vulnerability Assessment of the Transportation Infrastructure Relying on the Global Positioning System – Final Report. John A. Volpe National Transportation Systems Center, Cambridge, Massachusetts, August 29, 2001.

• GPS Jamming

“Car Jammers: Interference Analysis” by R. Bauernfeind, T. Kraus, D. Dötterböck, B. Eissfeller, E. Löhnert, and E. Wittmann in GPS World, Vol. 22, No. 10, October 2011, pp. 28–35.

“GPS Jamming: No Jam Tomorrow” in The Economist, Technology Quarterly Special Section, Vol. 398, Issue 8724, March 12, 2011, pp. 20–21.

Modern Communications Jamming Principles and Techniques, 2nd ed., by R.A. Poisel, published by Artech House, Boston, Massachusetts, 2011.

“Jamming GPS: Susceptibility of Some Civil GPS Receivers” by B. Forssell and R.B. Olsen in GPS World, Vol. 14, No. 1, January 2003, pp. 54–58.

“A Growing Concern: Radiofrequency Interference and GPS” by F. Butsch in GPS World, Vol. 13, No. 10, October 2002, pp. 40–50.

“Interference Effects and Mitigation Techniques” by J.J. Spilker Jr. and F.D. Natali, Chapter 20 in Global Positioning System: Theory and Applications, Volume I, published by the American Institute of Aeronautics and Astronautics, Inc., Washington, D.C., 1996, pp. 717–771.

• Government Regulations and Actions Against Jammers

“Twenty Online Retailers of Illegal Jamming Devices Targeted in Omnibus Enforcement Action,” a Federal Communications Commission press release issued October 5, 2011.

“FCC Enforcement Bureau Steps up Education and Enforcement,” a Federal Communications Commission press release issued February 9, 2011.

“Cell Jammers, GPS Jammers, and Other Jamming Devices,” Federal Communications Commission Enforcement Advisory No. 2011-04 issued February 9, 2011, for consumers.

“Cell Jammers, GPS Jammers, and Other Jamming Devices,” Federal Communications Commission Enforcement Advisory No. 2011-03 issued February 9, 2011, for retailers.

• Jamming Counter Measures

“Receiver Certification: Making the GNSS Environment Hostile to Jammers and Spoofers” by L. Scott. Presented to the National Space-Based Positioning, Navigation, and Timing (PNT) Advisory Board, 9th Meeting, November 9–10, 2011, Alexandria, Virginia.

“The Civilian Battlefield: Protecting GNSS Receivers from Interference and Jamming” by M. Jones in Inside GNSS, Vol. 6, No. 2, March/April 2011, pp. 40–49.

“Interference Heads-up: Receiver Techniques for Detecting and Characterizing RFI” by P.W. Ward in GPS World, Vol. 19, No. 6, June 2008, pp. 64–73.

“Jamming Protection of GPS Receivers, Part I: Receiver Enhancements” by S. Rounds in GPS World, Vol. 15, No. 1, January 2004, pp. 54–59.

“Jamming Protection of GPS Receivers, Part II: Antenna Enhancements” by S. Rounds in GPS World, Vol. 15, No. 2, February 2004, pp. 38–45.

“Antijamming and GPS for Critical Military Applications,” by A. Abbott in Crosslink, Vol. 3, No. 2, Summer 2003, pp. 36–41.

January 1, 2012
Innovation: Digging into GPS Integrity
Charting the Evolution of Signal-in-Space Performance by Data Mining 400,000,000 Navigation Messages

By Liang Heng, Grace Xingxin Gao, Todd Walter, and Per Enge

There are four important requirements of any navigation system: accuracy, availability, continuity, and integrity. In this month’s column we take a look at one particular aspect of GPS integrity: that of the signal in space and find out how trustworthy is the satellite ephemeris and clock information in the broadcast navigation message.

INNOVATION INSIGHTS by Richard Langley

BUT THE GREATEST OF THESE IS INTEGRITY. There are four important requirements of any navigation system: accuracy, availability, continuity, and integrity.

Perhaps the most obvious navigation system requirement, accuracy describes how well a measured value agrees with a reference value, typically the true value. In the case of GPS, we might talk about the accuracy of a range measurement. A receiver actually measures a pseudorange — a biased and noisy measure of the geometric range between the receiver and the satellite. After correcting for satellite ephemeris and satellite clock errors (the primary so-called signal-in-space errors), receiver clock errors, and atmospheric effects, we can get an estimate of the geometric range. How well we account for these errors or biases, will determine the accuracy of the corrected pseudorange measurement and ultimately, the accuracy of a derived position.

A navigation system’s availability refers to its ability to provide the required function and performance within the specified coverage area at the start of an intended operation. In many cases, system availability implies signal availability, which is expressed as the percentage of time that the system’s transmitted signals are accessible for use. In addition to transmitter capability, environmental factors such as signal attenuation or blockage or the presence of interfering signals might affect availability.

Ideally, any navigation system should be continuously available to users. But, because of scheduled maintenance or unpredictable outages, a particular system may be unavailable at a certain time. Continuity, accordingly, is the ability of a navigation system to function without interruption during an intended period of operation. More specifically, it indicates the probability that the system will maintain its specified performance level for the duration of an operation, presuming system availability at the beginning of that process.

The integrity of a navigation system refers to its trustworthiness. A system might be available at the start of an operation, and we might predict its continuity at an advertised accuracy during the operation.

But what if something unexpectedly goes wrong? If some system anomaly results in unacceptable navigation accuracy, the system should detect this and warn the user. Integrity characterizes a navigation system’s ability to provide this timely warning when it fails to meet its stated accuracy. If it does not, we have an integrity failure and the possibility of conveying hazardously misleading information. GPS has built into it various checks and balances to ensure a fairly high level of integrity. However, GPS integrity failures have occasionally occurred.

In this month’s column we take a look at one particular aspect of GPS integrity: that of the signal in space and find out how trustworthy is the satellite ephemeris and clock information in the broadcast navigation message.

The Navstar Global Positioning System is so far the most widely used space-based positioning, navigation, and timing system. GPS works on the principle of trilateration, in which the measured distances from a user receiver to at least four GPS satellites in view, as well as the position and clock data for these satellites, are the prerequisites for the user receiver to fix its exact position. For most GPS Standard Positioning Service (SPS) users, real-time satellite positions and clocks are derived from ephemeris parameters and clock correction terms in navigation messages broadcast by GPS satellites. The GPS Control Segment routinely generates navigation message data on the basis of a prediction model and the measurements at more than a dozen monitor stations. The differences between the broadcast ephemerides/clocks and the truth account for signal-in-space (SIS) errors. SIS errors are usually undetectable and uncorrectable for stand-alone SPS users, and hence directly affect the positioning accuracy and integrity. Nominally, SPS users can assume that each broadcast navigation message is reliable and the user range error (URE) derived from a healthy SIS is at the meter level or even sub-meter level. In practice, unfortunately, SIS anomalies have happened occasionally and UREs of tens of meters or even more have been observed, which can result in an SPS receiver outputting a hazardously misleading position solution. Receiver autonomous integrity monitoring (RAIM) or advanced RAIM is a promising tool to protect stand-alone users from such hazards; however, most RAIM algorithms assume at most one satellite fault at a time. Knowledge about the SIS anomalies in history is very important not only for assessing the GPS SIS integrity performance but also for validating the fundamental assumption of RAIM.

A typical method for calculating SIS UREs is to compare the broadcast ephemerides/clocks with the precise, post-processed ones. Although this method is very effective in assessing the GPS SIS accuracy performance, few attempts have been made to use it to assess the GPS SIS integrity performance because broadcast ephemeris/clock data obtained from a global tracking network sometimes contain errors caused by receivers or data conversion processes and these errors usually result in false SIS anomalies. In this article, we introduce a systematic methodology to cope with this problem and screen out all the potential SIS anomalies in the past decade from when Selective Availability (SA) was turned off.

GPS SIS Integrity

The integrity of a navigation system refers — just as it does to a person — to its honesty, veracity, and trustworthiness. In the case of GPS, this includes the integrity of the ephemeris and clock data in the broadcast navigation messages. We refer to this as signal-in-space integrity.

GPS SIS URE. As indicated by the name, GPS SIS URE is the pseudorange modeling inaccuracy due to operations of the GPS ground control and the space vehicles. Specifically, SIS URE includes satellite ephemeris and clock errors, satellite antenna performance variations, and signal imperfections, but not ionospheric or tropospheric delay, multipath, or any errors due to user receivers. SIS URE is dominated by ephemeris and clock errors because antenna variations and signal imperfections are at a level of millimeters or centimeters.

In broadcast navigation messages, there is a parameter called user range accuracy (URA) that is intended to be a conservative representation of the standard deviation (1-sigma) of the URE at the worst-case location on the Earth. For example, a URA index value of 0 means that the 1-sigma URE is expected to be less than 2.4 meters, and a URA index value of 1 means that the 1-sigma URE is expected to be greater than 2.4 meters but less than 3.4 meters, and so on. In the past several years, most GPS satellites have a URA index value of 0. A nominal URA value, in meters, can be computed as X = 2^(1+N/2), where N is the index value, for index values of 6 or less. For 6 < N < 15, X = 2^(N-2).

GPS SPS SIS Integrity. In the SPS Performance Standard (PS), as well as the latest version of the Interface Specification (IS-GPS-200E), the GPS SPS SIS URE integrity standard assures that for any healthy SIS, there is an up-to-10−5 probability over any hour of the URE exceeding the not-to-exceed (NTE) tolerance without a timely alert during normal operation. The NTE tolerance is currently defined to be 4.42 times the upper bound (UB) on the URA value broadcast by the satellite. Before September 2008, the NTE tolerance was defined differently, as the maximum of 30 meters and 4.42 times URA UB. The reason for the “magic” number 4.42 here is the Gaussian assumption of the URE, although this assumption may be questionable. (4.42 sigma corresponds to a probability level of 99.999 percent (1 – 10^–5)).

In this article, a GPS SPS SIS anomaly is defined as a threat of an SIS integrity failure; that is, a condition during which an SPS SIS marked healthy results in a URE exceeding the NTE tolerance. Because the definition of the NTE tolerance is different before and after September 2008, we consider both of the two NTE tolerances for the sake of completeness and consistency.

Methodology

The SIS anomalies are screened out by comparing broadcast ephemerides/clocks with precise ones. As shown in Figure 1, the whole process consists of three steps: data collecting, data cleansing, and anomaly screening.

Figure 1. Framework of the whole process. XYZB values refer to the coordinates of satellite position and satellite clock bias.

In the first step, the navigation message data files are downloaded from the International GNSS Service (IGS). In addition, two different kinds of precise ephemeris/clock data are downloaded from IGS and the National Geospatial-Intelligence Agency (NGA), respectively. The details about these data sources will be discussed in the next section.

Since each GPS satellite can be observed by many IGS stations at any instant, each navigation message is recorded redundantly. In the second step, a data-cleansing algorithm exploits the redundancy to remove the errors caused on the ground. This step distinguishes our work from that of most other researchers because the false anomalies due to corrupted data can be mostly precluded.

The last step is computing worst-case SIS UREs as well as determining potential SIS anomalies. The validated navigation messages prepared in the second step are used to propagate broadcast orbits/clocks at 15-minute intervals that coincide with the precise ones. A potential SIS anomaly is claimed when the navigation message is healthy and in its fit interval with the worst-case SIS URE exceeding the SIS URE NTE tolerance.

Data Sources

We obtained broadcast navigation message data and precise ephemeris and clock data from publicly available sources.

Broadcast Navigation Message Data. Broadcast GPS navigation message data files are available at IGS Internet sites. All the data are archived in Receiver Independent Exchange (RINEX) navigation file format, which includes not only the ephemeris/clock parameters broadcast by the satellites but also some information produced by the ground receivers, such as the pseudorandom noise (PRN) signal number and the transmission time of message (TTOM).

The IGS tracking network is made up of more than 300 volunteer stations all over the world (a map is shown in Table 1) ensuring seamless, redundant data logging. Since broadcast navigation messages are usually updated every two hours, no single station can record all navigation messages. For the ease of users, two IGS archive sites, the Crustal Dynamics Data Information System (CDDIS) and the Scripps Orbit and Permanent Array Center (SOPAC), provide two kinds of ready-to-use daily global combined broadcast navigation message data files, brdcddd0.yyn and autoddd0.yyn, respectively, where ddd is the day of year yy. Unfortunately, these files sometimes contain errors that can cause false anomalies.

Table 1. Comparison of IGS and NGA precise ephemeris/clock data.

Therefore, we devised and implemented a data-cleansing algorithm to generate the daily global combined navigation messages, which are as close as possible to the navigation messages that the satellites actually broadcast, from all available navigation message data files of all IGS stations. The data-cleansing algorithm is based on majority vote, and hence all values in our data are cross validated. Accordingly, we name our daily global combined navigation messages “validated navigation messages,” as shown in Figure 1.

Precise Ephemeris and Clock Data. Precise GPS ephemerides/clocks are generated by some organizations such as IGS and NGA that routinely post-process observation data. Precise ephemerides/clocks are regarded as “truth” because of their centimeter-level accuracy.

Table 1 shows a side-by-side comparison between IGS and NGA precise ephemeris/clock data, in which the green- and red-colored text implies pros and cons, respectively. For NGA data, the only con is that the data have been publicly available only since January 4, 2004. As a result, for the broadcast ephemerides/clocks before this date, IGS precise ephemerides/clocks are the only references. Nevertheless, care must be taken when using IGS precise ephemerides/clocks due to the following three issues.

The first issue with the IGS precise ephemerides/clocks is the relatively high rate of bad/absent data, as shown in the third row of Table 1. For a GPS constellation of 27 healthy satellites, 1.5 percent bad/absent data means no precise ephemerides or clocks for approximately 10 satellite-hours per day. This issue can result in undetected anomalies (false negatives).

The second issue is that, as shown in the fourth row of Table 1, IGS switched to IGS Time for its precise ephemeris/clock data on 22 February, 2004. The IGS clock is not synchronized to GPS Time, and the differences between the two time references may be as large as 3 meters. Fortunately, the time offsets can be extracted from the IGS clock data files. Moreover, a similar problem is that IGS precise ephemerides use a frame aligned to the International Terrestrial Reference Frame (ITRF) whereas broadcast GPS ephemerides are based on the World Geodetic System 1984 (WGS 84). The differences between ITRF and the versions of WGS 84 used since 1994 are on the order of a few centimeters, and hence a transformation is not considered necessary for the purpose of our work.

The last, but not the least important, issue with the IGS precise ephemerides is that the data are provided only for the center of mass (CoM) of the satellite. Since the broadcast ephemerides are based on the satellite antenna phase center (APC), the CoM data must be converted to the APC before being used. Both IGS and NGA provide antenna corrections for every GPS satellite. Although the IGS and the NGA CoM data highly agree with each other, the IGS satellite antenna corrections are quite different from the NGA’s, and the differences in z-offsets can be as large as 1.6 meters for some GPS satellites. The reason for these differences is mainly due to the different methods in producing the antenna corrections: the IGS antenna corrections are based on the statistics from more than 10 years of IGS data, whereas the NGA’s are probably from the calibration measurements on the ground. In order to know whose satellite antenna corrections are better, the broadcast orbits for all GPS satellites in 2009 were computed and compared with three different precise ephemerides: IGS CoM + IGS antenna corrections, IGS CoM + NGA antenna corrections, and NGA APC. Generally, the radial ephemeris error is expected to have a zero mean. However, the combination “IGS CoM + IGS antenna corrections” results in radial ephemeris errors with a non-zero mean for more than half of the GPS satellites. Therefore, the NGA antenna corrections were selected to convert the IGS CoM data to the APC.

Data Cleansing

Figure 2 shows a scenario of data cleansing. Owing to accidental bad receiver data and various hardware/software bugs, a small proportion of the navigation data files from the IGS stations have defects such as losses, duplications, inconsistencies, discrepancies, and errors. Therefore, more than just removing duplications, the generation of validated navigation messages is actually composed of two complicated steps.

Figure 2. A scenario of data cleansing: In the figure, the GPS satellite PRN32 started to transmit a new navigation message at 14:00. Receiver 1 had not observed the satellite until 14:36, and hence the TTOM in its record was 14:36. Additionally, Receiver 1 made a one-bit error in ∆n (4.22267589140 × 10-9 11823 × 2−43 π). Receiver 2 perhaps had some problems in its software: the IODC was unreported and both the toc and ∆n were written weirdly. Receiver n used an incorrect ranging code, PRN01, to despread and decode the signal of PRN32; fortunately, all the parameters except TTOM were perfectly recorded. Moreover, the three receivers interpreted URA (SV accuracy) differently. A computer equipped with our data cleansing algorithms is used to process all the data from the receivers. The receiver-caused errors are removed and the original navigation message is recovered.

First step. Suppose that we want to generate the validated navigation messages for day n. In the first step, we apply the following operations sequentially to each RINEX navigation data file from day n − 1 to day n + 1:

1) Parse the RINEX navigation file;

2) Recover least significant bit (LSB);

3) Classify URA values;

4) Remove the navigation messages not on day n;

5) Remove duplications;

6) Add all remaining navigation messages into the set O.

The reason why the data files from day n − 1 to day n + 1 are considered is that a few navigation messages around 00:00 can be included in some data files on day n − 1, and a few navigation messages around 23:59 can be included in some data files on day n + 1. The LSB recovery is used here to cope with the discrepant representations of floating-point numbers in RINEX navigation files. The URA classifier is employed to recognize and unify various representations of URA in the files. The duplication removal is applied because some stations write the same navigation messages repeatedly in one data file, which is unfavorable to the vote in the second step.

Second Step. At the end of the first step, we have a set O that includes all the navigation messages on day n. The set O still has duplications because a broadcast navigation message can be reported by many IGS stations. However, as shown in Figure 2, duplications of a broadcast navigation message may come with different errors and are not necessarily identical. Several other examples of such problems can be found in our journal paper listed in Further Reading. Fortunately, most orbital and clock parameters are seldom reported incorrectly, and even when errors happen, few stations agree on the same incorrect value. In our work, these parameters are referred to as robust parameters. On the contrary, some parameters, such as TTOM, PRN, URA and issue of data clock (IODC), are more likely to be erroneous and when errors happen, several stations may make the same mistake. These parameters are referred to as fragile parameters. The cause of the fragility is either the physical nature (for example, TTOM, PRN) or the carelessness in hardware/software implementations (for example, URA, IODC).

Majority vote is applied to all fragile parameters (except TTOM, which is determined by another algorithm described in our journal paper) under the principle that the majority is usually correct. Meanwhile, the robust parameters are utilized to identify the equivalence of two navigation messages — two navigation messages are deemed identical if and only if they agree on all the robust parameters, although their fragile parameters could be different. Therefore, the goal of duplication removal and majority vote is a set P, in which any navigation message must have at least one robust parameter different from any other and has all fragile parameters confirmed by the largest number of stations that report this navigation message.

After the operations above, we have a set P in which there are no duplicated navigation messages in terms of robust parameters and all fragile parameters are as correct as possible. A few navigation messages in P still have errors in their robust parameters. These unwanted navigation messages feature a small number of reporting stations. Finally, the navigation messages confirmed by only a few stations being discarded and the survivors are the validated broadcast navigation messages, stored in files sugldddm.yyn. For further details of our algorithms, see our journal paper.

Anomaly Screening

The validated broadcast navigation messages prepared using the algorithm described in the previous section were employed to propagate broadcast satellite orbits and clocks. For each 15-miniute epoch, t, that coincides with precise ephemerides/clocks, the latest transmitted broadcast ephemeris/clock is chosen to calculate the worst-case SIS URE – the maximum SIS URE that a user on Earth can experience.

Finally, a potential GPS SIS anomaly is claimed when all of the following conditions are fulfilled.
- The worst-case SIS URE exceeds the NTE tolerance;
- The broadcast navigation message is healthy; that is,
  - The RINEX field SV health is 0, and
  - The URA UB ≤ 48 meters;
- The broadcast navigation message is in its fit interval; that is, ∆t = t − TTOM ≤ 4 hours;
- The precise ephemeris/clock is available and healthy.
Results

A total of 397,044,414 GPS navigation messages collected by an average of 410 IGS stations from June 1, 2000 (one month after turning off SA), to August 31, 2010, have been screened. The NGA APC precise ephemerides/clocks and the IGS CoM precise ephemerides/clocks with the NGA antenna corrections were employed as the truth references. Both old and new NTE tolerances were used for determining anomalies.

Before interpreting the results, it should be noted that there are some limitations due to the data sources and the anomaly-determination criteria. First, false anomalies may be claimed because there may be some errors in the precise ephemerides/clocks or the validated navigation messages. Second, some short-lived anomalies may not show up if they happen to fall into the 15-minute gaps of the precise ephemerides/clocks. Third, some true anomalies may not be detected if the precise ephemerides/clocks are temporarily missing. The third limitation is especially significant for the results before January 3, 2004, because only the IGS precise ephemerides/clocks are available, which feature a high rate of bad/absent data. (For example, the clock anomaly of Space Vehicle Number (SVN) 23/PRN23 that occurred on January 1, 2004 is missed by our process because the IGS precise clocks for PRN23 on that day were absent.) Last but not least, users might not experience some anomalies because a satellite was not trackable at that time, or the users were notified via a Notice Advisory to Navstar Users (NANU). (A satellite may indicate that it is unhealthy through the use of non-standard code or data. The authors’ future work will include using observation data to verify the potential anomalies found in the results presented here.) Therefore, all the SIS anomalies claimed in this article are considered to be potential and under further investigation.

Potential SIS Anomalies. A total of 1,256 potential SIS anomalies were screened out under SPS PS 2008 (or 374 potential SIS anomalies under SPS PS 2001). Figure 3 shows all these anomalies in a Year-SVN plot. It can be seen that during the first year after SA was turned off, SIS anomalies occurred frequently for the whole constellation.

Figure 3. Potential SIS anomalies from June 1, 2000, to August 31, 2010. The horizontal lines depict the periods when the satellites were active (not necessarily healthy). The color of the lines indicates the satellites’ block type, as explained by the top left legend.

Moreover, 2004 is apparently a watershed: before 2004, anomalies occurred for all GPS satellites (except two satellites launched in 2003, SVN45/PRN21 and SVN56/PRN16) whereas after 2004, anomalies occurred much less frequently and more than 10 satellites have never been anomalous. Figure 4 further confirms the improving GPS SIS integrity performance in the past decade, no matter which SPS PS is considered.

Figure 4. Number of potential SIS anomalies per year. The SIS performance was improved during the past decade. There were 0 anomalies in 2009 according to SPS PS 2001 and this number is represented by 0.1 in the figure.

Therefore, it is possible to list all potential SIS anomalies from January 4, 2004, to August 31, 2010, in a compact table: Table 2. Most anomalies in the table have been confirmed by NANUs and other literature. The table reveals an important and exciting piece of information: never have two or more SIS anomalies occurred simultaneously since 2004. Accordingly, in the sense of historical GPS SIS integrity performance, it is valid for RAIM to assume at most one satellite fault at a time.

Table 2. List of potential anomalies from January 4, 2004, to August 31, 2010.

Validated Navigation Messages. For the purpose of comparison and verification, the IGS daily global combined broadcast navigation message data files brdcddd0.yyn and autoddd0.yyn were used to propagate broadcast satellite orbits and clocks as well. The NGA APC precise ephemerides/clocks were employed for the truth references. The SPS PS 2008 NTE tolerance was used for determining anomalies. The other criteria for anomaly screening that are the same as in the previous section were still applied.

All the potential SIS anomalies for 2006–2009 were found based on the three kinds of daily combined broadcast navigation messages. Table 3 shows a comparison of the total hours of the anomalies per year. It can be seen that brdcddd0.yyn and autoddd0.yyn result in approximately 11 times more false anomalies than true ones. Moreover, all potential anomalies derived from sugldddm.yyn are confirmed by brdcddd0.yyn and autoddd0.yyn, which indicates that our sugldddm.yyn does not introduce any more false anomalies than brdcddd0.yyn and autoddd0.yyn.

Table 3. Total hours of anomalies per year computed from three different kinds of daily global combined broadcast navigation messages.

Conclusion

In this article, the GPS SIS integrity performance in the past decade was assessed by comparing the broadcast ephemerides/clocks with the precise ones. Thirty potential anomalies were found. The fundamental assumption of RAIM is valid based on a review of the GPS SIS integrity performance in the past seven years.

Acknowledgments

The authors gratefully acknowledge the support of the Federal Aviation Administration. This article contains the personal comments and beliefs of the authors, and does not necessarily represent the opinion of any other person or organization.

The authors would like to thank Mr. Tom McHugh, William J. Hughes FAA Technical Center, for his valuable input to the data-cleansing algorithm. This article is based on the paper “GPS Signal-in-Space Integrity Performance Evolution in the Last Decade: Data Mining 400,000,000 Navigation Messages from a Global Network of 400 Receivers” to appear in the Institute of Electrical and Electronics Engineers (IEEE) Transactions on Aerospace and Electronic Systems..

Liang Heng is a Ph.D. candidate under the guidance of Professor Per Enge in the Department of Electrical Engineering at Stanford University.

Grace Xingxin Gao is a research associate in the GPS Research Laboratory of Stanford University.

Todd Walter is a senior research engineer in the Department of Aeronautics and Astronautics at Stanford University.

Per Enge is a professor of Aeronautics and Astronautics at Stanford University, where he is the Kleiner-Perkins, Mayfield, Sequoia Capital Professor in the School of Engineering. He directs the GPS Research Laboratory, which develops satellite navigation systems based on GPS.

FURTHER READING

• Authors’ Research Papers

“GPS Signal-in-Space Integrity Performance Evolution in the Last Decade: Data Mining 400,000,000 Navigation Messages from a Global Network of 400 Receivers” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Transactions on Aerospace and Electronic Systems, the Institute of Electrical and Electronics Engineers, accepted for publication.

“GPS Signal-in-Space Anomalies in the Last Decade: Data Mining of 400,000,000 GPS Navigation messages” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Proceedings of ION GNSS 2010, the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation, Portland, Oregon, September 21–24, 2010, pp. 3115–3122.

“GPS Ephemeris Error Screening and Results for 2006–2009” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Proceedings of ION ITM 2010, the 2010 International Technical Meeting of the Institute of Navigation, San Diego, California, January 24–26, 2010, pp. 1014–1022.

• Earlier Work on Assessing GPS Broadcast Ephemerides and Clocks

“GPS Orbit and Clock Error Distributions” by C. Cohenour and F. van Graas in Navigation, Vol. 58, No. 1, Spring 2011, pp. 17–28.

“Statistical Characterization of GPS Signal-in-Space Errors” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Proceedings of ION ITM 2011, the 2011 International Technical Meeting of the Institute of Navigation, San Diego, California, January 24–26, 2011, pp. 312–319.

“Broadcast vs. Precise GPS Ephemerides: A Historical Perspective” by D.L.M. Warren and J.F. Raquet in GPS Solutions, Vol. 7, No. 3, 2003, pp. 151–156, doi: 10.1007/s10291-003-0065-3.

“Accuracy and Consistency of Broadcast GPS Ephemeris Data” by D.C. Jefferson and Y.E. Bar-Sever in Proceedings of ION GPS-2000, the 13th International Technical Meeting of the Satellite Division of The Institute of Navigation, Salt Lake City, Utah, September 19–22, 2000, pp. 391–395.

“The GPS Broadcast Orbits: An Accuracy Analysis” by R.B. Langley, H. Jannasch, B. Peeters, and S. Bisnath, presented in Session B2.1-PSD1, New Trends in Space Geodesy at the 33rd COSPAR Scientific Assembly, Warsaw, July 16–23, 2000.

• Signal-in-Space Anomalies

“GNSS: The Present Imperfect” by D. Last in Inside GNSS, Vol. 5, No. 3, May 2010, pp. 60–64.

“Investigation of Upload Anomalies Affecting IIR Satellites in October 2007” by K. Kovach, J. Berg, and V. Lin in Proceedings of ION GNSS 2008, the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, September 16–19, 2008, pp. 1679–1687.

Global Positioning System (GPS) Standard Positioning Service (SPS) Performance Analysis Report No. 58, July 31, 2007, Reporting Period: 1 April – 30 June 2007.

Discrepancy Report, DR No. 55, “GPS Satellite PRN18 Anomaly Affecting SPS Performance” by N. Vary, FAA William J. Hughes Technical Center, Pomona, New Jersey, April 11, 2007.

“GPS Receiver Responses to Satellite Anomalies” by J.W. Lavrakas and D. Knezha in Proceedings of the 1999 National Technical Meeting of The Institute of Navigation, San Diego, California, January 25–27, 1999, pp. 621–626.

• GPS Integrity and Receiver Autonomous Integrity Monitoring

“Prototyping Advanced RAIM for Vertical Guidance” by J. Blanch, M.J. Choi, T. Walter, P. Enge, and K. Suzuki in Proceedings of ION GNSS 2010, the 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 21–24, 2010, pp. 285–291.

“The Integrity of GPS” by R.B. Langley in GPS World, Vol. 10, No. 3, March 1999, pp. 60–63.

• International GNSS Service Ephemerides and Clocks

“On the Precision and Accuracy of IGS Orbits” by J. Griffiths and J.R. Ray in Journal of Geodesy, Vol. 83, 2009, pp. 277–287, doi: 10.1007/s00190-008-0237-6.

“The International GNSS Service: Any Questions?” by A.W. Moore in GPS World, Vol. 18, No. 1, January 2007, pp. 58–64.

International GNSS Service Central Bureau website.

• National Geospatial-Intelligence Agency Ephemerides and Clocks

“NGA’s Role in GPS” by B. Wiley, D. Craig, D. Manning, J. Novak, R. Taylor, and L. Weingarth in Proceedings of ION GNSS 2006, the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 26–29, 2006, pp. 2111–2119.

National Geospatial-Intelligence Agency, Geoint Sciences Office, Global Positioning System Division website.

• Antenna Phase Center Corrections

“Generation of a Consistent Absolute Phase-center Correction Model for GPS Receiver and Satellite Antennas” by R. Schmid, P. Steigenberger, G. Gendt, M. Ge, and M. Rothacher in Journal of Geodesy, Vol. 81, No. 12, 2007, pp. 781–798, doi: 10.1007/s00190-007-0148-y.

“The Block IIA Satellite: Calibrating Antenna Phase Centers” by G.L. Mader and F.M. Czopek in GPS World, Vol. 13, No. 5, May 2002, pp. 40–46.

• GPS Interface and Performance Specifications

Navstar GPS Space Segment / Navigation User Interfaces, Interface Specification, IS-GPS-200 Revision E, prepared by Science Applications International Corporation, El Segundo, California, for Global Positioning System Wing, June 2010.

Global Positioning System Standard Positioning Service Performance Standard, 4th edition, by the U.S. Department of Defense, Washington, D.C., September 2008.

Global Positioning System Standard Positioning Service Performance Standard, 3rd edition, by the U.S. Department of Defense, Washington, D.C., October 2001.
November 1, 2011
Innovation: Filling in the Gaps

Improving Navigation Continuity Using Parallel Cascade Identification

By Umar Iqbal, Jacques Georgy, Michael J. Korenberg, and Aboelmagd Noureldin

To reliably navigate with fewer than four satellites, GPS pseudoranges needs to be augmented with measurements from other sensors, such as a reduced inertial sensor system or RISS. What is the best way to combine the RISS measurements with the GPS measurements? The classic approach is to integrate the measurements in a conventional tightly coupled Kalman filter. But in this month’s column, we look at how a mathematical procedure called parallel case identification can improve the Kalman filter’s job, when navigating with three, two, one, or even no GPS satellites.

INNOVATION INSIGHTS by Richard Langley

THREE, TWO, ONE, ZERO! Can you still navigate with just a GPS receiver when the number of tracked GPS satellites drops from four to none? As we know, pseu- doranges from a minimum of four satellites, preferably well spaced out in the sky, are required for three-dimensional positioning. That’s because there are four unknowns to estimate: the three position coordinates (latitude, longitude, and height) and the offset of the receiver clock from GPS System Time. If we had a stable clock in the receiver, then we could hold the clock offset constant and have 3D navigation with just three satellites. But for every 3 nanoseconds of clock drift, we will have about 1 meter of pseudorange error, which will lead to several meters of position error depend- ing on the receiver-satellite geometry. On the other hand, we could hold the height coor- dinate constant (viable for navigation over slowly changing topography or at sea) and estimate the horizontal coordinates and the receiver clock offset. So far, so good.

What if the number of tracked satellites then drops to two? We can now only esti- mate two unknowns. They could be the two horizontal coordinates, if we hold both the receiver clock offset and the height fixed. Any errors in those fixed values will propagate into the estimated horizontal coordinates but the resulting position errors might still be acceptable. Instead of holding the clock offset
fixed, we could assume a constant heading and compute the position along the assumed trajectory. However, navigation will rapidly deteriorate as soon as we make the first turn. And one satellite? We would have to make assumptions about the vehicle trajectory, the height, and the clock offset, with likely very poor results. And with no satellites? We might be able to navigate over a short period of time by “dead reckoning,” assuming a constant trajectory and speed, but the resulting positions will be educated guesses at best.

Clearly, if we want to reliably navigate with fewer than four satellites we need to augment the GPS pseudoranges with measurements from some other sensors. A common approach is to use inertial measurement units or IMUs. A complete IMU consists of three accelerometers and three gyroscopes, and small, cost-effective microelectromechanical IMUs are readily available. For land navigation, however, it can be advantageous to use a reduced inertial sensor system or RISS, consisting of one single-axis gyroscope, two accelerometers, and the vehicle speedometer. We can also make use of GPS pseudorange rates along with the pseudoranges.

But what is the best way to combine the RISS measurements with the GPS measurements? The classic approach is to integrate the measurements in a conventional tightly coupled Kalman filter. But in this month’s column, we look at how a mathematical procedure called parallel cascade identification can improve the Kalman filter’s job, when navigating with three, two, or even one GPS satellite.

The Global Positioning System meets the requirements for numerous navigational applications when there is direct line-of-sight (LOS) to four or more GPS satellites. Vehicular navigation systems and personal positioning systems may suffer from satellite signal blockage as LOS to at least four satellites may not be readily available when operating in urban landscapes with high buildings, underpasses, and tunnels, or in the countryside with thick forested areas. In such environments, a typical GPS receiver will have difficulties attaining and maintaining signal tracking, which causes GPS outages resulting in degraded or non-existent positioning information. Due to these well-known limitations of GPS, multi-sensor system integration is often employed. By integrating GPS with complementary motion sensors, a solution can be obtained that is often more accurate than that of GPS alone.

Microelectromechanical systems (MEMS) inertial sensors have enabled production of lower-cost and smaller-size inertial measurement units (IMUs) with little power consumption. A complete IMU is composed of three accelerometers and three gyroscopes. These MEMS sensors have composite error characteristics that are stochastic in nature and difficult to model. In traditional low-cost MEMS-based IMU/GPS integration, a few minutes of degraded GPS signals can cause position errors, which can reach several hundred meters. For full 3D land vehicle navigation, we had earlier proposed a low-cost MEMS-based reduced inertial sensor system (RISS) based on only one single-axis gyroscope, two accelerometers, and the vehicle odometer, and we have integrated this system with GPS. RISS mitigates several error sources in the full-IMU solution; moreover, RISS reduces system cost further due to the use of fewer sensors. Another enhancement can be achieved by using tightly coupled integration, which can provide GPS aiding for a navigation solution when the number of visible satellites is three or lower, removing the foremost requirement of loosely coupled integration, which is visibility of at least four satellites. GPS aiding during limited GPS satellite availability can improve the operation of the navigation system for tightly coupled systems. Thus, in our reseach, a Kalman filter (KF) is used to integrate low-cost MEMS-based RISS with GPS in a tightly coupled scheme.

The KF employed in tightly coupled RISS/GPS integration utilizes pseudoranges and pseudorange rates measured by the GPS receiver. The accuracy of the position estimates is highly dependent on the accuracy of the range measurements. The tightly coupled solutions presented in the literature assume that the pseudorange measurement, after correcting for ionospheric and tropospheric delays, satellite clock errors, and ephemeris errors, only have errors due to the receiver clock and white noise. These latter two are the only errors modeled inside the measurement model in the tightly coupled solutions presented in the literature. Experimental investigation of the GPS pseudoranges for vehicle trajectories in different areas and for different scenarios showed that, in addition, there are residual correlated errors. Since it has been experimentally proven that there are residual correlated errors in addition to white noise and receiver clock errors, we have proposed using a nonlinear system identification technique called parallel cascade identification (PCI) to model such correlated errors in pseudorange measurements.

We propose that the PCI model for the residual pseudorange errors be cascaded with a KF since this nonlinear model cannot be included inside the KF measurement model. The normal operation of a KF is as follows: the difference between the measured pseudorange and pseudorange rate from the mth GPS satellite and the corresponding RISS-predicted estimates of pseudorange and pseudorange rate are used as a measurement update for the KF integration, which computes the estimated RISS errors and corrects the mechanization output. We propose the use of a PCI module, where the role of PCI is to model the pseudorange residual errors. When GPS is available, estimated full 3D position, velocity, and attitude are obtained by integrating the MEMS-based RISS with GPS. In parallel, as a background routine, a PCI model is built for each visible satellite to model its pseudorange error. The actual pseudorange of each visible satellite is used as the input to the model; the target output is the error between the corrected pseudorange (calculated based on corrected receiver position from the integrated solution) and the actual pseudorange. This target output provides the reference output to build the PCI model of the pseudorange residual error. Dynamic characteristics between system input and output help to identify a nonlinear PCI model and the algorithm can then achieve a residual pseudorange error model.

When fewer than four satellites are visible, the identified parallel cascades for the remaining visible satellites will be used to predict the pseudorange errors for these satellites and correct the pseudorange values to be provided to the KF. This improvement of pseudorange measurements will result in a more accurate aiding for RISS, and thus more accurate estimates of position and velocities.

We examined the performance of the proposed technique by conducting road tests with real-life trajectories using a low-cost MEMS-based RISS. The ultimate check for the proposed system’s accuracy is during GPS signal degradation and blockage. This work presents both downtown scenarios with natural GPS degradation and scenarios with simulated GPS outages where the number of visible satellites was varied from three to zero. The results are examined and compared with KF-only tightly coupled RISS/GPS integration without pseudorange correction using a PCI module. This comparison clearly demonstrates the advantage of using a PCI module for correcting pseudoranges for tightly coupled integration.

RISS/GPS Integration

Earlier, we proposed the reduced inertial sensor system to reduce the overall cost of a positioning system for land vehicles without appreciable performance compromise depending on the fact that land vehicles mostly stay in the horizontal plane. It is the gyroscope technology that contributes the most both to the overall cost of an IMU and to the performance of the INS. In RISS mechanization, the heading (azimuth) angle is obtained by integrating the gyroscope measurement, ω_z. Since this measurement includes the component of the Earth’s rotation as well as rotation of the local level frame on the Earth’s curved surface, these quantities are removed from the measurement before integration. Assuming relatively small pitch and roll angles for land vehicle applications, we can write the rate of change of the azimuth angle directly in the local level frame as:
(1)
where ω^e is the Earth’s rotation rate, φ is the latitude, v_e is the east velocity of the vehicle, h is the altitude of the vehicle and R_N is the normal (prime vertical) radius of curvature of the vehicle’s position on the reference ellipsoid.

The two horizontal accelerometers can be employed for obtaining the pitch and roll angles of the vehicle. Thus, a 3D navigation solution can be achieved to boost the performance of the solution. When the vehicle is moving, the forward accelerometer measures the forward vehicle acceleration as well as the component due to gravity, g. To calculate the pitch angle, the vehicle acceleration derived from the odometer measurements, a_od, is removed from the forward accelerometer measurements, f_y. Consequently, the pitch angle is computed as:

(2)

Similarly, the transversal accelerometer measures the normal component of the vehicle acceleration as well as the component due to gravity. Thus, to calculate the roll angle, the transversal accelerometer measurement, f_x, must be compensated for the normal component of acceleration. The roll angle is then given by:

(3)

The computed azimuth and pitch angles allow the transformation of the vehicle’s speed along the forward direction, v_od (obtained from the odometer measurements) to east, north, and up velocities (v_e, v_n, and v_u respectively) as follows:
(4)
where is the rotation matrix that transforms velocities in the vehicle body frame to the navigation frame. The east and north velocities are transformed and integrated to obtain position in geodetic coordinates (latitude, φ, and longitude, λ). The vertical component of velocity is integrated to obtain altitude, h. The following equation shows these operations:
(5)

where, in addition to the terms already defined, RM is the meridional radius of curvature. We have used the KF as the estimation technique for tightly coupled RISS/GPS integration in our approach. KF is an optimal estimation tool that provides a sequential recursive algorithm for the optimal least mean variance (LMV) estimation of the system states. In addition to its benefits as an optimal estimator, the KF provides real-time statistical data related to the estimation accuracy of the system states, which is very useful for quantitative error analysis. The filter generates its own error analysis with the computation of the error covariance matrix, which gives an indication of the estimation accuracy.

In tightly coupled RISS/GPS system architecture, instead of using the position and velocity solution from the GPS receiver as input for the fusion algorithm, raw GPS observations such as pseudoranges and Doppler shifts are used. The range measurement is usually known as a pseudorange due to the contamination of errors, such as atmospheric errors, as well as synchronization errors between the satellite and receiver clocks.

After correcting for the satellite clock error and the ionospheric and tropospheric errors, we can obtain a corrected pseudorange. The receiver clock error and the residual errors remaining in the corrected pseudorange, assumed as white Gaussian noise, are the only errors modeled inside the measurement model in the tightly coupled solutions presented in the literature. Experimental investigation of the GPS pseudoranges in trajectories in different areas and under different scenarios showed that the residual errors are not just white noise as assumed in the literature, but, in fact, are correlated errors. As the GPS observables are used to update the KF, a technique must be developed to adequately model these errors to improve the overall performance of the KF. We propose using PCI to model these correlated errors. A PCI module models these errors, and then provides corrections prior to sending the GPS pseudoranges to aid the KF during periods of GPS partial outages (when the number of visible satellites drops below four).

Parallel Cascade Identification

What is PCI? System identification is a procedure for inferring the dynamic characteristics between system input and output from an analysis of time-varying input-output data. Most of the techniques assume linearity due to the simplicity of analysis since nonlinear techniques make analysis much more complicated and difficult to implement than for the linear case. However, for more realistic dynamic characterization nonlinear techniques are suggested. PCI is a nonlinear system identification technique proposed by one of us [MJK]. This technique models the input/output behavior of a nonlinear system by a sum of parallel cascades of alternating dynamic linear (L) and static nonlinear (N) elements. The parallel array shown in Figure 1 can be built up one cascade at a time.

Figure 1. Block diagram of parallel cascade identification.

It has been proven that any discrete-time Volterra series with finite memory and anticipation can be uniformly approximated by a finite sum of parallel LNL cascades, where the static nonlinearities, N, are exponentials and logarithmic functions. [A Volterra series, named after the Italian mathematician and physicist Vito Volterra, is similar to the more familiar infinite Taylor series expansion of a function used, for example, in systems analysis, but the Volterra series can include system “memory” effects.] It has been shown that any discrete-time doubly finite (finite memory and order) Volterra series can be exactly represented by a finite sum of LN cascades where the N are polynomials. A key advantage of this technique is that it is not dependent on a white or Gaussian input, but the identified individual L and N elements may vary depending on the statistical properties of the input chosen. The cascades can be found one at a time and nonlinearities in the models are localized in static functions. This reduces the computation as higher order nonlinearities are approximated using higher degree polynomials in the cascades rather than higher order kernels in a Volterra series approximation.

The method begins by approximating the nonlinear system by a first such cascade. The residual (that is, the difference between the system and the cascade outputs) is treated as the output of a new nonlinear system, and a second cascade is found to approximate the latter system, and thus the parallel array can be built up one cascade at a time. Let y_k(n) be the residual after fitting the kth cascade, with y_o(n) = y(n). Let z_k(n) be the output of the kth cascade, so
(6)
where k = 1, 2, …

The dynamic linear elements in the cascades can be determined in a number of ways. The method we have employed uses cross correlations of the input with the current residual. Best fitting of the current residuals was used to find the polynomial coefficients of the static nonlinearities. These resulting cascades are such that they drive the cross-correlations of the input with the residuals to zero. However, a few basic parameters have to be specified in order to identify a parallel cascade model, including the memory length of the dynamic linear element that begins each cascade, the degree of the polynomial static nonlinearity that follows the linear element (this polynomial is best fit to minimize the mean-square error (MSE) of the approximation of the residual), the maximum number of cascades allowable in the model, and a threshold based on a standard correlation test for determining whether a cascade’s reduction of the MSE justifies its addition to the model.

Augmented Kalman Filter

In the previous section, the parallel cascade model was briefly presented, together with a simple method for building up the model to approximate the behavior of a dynamic nonlinear system, given only its input and output. In order to apply PCI to 3D RISS/GPS integration, we propose the use of a KF-PCI module, where the role of PCI is to model the residual errors of GPS pseudoranges.

In full GPS coverage when four or more satellites are available to the GPS receiver, the KF integrated solution provides an adequate position benefiting from both GPS and RISS readings, and the PCI builds the model for the pseudorange errors for each visible satellite. The input of each PCI module is the pseudorange of the visible mth GPS satellite, and the reference output is the difference between the observed pseudorange and the estimated pseudorange from the corrected navigation solution.

The reference output has no corrections during full GPS coverage. It is only used to build the PCI model. Dynamic characteristics between system input and output help to achieve a residual pseudorange error model as shown in the Figure 2.

Figure 2. Block diagram of augmented KF-PCI module for pseudoranges during GPS availability.

During partial GPS coverage, when there are fewer than four satellites available, the PCI modules for all satellites cease training, and the available PCI model for each visible satellite is used to predict the corresponding residual pseudorange errors, as shown in Figure 3. The KF operates as usual, but in this instance the GPS observed pseudorange is corrected by the output of the corresponding PCI. The pre-built PCI models, only for the visible satellites during the partial outage, predict the corresponding residual pseudorange errors to obtain a correction. Thus, the corrected pseudorange can then be obtained.

During a full GPS outage, when no satellites are available, the KF operates in prediction mode and the PCI modules neither provide corrections nor operate in training mode.

FIGURE 3 Block diagram of augmented KF-PCI module for pseudoranges during limited availability of GPS.

Experimental Setup

The performance of the developed navigation solution was examined with road test experiments in a land vehicle. The experimental data collection was carried out using a full-size passenger van carrying a suite of measurement equipment that included inertial sensors, GPS receivers, antennae, and computers to control the instruments and acquire the data as shown in the Figure 4. The inertial sensors used in our tests are packaged in a MEMS-grade IMU. The specifications of the IMU are listed in Table 1.

Table 1. IMU specifications.

The vehicle’s forward speed readings were obtained from vehicle built-in sensors through the On-Board Diagnostics version II (OBD II) interface. The sample rate for the collection of speed readings was 1 Hz. The GPS receiver used in our integrated system was a high-end dual-frequency unit. Our results were evaluated with respect to a reference solution determined by a system consisting of another receiver of the same type, integrated with a tactical grade IMU.

This system provided the reference solution to validate the proposed method and to examine the overall performance during simulated GPS outages.
Several road test trajectories were carried out using the setup described above. The road test trajectory considered for this article was performed in the city of Kingston, Ontario, Canada, and is shown in Figure 5. This road test was performed for nearly 48 minutes of continuous vehicle navigation and a distance of around 22 kilometers. Ten simulated GPS outages of 60 seconds each were introduced in post-processing (they are shown as blue circles overlaid on the map in Figure 5) during good GPS availability. The trajectory was run four times with the simulated partial outages having three, two, one, and zero visible satellites, respectively. The case with no satellites seen is like a scenario that would occur in loosely coupled integration. The errors estimated by KF-PCI and KF-only solutions were evaluated with respect to the reference solution.

Experimental Results

The results in Figure 6 and Figure 7 demonstrate the benefits of the proposed PCI module. The main benefit of using PCI for pseudorange correction is the modeling capability, which enables correction of the raw GPS measurements. The benefit of more satellite availability can also be seen from these results. Figures 6 and 7 clearly show that both the average maximum position error and the average root-mean-square (RMS) position error are lower with the KF-PCI approach compared to the conventional KF, even when data from only one satellite is available.

Figure 6. Bar graph showing average maximum positional errors for all outages.

Figure 7. Bar graph for RMS positional errors for all outages.

To gain more insight about the performance of the proposed technique to enhance the aiding of the KF by correcting the pseudoranges, we can look at the results of KF-PCI and KF approaches with different numbers of satellites visible to the receiver for one of the artificial outages. Figure 8 shows a map featuring the different compared solutions during outage number 8. Eight solutions are presented for the cases of three, two, one, and zero satellites observed for the standard KF and KF with PCI. To get some idea of the vehicle dynamics during this outage, we can examine Figure 9, which depicts the forward speed of the vehicle as well as its azimuth angle as obtained from the reference solution. There is a significant variation in speed, with only a small variation in azimuth.

Figure 8. Performance of tightly coupled 3D-RISS during outage #8.

Figure 9. Vehicle dynamics (speed and azimuth) during GPS outage #8.

Figure 10 illustrates the performance differences between the KF-PCI and KF-only solutions for different numbers of satellites for this outage. Similar to Figure 7, Figure 10 shows the average RMS position differences between the KF-PCI and KF-only solutions and the reference solution (without the artificial outages). While the differences increase as the number of available satellites decreases, the accuracies may still be acceptable for many navigation purposes.

And while the differences between the KF-PCI and KF-only approaches for this particular outage are small, the KF-PCI approach consistently provides better accuracy.

Figure 10. Performance of PCI-KF (shades of blue for different number of satellites) and KF (shades of green for different number of satellites) of tightly coupled 3D-RISS during outage #8.

Conclusion

In this article, we have described a novel design for a navigation system that augments a tightly coupled KF system with PCI modules using low-cost MEMS-based 3D RISS and GPS observations to produce an integrated positioning solution. A PCI module is built for each satellite during good signal availability where the integrated solution presents a good position estimate. The output of each PCI module provides corrections to the GPS pseudoranges of the corresponding visible satellite during GPS partial outages, thereby decreasing residual errors in the GPS observations. This KF-PCI module was tested with real road-test trajectories and compared to a KF-only approach and was shown to improve the overall maximum position error during GPS partial outages.

Future work with PCI for modeling the residual pseudorange errors will consider replacing the KF with a particle filter to provide more robust integration and a consistent level of accuracy.

Acknowledgments

The research discussed in this article was supported, in part, by grants from the Natural Sciences and Engineering Research Council of Canada, the Geomatics for Informed Decisions (GEOIDE) Network of Centres of Excellence, and Defence Research and Development Canada. The equipment was acquired by research funds from the Directorate of Technical Airworthiness and Engineering Support, the Canada Foundation for Innovation, the Ontario Innovation Trust, and the Royal Military College of Canada. The article is based on the paper “Modeling Residual Errors of GPS Pseudoranges by Augmenting Kalman Filter with PCI for Tightly Coupled RISS/GPS Integration” presented at ION GNSS 2010, the 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation held in Portland, Oregon, September 21–24, 2010.

Manufacturers

The test discussed in this article used a NovAtel Inc. OEM4 dual-frequency GPS receiver and a Crossbow Technology Inc., now Moog Crossbow IMU300CC-100 MEMS-grade IMU. The On-Board Diagnostics data was accessed with a Davis Instruments CarChip Pro data logger. The reference solutions were provided by a NovAtel G2 Pro-Pack SPAN unit, interfacing a NovAtel OEM4 receiver with a Honeywell HG1700 tactical grade IMU.

Umar Iqbal is a doctoral candidate at Queen’s University, Kingston, Ontario, Canada. He received a master’s of electrical engineering degree in integrated positioning and navigation systems from Royal Military College (RMC) of Canada, Kingston, in 2008. He also holds an M.Sc. in electronics engineering from the Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, Topi, Pakistan, and a B.Sc. in electrical engineering from the University of Engineering and Technology, Lahore, Pakistan. His research focuses on the development of enhanced performance navigation and guidance systems that can be used in several applications including car navigation.

Jacques Georgy received his Ph.D. degree in electrical and computer engineering from Queen’s University in 2010. He received B.Sc. and M.Sc. degrees in computer and systems engineering from Ain Shams University, Cairo, Egypt, in 2001 and 2007, respectively. He is working in positioning and navigation systems for vehicular, machinery, and portable applications with Trusted Positioning Inc., Calgary, Alberta, Canada. He is also a member of the Navigation and Instrumentation Research Group at RMC. His research interests include linear and nonlinear state estimation, positioning and navigation by inertial navigation system/global positioning system integration, autonomous mobile robot navigation, and underwater target tracking.

Michael J. Korenberg is a professor in the Department of Electrical and Computer Engineering at Queen’s University. He holds an M.Sc. (mathematics) and a Ph.D. (electrical engineering) from McGill University, Montreal, Quebec, Canada, and has published extensively in the areas of nonlinear system identification and time-series analysis.

Aboelmagd Noureldin is a cross-appointment associate professor with the Department of Electrical and Computer Engineering at Queen’s University and the Department of Electrical and Computer Engineering at RMC. He is also the founder and leader of the Navigation and Instrumentation Research Group at RMC. He received the B.Sc. degree in electrical engineering and the M.Sc. degree in engineering physics from Cairo University, Giza, Egypt, in 1993 and 1997, respectively, and the Ph.D. degree in electrical and computer engineering from The University of Calgary, Calgary, Alberta, Canada, in 2002. His research is related to artificial intelligence, digital signal processing, spectral estimation and de-noising, wavelet multiresolution analysis, and adaptive filtering, with emphasis on their applications in mobile multisensor system integration for navigation and positioning technologies.

FURTHER READING

◾ Reduced Inertial Sensing Systems

Integrated Reduced Inertial Sensor System/GPS for Vehicle Navigation: Multi-sensor Positioning System for Land Applications Involving Single-Axis Gyroscope Augmented with Vehicle Odometer and Integrated with GPS by U. Iqbal and A. Noureldin, published by VDM Verlag Dr. Müller, Saarbrucken, Germany, 2010.

“A Tightly-Coupled Reduced Multi- Sensor System for Urban Navigation” by T.B. Karamat, J. Georgy, U. Iqbal, and A. Noureldin in Proceedings of ION GNSS 2009, the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, September 22–25, 2009, pp. 582–592.

“An Integrated Reduced Inertial Sensor System – RISS/GPS for Land Vehicle” by U. Iqbal, A.F. Okou, and A. Noureldin, in Proceedings of PLANS 2008, IEEE/ION Position Location and Navigation Symposium, Monterey, California, May 5–8, 2008, pp. 912– 922, doi: 0.1109/PLANS.2008.4570075.

◾ Integrated Positioning

“Experimental Results on an Integrated GPS and Multisensor System for Land Vehicle Positioning” by U. Iqbal, T.B. Karamat, A.F. Okou, and A. Noureldin in International Journal of Navigation and Observation, Hindawi Publishing Corporation, Vol. 2009, Article ID 765010, 18 pp., doi: 10.1155/2009/765010.

“Performance Enhancement of MEMS Based INS/GPS Integration for Low Cost Navigation Applications” by A. Noureldin, T.B. Karamat, M.D. Eberts, and A. El-Shafie in IEEE Transactions on Vehicular Technology, Vol. 58, No. 3, March 2009, pp. 1077–1096, doi: 10.1109/TVT.2008.926076.

Aided Navigation: GPS with High Rate Sensors by J.A. Farrell, published by McGraw-Hill, New York, 2008.

Global Positioning Systems, Inertial Navigation, and Integration by M.S. Grewal, L.R. Weill, and A.P. Andrews, 2nd ed., published by Wiley- Interscience, Hoboken, New Jersey, 2007.

“Continuous Navigation: Combining GPS with Sensor-based Dead Reckoning by G. zur Bonsen, D. Ammann, M. Ammann, E. Favey, and P. Flammant in GPS World, Vol. 16, No. 4, April 2005, pp. 47–54.

“Inertial Navigation and GPS” by M.B. May in GPS World, Vol. 4, No. 9, September 1993, pp. 56–66.

◾ Kalman Filtering

Kalman Filtering: Theory and Practice Using MATLAB, 2nd ed., by M.S. Grewal and A.P. Andrews, published by John Wiley & Sons Inc., New York, 2001.

“The Kalman Filter: Navigation’s Integration Workhorse” by L.J. Levy, in GPS World, Vol. 8, No. 9, September, 1997, pp. 65–71.

Applied Optimal Estimation by the Technical Staff, Analytic Sciences Corp., ed. A. Gelb, published by The MIT Press, Cambridge, Massachusetts, 1974.

◾ Parallel Cascade Identification

“Simulation of Aircraft Pilot Flight Controls Using Nonlinear System Identification” by J.M. Eklund and M.J. Korenberg in Simulation, Vol. 75, No. 2, August 2000, pp.72–81, doi: 10.1177/003754970007500201.

“Parallel Cascade Identification and Kernel Estimation for Nonlinear Systems” by M.J. Korenberg in Annals of Biomedical Engineering, Vol. 19, 1991, pp. 429–455, doi: 10.1007/ BF02584319.

“Statistical Identification of Parallel Cascades of Linear and Nonlinear Systems” by M.J. Korenberg in Proceedings of the Sixth International Federation of Automatic Control Symposium on Identification and System Parameter Estimation, Washington, D.C., June 7–11, 1982, Vol. 1, pp. 580–585.

◾ On-Board Diagnostics

“Low-cost PND Dead Reckoning using Automotive Diagnostic Links” by J.L. Wilson in Proceedings of ION GNSS 2007, the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 25–28, 2007, pp. 2066–2074.

October 1, 2011
Innovation: The Right Attitude

Experimenting with GPS on Board High-Altitude Balloons

By Peter J. Buist, Sandra Verhagen, Tatsuaki Hashimoto, Shujiro Sawai, Shin-Ichiro Sakai, Nobutaka Bando, and Shigehito Shimizu

In this month’s column, we look at how a team of Dutch and Japanese researchers is using GPS to determine the attitude of a payload launched from a high-altitude balloon.

INNOVATION INSIGHTS by Richard Langley

IT IS NOT WIDELY RECOGNIZED that relative or differential positioning using GNSS carrier-phase measurements is an interferometric technique. In interferometry, the difference in the phase of an electromagnetic wave at two locations is precisely measured as a function of time. The phase differences depend, amongst other factors, on the length and orientation of the baseline connecting the two locations. The classic demonstration of interferometry, showing that light could be interpreted as a wave phenomenon, was the 1803 double-slit experiment of the English polymath, Thomas Young. Many of us recreated the experiment in high school or university physics classes. A collimated beam of light is shone through two small holes or narrow slits in a barrier placed between the light source and a screen. Alternating light and dark bands are seen on the screen. The bands are called interference fringes and result from the waves emanating from the two slits constructively and destructively interfering with each other. The colors seen on the surface of an audio CD, the colors of soap film, and those of peacock feathers and the wings of the Morpho butterfly are all examples of interference.

Interference fringes also reveal information about the source of the waves. In 1920, the American Nobel-prize-winning physicist, Albert Michelson, used an interferometer attached to a large telescope to measure the diameter of the star Betelgeuse. Radio astronomers extended the concept to radio wavelengths, using two antennas connected to a receiver by cables or a microwave link. Such radio interferometers were used to study the structure of various radio sources including the sun. Using atomic frequency standards and magnetic tape recording, astronomers were able to sever the real-time links between the antennas, giving birth to very long baseline interferometry (VLBI) in 1967. The astronomers used VLBI to study extremely compact radio sources such as the enigmatic quasars. But geodesists realized that high resolution VLBI could also be used to determine — very precisely — the components of the baseline connecting the antennas, even if they were on separate continents.

That early work in geodetic VLBI led to the concept developed by Charles Counselman III and others at the Massachusetts Institute of Technology in the late 1970s of recording the carrier phase of GPS signals with two separate receivers and then differencing the phases to create an observable from which the components of the baseline connecting the receivers’ antennas could be determined. This has become the standard high-precision GPS surveying technique. Later, others took the concept and applied it to short baselines on a moving platform allowing the attitude of the platform to be determined.

In this month’s column, we look at how a team of Dutch and Japanese researchers is using GPS to determine the attitude of a payload launched from a high-altitude balloon.

The Japan Aerospace Exploration Agency (JAXA) is developing a system to provide a high-quality, long duration microgravity environment using a capsule that can be released from a high-altitude balloon. Since 1981, an average of 100 million dollars is spent every year on microgravity research by space agencies in the United States, Europe, and Japan. There are many ways to achieve microgravity conditions such as (in order of experiment duration) drop towers, parabolic flights, balloon drops, sounding rockets, the Space Shuttle (unfortunately, no longer), recoverable satellites, and the International Space Station. The order of those options is also approximately the order of increasing experiment cost, with the exception of the balloon drop. Besides being cost-efficient, a balloon-based system has the advantage that no large acceleration is required before the experiment can be performed, which could be important for any delicate equipment that is carried aloft.

In this article, we will describe JAXA’s Balloon-based Operation Vehicle (BOV) and the experiments carried out in cooperation with Delft University of Technology (DUT) using GPS on the gondola of the balloon in 2008 (single baseline estimation) and 2009 (full attitude determination and relative positioning). The attitude calculated using observations from the onboard GPS receiver during the 2009 experiment is compared with that from sun and geomagnetic sensors as well as that provided by the GPS receiver itself.

Nowadays, GNSS is used for absolute and relative positioning of aircraft and spacecraft as well as determination of their attitude. What these applications have in common is that, in general, the orientation of the platform is changing relatively slowly and, to a large extent, predictably. Here, we will discuss a balloon-based application where the orientation of the platform, at times, varies very dynamically and unpredictably.

Balloon Experiments

Scientific balloons have been launched in Japan by the Institute of Space and Astronautical Science (ISAS), now a division of JAXA, since 1965, and it holds the world record for the highest altitude reached by a balloon — 53 kilometers. Recently, balloon launches have taken place from the Multipurpose Aviation Park (MAP) in Taiki on the Japanese island of Hokkaido. The balloons are launched using a so-called sliding launcher. The sliding launcher and the hanger at MAP are shown in FIGURE 1.

Balloon-Based Operation Vehicle. As previously mentioned, JAXA’s BOV has been designed for microgravity research. The scenario of a microgravity experiment is illustrated in FIGURE 2. The vehicle is launched with a balloon, which carries it to an altitude of more than 40 kilometers, where it is released.

Figure 2. Microgravity experiment procedure.

After separation, the BOV is in free fall until the parachute is released so that the vehicle can make a controlled landing in the sea. The BOV is recovered by helicopter and can be reused. The capsule has a double-shell drag-free structure and it is controlled so as not to collide with the inner shell. The flight capsule, shown hanging at the sliding launcher in Figure 1, consists of a capsule body (the outer shell), an experiment module (the inner shell), and a propulsion system. The inner capsule shown in FIGURE 3 is kept in free-falling condition after release of the BOV from the balloon, and no disturbance force acts on this shell and the microgravity experiment it contains.

Figure 3. Balloon-based Operation Vehicle overview.

The outer shell has a rocket shape to reduce aerodynamic disturbances. The distance between the outer and inner shells is measured using four laser range sensors. Besides the attitude of the BOV, the propulsion system controls the outer shell so that it does not collide with the inner s
hell. The propulsion system uses 16 dry-air gas-jet thrusters of 60 newtons, each controlling it not only in the vertical direction but also in the horizontal direction to compensate disturbances from, for example, wind.

Flight experiments with the BOV were carried out in 2006 (BOV1) and in 2007 (BOV2), when a fine microgravity environment was established successfully for more than 7 and 30 seconds, respectively.

Attitude Determination. Balloon experiments are performed for a large number of applications, some of which require attitude control. Observations from balloon-based telescopes are an example of an application in which stratospheric balloons have to carry payloads of hundreds of kilograms to an altitude of more than 30 kilometers to be reasonably free of atmospheric disturbances. In this application, the typical requirement for the control of the azimuth angle of the platform is to within 0.1 degrees.

JAXA is developing the Attitude Determination Package (ADP, see TABLE 1) for a future version of the BOV, which contains Sun Aspect Sensors (SAS), the Geomagnetic Aspect Sensor (GAS), an inclinometer, and a gyroscope. Each SAS determines the attitude with a resolution of one degree around one axis and the ADP has four of these sensors pointing in different directions. Inherently, this type of sensor can only provide attitude information if the sun is within the field of view of the sensor. The GAS also determines one-axis attitude. The resolution of magnetic flux density measured by the GAS and applied to obtain an attitude estimate is 50 parts per million. This results in an attitude determination accuracy of the GAS of 1.5 degrees with dynamic bias compensation. The inclinometer determines two-axis attitude with a resolution of 0.2 degrees.

Table 1. Sensor specifications.

Background GPS Experiment. DUT is involved in a precise GPS-based relative positioning and attitude determination experiment onboard the BOV and the gondola of the balloon. Not only is the BOV a challenging environment, but so is the gondola itself, because of the rather rapidly varying attitude (due to wind and — especially at takeoff and separation — rotation) and the high altitude. For a GPS experiment, the altitude of around 40 kilometers is interesting as not many experiments have been performed at this height, which is higher than the altitude reachable by most aircraft but below the low earth orbits for spacecraft. An altitude of about 40 kilometers is a harsh environment for electrical devices because the pressure is about 1/1000 of an atmosphere and the temperature ranges from –60 to 0 degrees Celsius. Furthermore, the antennas are placed under the balloon, which affects the received GPS signals. Later on, we will describe in detail two experiments performed in 2008 and 2009, respectively.

The GPS receivers on the first flight in 2008 were a navigation-type receiver, not especially adapted for such an experiment. The data was collected on a single baseline with two dual-frequency receivers. The receivers were controlled by, and the data stored on, an ARM Linux board using an RS-232 serial connection.

For the second flight in 2009, we used a multi-antenna receiver, for which the Coordinating Committee for Multilateral Export Controls altitude restriction was explicitly removed. This receiver has three RF inputs that can be connected to three antennas, so the observations from the three antennas are time-synchronized by a common clock. The receiver has the option to store observations internally, which simplified the control of the GPS experiment. We used three antennas: one L1/L2 antenna as the main antenna and two L1 antennas as auxiliary antennas.

Theory of Attitude Determination

In this section, we will provide background information on the models applied in our GPS experiment. More details can be found in the publications listed in Further Reading.

Standard LAMBDA. Most GNSS receivers make use of two types of observations: pseudorange (code) and carrier phase. The pseudorange observations typically have a precision of decimeters, whereas carrier-phase observations have precisions up to the millimeter level.

Carrier-phase observations are affected, however, by an unknown number of integer-cycle ambiguities, which have to be resolved before we can exploit the higher precision of these observations. The observation equations for the double-difference (between satellites and between antennas/receivers) can be written for a single baseline as a system of linearized observation equations:

(1)

where E(y) is the expected value and D(y) is the dispersion of y. The vector of observed-minus-computed double-difference carrier-phase and code observations is given by y; z is the vector of unknown ambiguities expressed in cycles rather than distance units to maintain their integer character; b is the baseline vector, which is unknown for relative navigation applications but for which the length in attitude determination is generally known; A is a design matrix that links the data vector to the vector z; and B is the geometry matrix containing normalized line-of-sight vectors. The variance-covariance matrix of y is represented by the positive definite matrix Qyy, which is assumed to be known.

The least-squares solution of the linear system of observation equations as introduced in Equation (1) is obtained using from:

. (2)

The integer solution of this system can be obtained by applying the standard Least-Squares Ambiguity Decorrelation Adjustment (LAMBDA) method.

Constrained LAMBDA. In applications for which some of the baseline lengths are known and constant, for example GNSS-based attitude determination, we can exploit the so-called baseline-constrained model. Then, the baseline-constrained integer ambiguity resolution can make use of the standard GNSS model by adding the length constraint of the baseline, ||b|| = , where is known. The least-squares criterion for this problem reads:

.(3)

The solution can be obtained with the baseline-constrained (or C-)LAMBDA method, which is described in referred literature listed in Further Reading. Later on, we will refer to the attitude calculated by this approach simply as C-LAMBDA.

For platforms with more than one baseline, the C-LAMBDA method can be applied to each baseline individually, and the full attitude can be determined using those individual baseline solutions. For completeness, we also mention a recently developed solution of this problem, called the multivariate-constrained (MC-) LAMBDA, which integrally accounts for both the integer and attitude matrix. Both approaches are applied in the analyses of the BOV data.

Onboard Attitude Determination. In this article, we also use the onboard estimate of the attitude as provided by the multi-antenna receiver. The method applied in the receiver is based on a Kalman filter and the ambiguities are resolved by the standard LAMBDA method. The baseline length, if the information is provided to the receiver a priori, is used to validate the results. For baseline lengths of about 1 meter, the receiver’s pitch and roll accuracy is about 0.60 degrees, and heading about 0.30 degrees according to the receiver manual. We will refer to the attitude as provided by the receiver as KF.

Flight Experiments

In this section, we will discuss our analyses of the GPS data from two of the BOV experiments.

Gondola Experimental Flight 2008. In September 2008, we performed a test of the ADP for a future version of the BOV and a GPS system containing two navigation-grade GPS receivers. The goal of the experiment was to confirm nominal performance in the real environment of the ADP sensors and GPS receivers on the gondola; therefore, the BOV was not launched. The data from the single baseline was used to determine the pointing direction of the gondola, an application referred to as the GNSS compass. The receivers and the controller were stored in an airtight container (see FIGURE 4) and the antennas were sealed in waterproof bags. The location of the two GPS antennas on the gondola is indicated in Figure 4. The baseline length was 1.95 meters. Both receivers used their own individual clocks, so observations were not synchronized. The trajectory (altitude) of this flight is shown in the right-hand side of Figure 4, with the longitude and latitude shown in FIGURE 5. This is a typical flight profile for our application. The flight takes about three hours and reaches an altitude of more than 40 kilometers.

Figure 4B. Single baseline experiment performed in September 2008, the flight trajectory (altitude).

First, the balloon makes use of the wind direction in the lower layers of the atmosphere, which brings it eastwards. During this part of the flight, the balloon is kept at a maximum altitude of about 12 kilometers. After about 30 minutes, the altitude is increased to make use of a different wind direction that carries the balloon back in the westerly direction toward the launch base in order to ease the recovery of the capsule and/or the gondola.

At the end of the flight, there is a parachute-guided fall over 40 kilometers to sea level, for both the gondola and the BOV (if it is launched), which takes about 30 minutes. In this experiment, we could confirm the nominal operation of some of the sensors and reception of the GPS signals on the gondola under the large balloon.

Gondola Experimental Flight 2009. In May 2009, the third flight of the BOV was performed. The three GPS receiver antennas and the other attitude sensors were placed on an alignment frame for stiffness, which was then attached to the gondola. Furthermore, we used a ground station to demonstrate the combination of GPS-based attitude determination and relative positioning between the platform and the ground station. As the motion of the system is rather unpredictable, we used a kinematic approach for both attitude determination and relative positioning.

Preflight static test: Before the flight, we did a ground test using the actual antenna frame of the gondola (see FIGURE 6). The roll, pitch, and heading angles for this static test are shown on the right-hand side of this figure. Due to the geometry of the baselines, the heading angle is more accurate. For this static test, we can calculate the standard deviation of the three angles to confirm the accuracy achievable for the flight test. These results are summarized in TABLE 2. For the baselines with a length of about 1.4 meters, we achieved an accuracy of about 0.25 degrees for the roll and pitch angles and 0.1 degrees for heading, which is as expected from the lengths and geometry of the baselines. Using single-epoch data, we could resolve the ambiguities correctly for more than 99 percent of the epochs (see TABLE 3). Also, the standard deviation of the receiver’s Kalman-filter-based attitude estimate (KF) is included in the table. The accuracy is, after convergence of the filter, similar to our C-LAMBDA result, although the applied method is very different. The Kalman filter takes about 10 seconds to converge for this static experiment, whereas the C-LAMBDA method provides this accuracy from the very first epoch. For completeness, the instantaneous success rate of the standard LAMBDA and MC-LAMBDA methods are also included in Table 3.

Figure 6. Static experiment: C-LAMBDA-based attitude estimates.

Table 2. Standard deviation of attitude angles for static test.

Table 3. Single-epoch, overall success rate for baseline 1-2 (static experiment).

Gondola nominal flight: Next, we applied the same GPS configuration on the gondola. An important difference with respect to the static field experiment is that the antennas were now placed under the balloon and inside waterproof bags (see the picture on the left-hand side of FIGURE 7). The right-hand side of Figure 7 shows the flight trajectory (altitude) of the experiment. At 21:05 UTC (07:05 Japan Standard Time), the balloon was released from the sliding launcher (Figure 1). In 2.5 hours, the balloon reached an altitude of more than 41 kilometers from which the BOV was dropped. At 23:55, the BOV was released from the Gondola, and at 23:59 the gondola was separated from the balloon. After the release of the BOV, the balloon and gondola ascended more than 2 kilometers because of the reduced mass of the system. For this flight, the attitude determination package and the GPS system were installed on the gondola to confirm the nominal performance of all the sensors.

Figure 7A. Full attitude experiment performed in May 2009, sensor configuration.

Figure 7B. Full attitude experiment performed in May 2009, flight trajectory (altitude).

Using the new GPS receiver with three antennas, we are able to calculate the full attitude of the gondola. The roll and pitch estimates, from both C-LAMBDA and KF, are shown in FIGURE 8. The heading angle from the GPS-based C-LAMBDA and KF, and that from the GAS and SAS sensors are shown in FIGURE 9. As explained in a previous section, the four SAS sensors will only output an attitude estimate if the sun is in the field of view of a sensor. Therefore we can distinguish four bands in the heading estimate of the SAS, corresponding to the individual sensors (indicated in Figure 7 as SAS1 to SAS4).

Figure 8A. GPS results for roll angles during nominal flight.

Figure 8B. GPS results for pitch angles during nominal flight.

Figure 9A. GPS results for heading angle during nominal flight.

Figure 9B. GAS and SAS results for heading angle during nominal flight.

The number of locked GPS satellites at the main antenna is shown on the right-hand side of Figure 7. Before takeoff, we saw that the number of locked channels varies rapidly due to obstructions, but after takeoff the number is rather constant until the BOV is separated from the gondola. Before takeoff, the GPS observations are affected by the obstruction of the sliding launcher and therefore ambiguity resolution is only possible on the second baseline (see Figure 8). Also, the GPS receiver itself does not provide an attitude estimation during this phase of the experiment. During takeoff, we see large variations in orientation of the gondola (up to 20 degrees (±10 degrees) for both roll and pitch), which can be estimated well by both C-LAMBDA and KF. Again, the Kalman filter takes a few epochs to converge (in this case, 15 seconds from takeoff), whereas the C-LAMBDA method provides an accurate solution from the very first epoch. After takeoff, the attitude of the gondola stabilizes and the C-LAMBDA and KF attitude estimates are very similar.

We investigated the difference between the attitude estimation from the different sensors during nominal flight. The mean and standard deviations of the differences are shown in TABLE 4. If we compare the C-LAMBDA and KF attitudes, we observe biases for all angles. This is something we have to investigate further, but the most likely cause for this bias is the time delay of the Kalman filter in response to changes in attitude, as we observed in the static experiment in the form of convergence time.

Table 4. Attitude differences (offset/standard deviation) for flight test of 2009.

The standard deviation for the difference in the estimates of roll, pitch, and heading is as expected. For the comparison with the other sensors, we use the C-LAMBDA attitude as the reference. Between C-LAMBDA and GAS/SAS, we observe a bias, most likely due to minor misalignment issues between the sensors. The standard deviations in Table 4 are in line with expectation based on the sensor specifications. During this part of the flight, we achieved a single-epoch, single-frequency empirical overall success rate for ambiguity resolution on the two baselines of 95.09 percent. As a reference, we also include in TABLE 5 the success rate for standard LAMBDA using observations from a single epoch. If we make use of the MC-LAMBDA method, the success rate is increased to 99.88 percent as shown in the table. The success rate is higher as the integrated model for all the baselines is stronger.

Table 5. Single-epoch, overall success rate for baseline 1-2 (flight experiment).

Gondola flight after BOV separation: After the separation of the BOV from the gondola, the gondola starts to ascend and sway. FIGURE 10 contains roll and pitch estimates for this part of the flight until the gondola separation. In the figure, we see large variations in the orientation of the gondola (up to 40 (±20) degrees for roll and 20 (± 10) degrees for pitch). It is interesting that after BOV separation, during the large maneuvers of the gondola caused by the separation, both KF and C-LAMBDA estimates are available but to a certain extent are different. Table 4 also contains standard deviations and biases between C-LAMBDA and KF for this part of the flight.

Figure 10A. GPS results for roll angles during nominal flight.

Figure 10B. GPS results for pitch angles during nominal flight.

We conclude that the differences (standard deviation but also bias) between C-LAMBDA and KF — both for roll and pitch — are increased compared to the nominal part of the flight. This confirms our expectation that the Kalman-filter-based result lags behind the true attitude in dynamic situations, whereas the C-LAMBDA result based on single-epoch data should be able to provide the same accurate estimate as during the other phases of the flight.

Future Work

For the final phase of the experiment program, we would like to collect multi-baseline data from a number of vehicles. The preferred option for the experiment is three antennas (two independent baselines) on the BOV, and two antennas (one baseline) on the gondola. Furthermore, similar to our 2009 experiment, a number of antennas at a reference station could be used. The goal of the final phase of the program is to collect data for offline relative positioning and attitude determination, though real-time emulation, between a number of vehicles that form a network.

Acknowledgments

Peter Buist thanks Professor Peter Teunissen for support with the theory behind ambiguity resolution and, including Gabriele Giorgi, for the pleasant cooperation during our research. The MicroNed-MISAT framework is kindly thanked for their support. The research of Sandra Verhagen is supported by the Dutch Technology Foundation STW, the Applied Science Division of The Netherlands Organisation for Scientific Research (NWO), and the Technology Program of the Ministry of Economic Affairs. This article is based on the paper “GPS Experiment on the Balloon-based Operation Vehicle” presented at the Institute of Electrical and Electronics Engineers / Institute of Navigation Position Location and Navigation Symposium 2010, held in Indians Wells, California, May 6–8, 2010, where it received a best-paper-in-track award.

Manufacturers

The Attitude Determination Package’s Sun Aspect Sensor is based on photodiodes manufactured by Hamamatsu Photonics K.K.; the Geomagnetic Aspect Sensor is based on magnetometers manufactured by Bartington Intruments Ltd.; the inclinometer is based on a module manufactured by Measurement Specialties; and the gyro is manufactured by Silicon Sensing Systems Japan, Ltd. For the 2009 experiment, we used a Septentrio N.V. PolaRx2@ multi-antenna receiver with S67-1575-96 and S67-1575-46 antennas from Sensor Systems Inc. Details on the receivers and antennas used for the 2008 experiment are not publicly available. A Trimble Navigation Ltd. R7 receiver and two NovAtel Inc. OEMV receivers were used at the reference ground station. The ARM-Linux logging computer is an Armadillo PC/104 manufactured by Atmark Techno, Inc.

Peter J. Buist is a researcher at Delft University of Technology in Delft, The Netherlands. Before rejoining DUT in 2006, he developed GPS receivers for the SERVIS-1, USERS, ALOS, and other satellites and the H2A rocket, and subsystems for QZSS in the Japanese space industry.

Sandra Verhagen is an assistant professor at Delft University of Technology in Delft, The Netherlands. Together with Peter Buist, she is working on the Australian Space Research Program GARADA project on synthetic aperture radar formation flying.

Tatsuaki Hashimoto received his Ph.D. in electrical engineering from the University of Tokyo in 1990. He is a professor of the Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA).

Shujiro Sawai received his Ph.D. in engineering from the University
of Tokyo in 1994. He is an associate professor at ISAS/JAXA.

Shin-Ichiro Sakai received his Ph.D. degree from the University of Tokyo in 2000. He joined ISAS/JAXA in 2001 and became associate professor in 2005.

Nobutaka Bando received a Ph.D. in electrical engineering from the University of Tokyo in 2005. He is an assistant professor at ISAS/JAXA.

Shigehito Shimizu received a master’s degree in engineering from Tohoku University in Sendai, Japan, in 2007. He is an engineer in the Navigation, Guidance and Control Group at JAXA.

FURTHER READING

• Authors’ Proceedings Paper
“GPS Experiment on the Balloon-based Operation Vehicle” by P.J. Buist, S. Verhagen, T. Hashimoto, S. Sawai, S-I. Sakai, N. Bando, and S. Shimizu in Proceedings of PLANS 2010, IEEE/ION Position Location and Navigation Symposium, Indian Wells, California, May 4–6, 2010, pp. 1287–1294, doi: 10.1109/PLANS.2010.5507346.

• Balloon Applications
“Development of Vehicle for Balloon-Based Microgravity Experiment and Its Flight Results” by S. Sawai, T. Hashimoto, S. Sakai, N. Bando, H. Kobayashi, K. Fujita, T. Yoshimitsu, T. Ishikawa, Y. Inatomi, H. Fuke, Y. Kamata, S. Hoshino, K. Tajima, S. Kadooka, S. Uehara, T. Kojima, S. Ueno, K. Miyaji, N. Tsuboi, K. Hiraki, K. Suzuki, and K. M. T. Nakata in Journal of the Japan Society for Aeronautical and Space Sciences, Vol. 56, No. 654, 2008, pp. 339–346, doi: 10.2322/jjsass.56.339.

“Development of the Highest Altitude Balloon” by T. Yamagami, Y. Saito, Y. Matsuzaka, M. Namiki, M. Toriumi, R. Yokota, H. Hirosawa, and K. Matsushima in Advances in Space Research, Vol. 33, No. 10, 2004, pp. 1653–1659, doi: 10.1016/j.asr.2003.09.047.

• Attitude Determination
“Testing of a New Single-Frequency GNSS Carrier-Phase Attitude Determination Method: Land, Ship and Aircraft Experiments” by P.J.G. Teunissen, G. Giorgi, and P.J. Buist in GPS Solutions, Vol. 15, No. 1, 2011, pp. 15–28, doi: 10.1007/s10291-010-0164-x, 2010.

“Attitude Determination Methods Used in the PolarRx2@ Multi-antenna GPS Receiver” by L.V. Kuylen, F. Boon, and A. Simsky in Proceedings of ION GNSS 2005, the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation, Long Beach, California, September 13–16, 2005, pp. 125–135.

“Design of Multi-sensor Attitude Determination System for Balloon-based Operation Vehicle” by S. Shimizu, P.J. Buist, N. Bando, S. Sakai, S. Sawai, and T. Hashimoto, presented at the 27th ISTS International Symposium on Space Technology and Science, Tsukuba, Japan, July 5–12, 2009.

“Development of the Integrated Navigation Unit; Combining a GPS Receiver with Star Sensor Measurements” by P.J. Buist, S. Kumagai, T. Ito, K. Hama, and K. Mitani in Space Activities and Cooperation Contributing to All Pacific Basin Countries, the Proceedings of the 10th International Conference of Pacific Basin Societies (ISCOPS), Tokyo, Japan, December 10–12, 2003, Advances in the Astronautical Sciences, Vol. 117, 2004, pp. 357–378.

“Solving Your Attitude Problem: Basic Direction Sensing with GPS” by A. Caporali in GPS World, Vol. 12, No. 3, March 2001, pp. 44–50.

• Ambiguity Estimation
“Instantaneous Ambiguity Resolution in GNSS-based Attitude Determination Applications: the MC-LAMBDA Method” by G. Giorgi, P.J.G. Teunissen, S. Verhagen, and P.J. Buist in Journal of Guidance, Control and Dynamics, accepted for publication, April 2011.

“Integer Least Squares Theory for the GNSS Compass” by P.J.G. Teunissen in Journal of Geodesy, Vol. 84, No. 7, 2010, pp. 433–447, doi: 10.1007/s00190-010-0380-8.

“The Baseline Constrained LAMBDA Method for Single Epoch, Single Frequency Attitude Determination Applications” by P.J. Buist in Proceedings of ION GPS 2007, the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 25–28, 2007, pp. 2962–2973.

“The LAMBDA Method for the GNSS Compass” by P.J.G. Teunissen in Artificial Satellites, Vol. 41, No. 3, 2006, pp. 89–103, doi: 10.2478/v10018-007-0009-1.

“Fixing the Ambiguities: Are You Sure They’re Right?” by P. Joosten and C. Tiberius in GPS World, Vol. 11, No. 5, May 2000, pp. 46–51.

“The Least-Squares Ambiguity Decorrelation Adjustment: a Method for Fast GPS Integer Ambiguity Estimation” by P.J.G. Teunissen in Journal of Geodesy, Vol. 70, No. 1–2, 1995, pp. 65–82, doi: 10.1007/BF00863419.

• Relative Positioning
“A Vectorial Bootstrapping Approach for Integrated GNSS-based Relative Positioning and Attitude Determination of Spacecraft” by P.J. Buist, P.J.G. Teunissen, G. Giorgi, and S. Verhagen in Acta Astronautica, Vol. 68, No. 7-8, 2011, pp. 1113–1125, doi: 10.1016/j.actaastro.2010.09.027.

September 1, 2011
Innovation: Multipath Minimization Method

Mitigation Through Adaptive Filtering for Machine Automation Applications

By Luis Serrano, Don Kim, and Richard B. Langley

Multipath is real and omnipresent, a detriment when GPS is used for positioning, navigation, and timing. The authors look at a technique to reduce multipath by using a pair of antennas on a moving vehicle together with a sophisticated mathematical model. This reduces the level of multipath on carrier-phase observations and thereby improves the accuracy of the vehicle’s position.

INNOVATION INSIGHTS by Richard Langley

“OUT, DAMNED MULTIPATH! OUT, I SAY!” Many a GPS user has wished for their positioning results to be free of the effect of multipath. And unlike Lady Macbeth’s imaginary blood spot, multipath is real and omnipresent. Although it may be considered beneficial when GPS is used as a remote sensing tool, it is a detriment when GPS is used for positioning, navigation, and timing — reducing the achievable accuracy of results.

Clearly, the best way to reduce the effects of multipath is to try avoiding it in the first place by siting the receiver’s antenna as low as possible and far away from potential reflectors. But that’s not always feasible. The next best approach is to reduce the level of the multipath signal entering the receiver by attenuating it with a suitably designed antenna. A large metallic ground plane placed beneath an antenna will modify the shape of the antenna’s reception pattern giving it reduced sensitivity to signals arriving at low elevation angles and from below the antenna’s horizon. So-called choke-ring antennas also significantly attenuate multipath signals. And microwave-absorbing materials appropriately placed in an antenna’s vicinity can also be beneficial.

Multipath can also be mitigated by special receiver correlator designs. These designs target the effect of multipath on code-phase measurements and the resulting pseudorange observations. Several different proprietary implementations in commercial receivers significantly reduce the level of multipath in the pseudoranges and hence in pseudorange-based position and time estimates. Some degree of multipath attenuation can be had by using the low-noise carrier-phase measurements to smooth the pseudoranges before they are processed. The effect of multipath on carrier phases is much smaller than that on pseudoranges. In fact, it is limited to only one-quarter of the carrier wavelength when the reflected signal’s amplitude is less than that of the direct signal. This means that at the GPS L1 frequency, the multipath contamination in a carrier-phase measurement is at most about 5 centimeters. Nevertheless, this is still unacceptably large for some high-accuracy applications.

At a static site, with an unchanging multipath environment, the signal reflection geometry repeats day to day and the effect of multipath can be reduced by sidereal filtering or “stacking” of coordinate or carrier-phase-residual time series. However, this approach is not viable for scenarios where the receiver and antenna are moving such as in machine control applications. Here an alternative approach is needed.

In this month’s column, I am joined by two of my UNB colleagues as we look at a technique that uses a pair of antennas on a moving vehicle together with a sophisticated mathematical model, to reduce the level of multipath on carrier-phase observations and thereby improve the accuracy of the vehicle’s position.

Real-time-kinematic (RTK) GNSS-based machine automation systems are starting to appear in the construction and mining industries for the guidance of dozers, motor graders, excavators, and scrapers and in precision agriculture for the guidance of tractors and harvesters. Not only is the precise and accurate position of the vehicle needed but its attitude is frequently required as well.

Previous work in GNSS-based attitude systems, using short baselines (less than a couple of meters) between three or four antennas, has provided results with high accuracies, most of the time to the sub-degree level in the attitude angles. If the relative position of these multiple antennas can be determined with real-time centimeter-level accuracy using the carrier-phase observables (thus in RTK-mode), the three attitude parameters (the heading, pitch, and roll angles) of the platform can be estimated.

However, with only two GNSS antennas it is still possible to determine yaw and pitch angles, which is sufficient for some applications in precision agriculture and construction. Depending on the placement of the antennas on the platform body, the determination of these two angles can be quite robust and efficient.

Nevertheless, even a small separation between the antennas results in different and decorrelated phase-multipath errors, which are not removed by simply differencing measurements between the antennas.

The mitigation of carrier-phase multipath in real time remains, to a large extent, very limited (unlike the mitigation of code multipath through receiver improvements) and it is commonly considered the major source of error in GNSS-RTK applications. This is due to the very nature of multipath spectra, which depends mainly on the location of the antenna and the characteristics of the reflector(s) in its vicinity. Any change in this binomial (antenna/reflectors), regardless of how small it is, will cause an unknown multipath effect.

Using typical choke-ring antennas to reduce multipath is typically not practical (not to mention cost prohibitive) when employing multiple antennas on dynamic platforms. Extended flat ground planes are also impractical. Furthermore, such antenna configurations typically only reduce the effects of low angle reflections and those coming from below the antenna horizon.

One promising approach to mitigating the effects of carrier-phase multipath is to filter the raw measurements provided by the receiver. But, unlike the scenario at a fixed site, the multipath and its effects are not repeatable. In machine automation applications, the machinery is expected to perform complex and unpredictable maneuvers; therefore the removal of carrier-phase multipath should rely on smart digital filtering techniques that adapt not only to the background multipath (coming mostly from the machine’s reflecting surfaces), but also to the changing multipath environment along the machine’s path.

In this article, we describe how a typical GPS-based machine automation application using a dual-antenna system is used to calibrate, in a first step, and then remove carrier-phase multipath afterwards. The intricate dynamical relationship between the platform’s two “rover” antennas and the changing multipath from nearby reflectors is explored and modeled through several stochastic and dynamical models. These models have been implemented in an extended Kalman filter (EKF).

MIMICS Strategy

Any change in the relative position between a pair of GNSS antennas most likely will affect, at a small scale, the amplitude and polarization of the reflected signals sensed by the antennas (depending on their spacing). However, the phase will definitely change significantly along the ray trajectories of the plane waves passing through each of the antennas.

This can be seen in the equation that describes the single-difference multipath between two close-by antennas (one called the “master” and the other the “slave”):

(1)

where the angle is the relative multipath phase delay between the antennas and a nearby effective reflector (α₀ is the multipath signal amplitude in the master and slave antennas, and is dependent on the reflector characteristics, reflection coefficient, and receiver tracking loop).

As our study has the objective to mimic as much as possible the multipath effect from effective reflectors in kinematic scenarios with variable dynamics, we decided to name the strategy MIMICS, a slightly contrived abbreviation for “Multipath profile from between receIvers dynaMICS.”

The MIMICS algorithm for a dual-antenna system is based on a specular reflector ray-tracing multipath model (see Figure 1).

Figure 1. 3D ray-tracing modeling of phase multipath for a GNSS dual-antenna system. 0 designates the “master” antenna; 1, the “slave” antenna; Elev and Az, the elevation angle and the azimuth of the satellite, respectively. The other symbols are explained in the text.

After a first step of data synchronization and data-snooping on the data provided by the two receiver antennas, the second step requires the calculation of an approximate position for both antennas, relaxed to a few meters using a standard code solution.

A precise estimation of both antennas’ velocity and acceleration (in real time) is carried out using the carrier-phase observable. Not only should the antenna velocity and acceleration estimates be precisely determined (on the order of a few millimeters per second and a few millimeters per second squared, respectively) but they should also be immune to low-frequency multipath signatures. This is important in our approach, as we use the antennas’ multipath-free dynamic information to separate the multipath in the raw data.

We will start from the basic equations used to derive the single-difference multipath observables.

The observation equation for a single-difference between receivers, using a common external clock (oscillator), is given (in distance units) by:

(2)

where m indicates the master antenna; s, the slave antenna; prn, the satellite number; Δ, the operator for single differencing between receivers; Φ, the carrier-phase observation; ρ, the slant range between the satellite and receiver antennas; N, the carrier-phase ambiguity; M, the multipath; and ε, the system noise.

By sequentially differencing Equation (2) in time to remove the single-difference ambiguity from the observation equation, we obtain (as long as there is no loss of lock or cycle slips):

(3)

where

(4)

One of the key ideas in deriving the multipath observable from Equation (3) is to estimate given by Equation (4). We will outline our approach in a later section.

From Equation (3), at the second epoch, for example, we will have:

(5)

If we continue this process up to epoch n, we will obtain an ensemble of differential multipath observations.

If we then take the numerical summation of these, we will have

(6)

Note that n samples of differential multipath observations are used in Equation (6). Therefore, we need n + 1 observations.

Assume that we perform this process taking n = 1, then n = 2, and so on until we obtain r numerical summations of Equation (6) and then take a second numerical summation of them, we will end up with the following equation:

(7)

where E is the expectation operator.

Another key idea in our approach is associated with Equation (7). To isolate the initial epoch multipath, , from the differential multipath observations, the first term on the right-hand side of Equation (7), , should be removed.

This can be accomplished by mechanical calibration and/or numerical randomization. To summarize the idea, we have to create random multipath physically (or numerically) at the initialization step. When the isolation of the initial multipath epoch is completed, we can recover multipath at every epoch using Equation (5).

Digital Differentiators. We introduce digital differentiators in our approach to derive higher order range dynamics (that is, range rate, range-rate change, and so on) using the single-difference (between receivers connected to a common external oscillator) carrier-phase observations. These higher order range dynamics are used in Equation (4).

There are important classes of finite-impulse-response differentiators, which are highly accurate at low to medium frequencies. In central-difference approximations, both the backward and the forward values of the function are used to approximate the current value of the derivative.

Researchers have demonstrated that the coefficients of the maximally linear digital differentiator of order 2N + 1 are the same as the coefficients of the easily computed central-difference approximation of order N.

Another advantage of this class is that within a certain maximum allowable ripple on the amplitude response of the resultant differentiator, its pass band can be dramatically increased. In our approach, this is something fundamental as the multipath in kinematic scenarios is conceptually treated as high-frequency correlated multipath, depending on the platform dynamics and the distance to the reflector(s).

Adaptive Estimation. To derive single-difference multipath at the initial epoch, , a numerical randomization (or mechanical calibration) of the single-difference multipath observations is performed in our approach. A time series of the single-difference multipath observations to be randomized is given as

(8)

Then our goal is to achieve the following condition:

(9)

It is obvious that the condition will only hold if multipath truly behaves as a stochastic or random process. The estimation of multipath in a kinematic scenario has to be understood as the estimation of time-correlated random errors. However, there is no straightforward way to find the correlation periods and model the errors.

Our idea is to decorrelate the between-antenna relative multipath through the introduction of a pseudorandom motion. As one cannot completely rely only on a decorrelation through the platform calibration motion, one also has to do it through the mathematical “whitening” of the time series.

Nevertheless, the ensemble of data depicted in the above formulation can be modeled as an oscillatory random process, for which second or higher order autoregressive (AR) models can provide more realistic modeling in kinematic scenarios. (An autoregressive process is simply another name for a linear difference equation model where the input or forcing function is white Gaussian noise.) We can estimate the parameters of this model in real time, in a block-by-block analysis using the familiar Yule-Walker equations. A whitening filter can then be formed from the estimation parameters.

We obtain the AR coefficients using the autocorrelation coefficient vector of the random sequences. Since the order of the coefficient estimation depends on the multipath spectra (in turn dependent on the platform dynamics and reflector distance), MIMICS uses a cost function to estimate adaptively, in real time, the appropriate order. An order too low results in a poor whitener of the background colored noise, while an order too large might affect the embedded original signal that we are interested in detecting.

The cost function uses the residual sum of squared error. The order estimate that gives the lowest error is the one chosen, and this task is done iteratively until it reaches a minimum threshold value. Once this stage is fulfilled, the multipath observable can be easily obtained.

Testing

The main test that we have performed so far (using a pair of high performance dual-frequency receivers fed by compact antennas and a rubidium frequency standard, all installed in a vehicle) was designed to evaluate the amount of data necessary to perform the decorrelation, and to determine if the system was observable (in terms of estimating, at every epoch, several multipath parameters from just two-antenna observations). Receiver data was collected and post-processed (so-called RTK-style processing) although, with sufficient computing power, data processing could take place in real, or near real, time.

In a real-life scenario, the platform pseudorandom motions have the advantage that carrier-phase embedded dynamics are typically changing faster and in a three-dimensional manner (antennas sense different pitch and yaw angles). Thus a faster and more robust decorrelation is possible.

One can see from the bottom picture in Figure 2 the façade of the building behaving as the effective reflector. The vehicle performed several motions, depicted in the bottom panel of Figure 3, always in the visible parking lot, hence the building constantly blocked the view to some satellites. We used only the L1 data from the receivers recorded at a rate of 10 Hz.

In the bottom panel of Figure 3, one can also see the kind of motion performed by the platform. Accelerations, jerk, idling, and several stops were performed on purpose to see the resultant multipath spectra differences between the antennas. The reference station (using a receiver with capabilities similar to those in the vehicle) was located on a roof-top no more than 110 meters away from the vehicle antennas during the test. As such, most of the usual biases where removed from the solution in the differencing process and the only remaining bias can be attributed to multipath. The data from the reference receiver was only used to obtain the varying baseline with respect to the vehicle master antenna.

In the top panel of Figure 3, one can see the geometric distance calculated from the integer-ambiguity-fixed solutions of both antenna/receiver combinations. Since the distance between the mounting points on the antenna-support bar was accurately measured before the test (84 centimeters), we had an easy way to evaluate the solution quality. The “outliers” seen in the figure come from code solutions because the building mentioned before blocked most of the satellites towards the southeast. As a result, many times fewer than five satellites were available.

Figure 3. Correlation between vehicle dynamics (heading angle) and the multipath spectra.

Looking at the first nine minutes of results in Figure 4, one can see that when the vehicle is still stationary, the multipath has a very clear quasi-sinusoidal behavior with a period of a few minutes. Also, one can see that it is zero-mean as expected (unlike code multipath). When the vehicle starts moving (at about the four-minute mark), the noise figure is amplified (depending on the platform velocity), but one can still see a mixture of low-frequency components coming from multipath (although with shorter periods).

These results indicate, firstly, that regardless of the distance between two antennas, multipath will not be eliminated after differencing, unlike some other biases. Secondly, when the platform has multiple dynamics, multipath spectra will change accordingly starting from the low-frequency components (due to nearby reflectors) towards the high-frequency ones (including diffraction coming from the building edges and corners). As such, our approach to adaptively model multipath in real time as a quasi-random process makes sense.

Figure 4. Position results from the kinematic test, showing the estimated distance between the two vehicle antennas (upper plot) and the distance between the master antenna and the reference antenna.

Multipath Observables. The multipath observables are obtained through the MIMICS algorithm. It is quite flexible in terms of latency and filter order when it comes to deriving the observables. Basically, it is dependent on the platform dynamics and the amplitude of the residuals of the whitened time series (meaning that if they exceed a certain threshold, then the filtering order doesn’t fit the data).

When comparing the observations delivered every half second for PRN 5 with the ones delivered every second, it is clear that the larger the interval between observations, the better we are able to recover the true biased sinusoidal behavior of multipath. However, in machine control, some applications require a very low latency. Therefore, there must be a compromise between the multipath observable accuracy and the rate at which it is generated.

Multipath Parameter Estimation. Once the multipath observables are derived, on a satellite-by-satellite basis, it is possible to estimate the parameters (a₀, the reflection coefficient; γ₀, the phase delay; φ₀, the azimuth of reflected signal; and θ₀, the elevation angle of reflected signal) of the multipath observable described in Equation (1) for each satellite. As mentioned earlier, an EKF is used for the estimation procedure.

When the platform experiences higher dynamics, such as rapid rotations, acceleration is no longer constant and jerk is present. Therefore, a Gauss-Markov model may be more suitable than other stochastic models, such as random walk, and can be implemented through a position-velocity-acceleration dynamic model.

As an example, the results from the multipath parameter estimation are given for satellite PRN 5 in Figure 5. One can see that it takes roughly 40 seconds for the filter to converge. This is especially seen in the phase delay.

Converted to meters, the multipath phase delay gives an approximate value of 10 meters, which is consistent with the distance from the moving platform to the dominant specular reflector (the building’s façade).

Figure 5. PRN 5 multipath parameter estimation.

Multipath Mitigation. After going through all the MIMICS steps,
from the initial data tracking and synchronization between the dual-antenna system up to the multipath parameter estimation for each continuously observed satellite, we can now generate the multipath corrections and thus correct each raw carrier-phase observation.

One can see in Figure 6 three different plots from the solution domain depicting the original raw (multipath-contaminated) GPS-RTK baseline up-component (top), the estimated carrier-phase multipath signal (middle), and the difference between the two above time series; that is, the GPS-RTK multipath-ameliorated solution (bottom). A clear improvement is visible. In terms of numbers, and only considering the results “cleaned” from outliers and differential-code solutions (provided by the RTK post-processing software, when carrier-phase ambiguities cannot be fixed), the up-component root-mean-square value before was 2.5 centimeters, and after applying MIMICS it stood at 1.8 centimeters.

Figure 6. MIMICS algorithm results for the vehicle baseline from the first 9 minutes of the test.

Concluding Remarks

Our novel strategy seems to work well in adaptively detecting and estimating multipath profiles in simulated real time (or near real time as there is a small latency to obtain multipath corrections from the MIMICS algorithm). The approach is designed to be applied in specular-rich and varying multipath environments, quite common at construction sites, harbors, airports, and other environments where GNSS-based heading systems are becoming standard. The equipment setup can be simplified, compared to that used in our test, if a single receiver with dual-antenna inputs is employed.

Despite its success, there are some limitations to our approach. From the plots, it’s clear that not all multipath patterns were removed, even though the improvements are notable. Moreover, estimating multipath adaptively in real time can be a problem from a computational point of view when using high update rates. And when the platform is static and no previous calibration exists, the estimation of multipath parameters is impossible as the system is not observable. Nevertheless, the approach shows promise and real-world tests are in the planning stages.

Acknowledgments

The work described in this article was supported by the Natural Sciences and Engineering Research Council of Canada. The article is based on a paper given at the Institute of Electrical and Electronics Engineers / Institute of Navigation Position Location and Navigation Symposium 2010, held in Indian Wells, California, May 6–8, 2010.

Manufacturers

The test of the MIMICS approach used two NovAtel OEM4 receivers in the vehicle each fed by a separate NovAtel GPS-600 “pinweel” antenna on the roof. A Temex Time (now Spectratime) LPFRS-01/5M rubidium frequency standard supplied a common oscillator frequency to both receivers. The reference receiver was a Trimble 5700, fed by a Trimble Zephyr geodetic antenna.

Luis Serrano is a senior navigation engineer at EADS Astrium U.K., in the Ground Segment Group, based in Portsmouth, where he leads studies and research in GNSS high precision applications and GNSS anti-jamming/spoofing software and patents. He is also a completing his Ph.D. degree at the University of New Brunwick (UNB), Fredericton, Canada.

Don Kim is an adjunct professor and a senior research associate in the Department of Geodesy and Geomatics Engineering at UNB where he has been doing research and teaching since 1998. He has a bachelor’s degree in urban engineering and an M.Sc.E. and Ph.D. in geomatics from Seoul National University. Dr. Kim has been involved in GNSS research since 1991 and his research centers on high-precision positioning and navigation sensor technologies for practical solutions in scientific and industrial applications that require real-time processing, high data rates, and high accuracy over long ranges with possible high platform dynamics.

FURTHER READING

• Authors’ Proceedings Paper
“Multipath Adaptive Filtering in GNSS/RTK-Based Machine Automation Applications” by L. Serrano, D. Kim, and R.B. Langley in Proceedings of PLANS 2010, IEEE/ION Position Location and Navigation Symposium, Indian Wells, California, May 4–6, 2010, pp. 60–69, doi: 10.1109/PLANS.2010.5507201.

• Pseudorange and Carrier-Phase Multipath Theory and Amelioration Articles from GPS World
“It’s Not All Bad: Understanding and Using GNSS Multipath” by A. Bilich and K.M. Larson in GPS World, Vol. 20, No. 10, October 2009, pp. 31–39.

“Multipath Mitigation: How Good Can It Get with the New Signals?” by L.R. Weill, in GPS World, Vol. 14, No. 6, June 2003, pp. 106–113.

“GPS Signal Multipath: A Software Simulator” by S.H. Byun, G.A. Hajj, and L.W. Young in GPS World, Vol. 13, No. 7, July 2002, pp. 40–49.

“Conquering Multipath: The GPS Accuracy Battle” by L.R. Weill, in GPS World, Vol. 8, No. 4, April 1997, pp. 59–66.

• Dual Antenna Carrier-phase Multipath Observable
“A New Carrier-Phase Multipath Observable for GPS Real-Time Kinematics Based on Between Receiver Dynamics” by L. Serrano, D. Kim, and R.B. Langley in Proceedings of the 61st Annual Meeting of The Institute of Navigation, Cambridge, Massachusetts, June 27–29, 2005, pp. 1105–1115.

“Mitigation of Static Carrier Phase Multipath Effects Using Multiple Closely-Spaced Antennas” by J.K. Ray, M.E. Cannon, and P. Fenton in Proceedings of ION GPS-98, the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, September 15–18, 1998, pp. 1025–1034.

• Digital Differentiation
“Digital Differentiators Based on Taylor Series” by I.R. Khan and R. Ohba in the Institute of Electronics, Information and Communication Engineers (Japan) Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E82-A, No. 12, December 1999, pp. 2822–2824.

• Autoregressive Models and the Yule-Walker Equations
Random Signals: Detection, Estimation and Data Analysis by K.S. Shanmugan and A.M. Breipohl, published by Wiley, New York, 1988.

• Kalman Filtering and Dynamic Models
Introduction to Random Signals and Applied Kalman Filtering: with MATLAB Exercises and Solutions, 3rd edition, by R.G. Brown and P.Y.C. Hwang, published by Wiley, New York, 1997.

“The Kalman Filter: Navigation’s Integration Workhorse” by L.J. Levy in GPS World, Vol. 8, No. 9, September 1997, pp. 65–71.

July 1, 2011
Innovation: MBOC Signal Options

Performance of Multiplexed Binary Offset Carrier Modulations for Modernized GNSS Systems

By E. Simona Lohan, Mohammad Z. H. Bhuiyan, and Heikki Hurskainen

A candidate for modernized GNSS civil signals in the L1/E1 band was BOC(1,1), a binary-offset-carrier signal with a “split spectrum” that has negligible impact on the existing GPS signals. However, a signal with better acquisition capabilities and improved multipath performance (while still compatible with the existing GPS signals) is a multiplexed BOC modulation, MBOC(6,1,1/11). The MBOC spectrum can be achieved by following one of several different signal-construction paths with some resulting differences in how a receiver tracks the signal and its associated performance.

INNOVATION INSIGHTS by Richard Langley

IN GEOFFREY CHAUCER’S 1391 ESSAY, A Treatise on the Astrolabe (one of the earliest known instruction manuals in English), he says (with modern spelling) “Right as diverse paths lead the folk the right way to Rome.” He was talking about the use of English rather than Latin or another language to convey the same information. And we now commonly use the shortened version of this expression — all roads lead to Rome — to express the sentiment that a particular problem can be solved in different ways.

So it was with the decision by the United States and Europe to use a common, interoperable signal for the new GPS III civil service and the Galileo Open Service on the L1/E1 frequency of 1575.42 MHz. The road to “Rome” was tedious, long, and a little bumpy at times. A number of studies and a lot of rhetoric centered on how to make the new signal compatible with the legacy GPS L1 signals, the C/A-code and the P(Y)-code, as well as the modernized GPS military signal on L1, the M-code.

A similar compatibility issue had been solved when the M-code was added to the legacy GPS signals, starting with the Block IIR-M satellites. The M-code is a binary-offset-carrier (BOC) signal — a split spectrum signal — that places most of its power near the edges of the allocated GPS frequency bands, thereby having negligible impact on the legacy signals. The M-code modulation, designated BOC(10.23,5.115) and commonly abbreviated BOC(10,5), uses a subcarrier frequency of 10.23 MHz and a spreading code rate of 5.115 megachips per second to achieve the desired spectral separation. This design provides military users with an improved signal with little impact on civil users.

Similar approaches were initially proposed for the new GPS L1C and Galileo E1/L1 OS signals with a BOC(1,1) modulation initially agreed on. However, further studies showed that a signal with better acquisition capabilities and improved multipath performance (while still compatible with the existing GPS signals) was a multiplexed BOC modulation, MBOC(6,1,1/11), formed by multiplexing a wideband signal, BOC(6,1), with a narrow-band signal, BOC(1,1), in such a way that 1/11th of the power is allocated, on average, to the high frequency component. Such a signal has the added benefit that one can choose whether to make use of just the low-frequency component in, say, a simple “mass market” receiver or also use the high-frequency component for more demanding applications.

It turns out that the agreed-upon MBOC spectrum can be achieved by following one of several different signal-construction paths with some resulting differences in how a receiver tracks the signal and its associated performance. In this month’s column, we take a look at some of the options.

In July 2007, the United States and Europe announced agreement on the use of the multiplexed binary offset carrier (MBOC) modulation as a common baseline for Galileo Open Service signals in the E1 band and GPS L1C signals in the L1 band. According to the most recent Galileo Signal-In-Space Interface Control Document (SIS-ICD; see Further Reading), the MBOC power spectral density (PSD) has been fixed to

(1)

where G_BOC(m,n)(f) is the normalized PSD of a BOC(m,n)-modulated pseudorandom noise (PRN) code with sine phasing. The indices m and n are related to the sub-carrier frequency, f_sc, and the chip frequency, f_c, via m = f_sc/f_ref and n = f_c/f_ref, respectively; f_ref = 1.023 MHz is the reference C/A-code frequency, and N_B = 2f_sc/f_c = 2m/n is the BOC modulation index.

The MBOC PSD is obtained by taking the data and pilot channels together. The data and pilot channels can use, independently, one of the following modulations: composite binary offset carrier (CBOC) or time-multiplexed binary offset carrier (TMBOC) modulations. CBOC and TMBOC, in turn, have several variants. Since the data and pilot channels are typically processed independently, it is important to understand the differences between various CBOC and TMBOC modulations and this is the primary goal of this article. There are several possible ways to achieve a PSD as given in Equation (1) and they are based on combining the data and pilot channels in the Galileo and modernized GPS systems. The main modulation types for pilot or data channels that can be used in order to achieve (when combined) the MBOC PSD can be summarized as follows:

1. The CBOC method: CBOC is formed via a weighted sum or difference of BOC(1,1)- and BOC(6,1)-modulated code symbols (where the BOC(1,1) part is passed through a delay block in order to match the rate of the BOC(6,1) part) as defined in Equation (2):

(2)

where s_BOC(1,1),h is the up-sampled BOC(1,1)-modulated code (that is, the code provided at the same rate as the s_BOC(6,1) signal), s_BOC(6,1) is the BOC(6,1)-modulated code, and w₁ and w₂ are amplitude weighting factors, chosen in such a way to match (as closely as possible, when both data and pilot channels are considered) the PSD of Equation (1), with w₁² + w₂² = 1. When the two right-hand terms are added in Equation (2), CBOC(+) is formed; when subtracted, CBOC(–) is formed. A third alternative for CBOC implementation is to use the CBOC(+/–) approach, where the odd-numbered chips are CBOC(+)-modulated and the even chips are CBOC(–)-modulated. The current Galileo SIS-ICD uses a CBOC(+) variant (also called CBOC in-phase) for the E1-B data channel and a CBOC(–) variant (also called CBOC anti-phase) for the E1-C data-less (or pilot) channel.

2. The time-multiplexed BOC (TMBOC) method: the whole signal is divided into blocks of N code symbols with M (<N) code symbols sine-BOC(1,1)-modulated, while N-M code symbols are sine-BOC(6,1)-modulated. The typical shorthand notation for this variety of TMBOC would be TMBOC(6,1,(N-M)/N), referring to the sine-BOC(6,1) component of the signal. This time-domain division may be applied for both pilot and data channels, individually. The choice of the N and M parameter values depends on the desired power percentage of the pilot channel with respect to the data channel. We have shown in earlier work (see Further Reading) that, from the point of view of the MBOC autocorrelation function, TMBOC and CBOC(+) implementations are equivalent, as long as the weights are related to the N and M values using w₁ = √(M/N) and w2 = √((N-M)/N). Various TMBOC implementations exist according to the values chosen for N and M and according to whether the BOC(1,1) code symbols are in phase or out of phase with the BOC(6,1) code symbols. For example, for a 50-percent/50-percent power split between the pilot and data channels using in-phase code symbols, M = 9 and N = 11 (that is, TMBOC(6,1,2/11) is used), while for a 75-percent/25-percent power split between the pilot and data channels (again, using in-phase code symbols), M = 29 and N = 33 (that is, TMBOC(6,1,4/33) is used).

A major difference between CBOC and TMBOC signals is that CBOC signals have four different levels (as a weighted sum or difference of two sub-carriers), while TMBOC signals have only two levels. The impact of these differences in the tracking stage of a receiver has been analyzed, for example, by a team of researchers led by Olivier Julien (see Further Reading). They showed that an optimal CBOC receiver should generate a local replica that also has four levels, resulting in a replica encoded on more than just one bit. This complicates the CBOC receiver architecture, compared to TMBOC 1-bit receiver architectures. In terms of performance, a CBOC(–) receiver proved to have the same delay-tracking variance performance as a TMBOC(6,1,4/33) receiver and both slightly outperform a TMBOC(6,1,1/11) receiver. And considering multipath error performance, a TMBOC(6,1,4/33) receiver was shown to give the best performance, followed very closely by a CBOC(–) receiver. Our research extends this earlier study.

Examples of CBOC and TMBOC waveforms are shown in Figure 1. Here, w₁ = (10/11) and the TMBOC waveform has every first chip BOC(6,1)-modulated (inside blocks of 11 chips). In the figure, only the first five modulated chips are shown for clarity.

Figure 1. Example of MBOC waveforms for a PRN sequence [1, -1, 1, -1, -1].
Our article addresses the following issues: First, we analyze the spectral differences between various CBOC and TMBOC modulations in terms of their effect on receiver performance. Secondly, we look at the navigation data error probability, the tracking error variance in the presence of noise, and the robustness of the signal in the presence of multipath and bandwidth limitations of MBOC variants, by taking into account the spectral differences between the different variants. Thirdly, we justify the choice of CBOC(+) for data channels and CBOC(–) for pilot channels in the Galileo SIS-ICD in terms of these receiver performance criteria.

Spectral Differences of CBOC/TMBOC Modulations

The spectral differences refer to the differences in the PSD of various waveforms. We recall that the PSD is the Fourier transform of the CBOC/TMBOC autocorrelation function. CBOC/TMBOC signals are formed from the convolution of PRN code waveforms, CBOC/TMBOC modulation waveforms, and navigation data (when present). If the same PRN code is used for the BOC(1,1) and BOC(6,1) modulations, some cross-correlation terms appear in the autocorrelation function, which will also appear in the frequency spectrum. Indeed, following the model, after straightforward derivations, we obtain the generic CBOC/TMBOC PSD as:

(3)

where H_BOC(1,1),h(f) and H_BOC(6,1)(f) are the following Fourier transforms of the modulation waveforms:

(4)

(5)

Above, T_B = T_C/12 is the BOC(6,1) sub-interval and sinc(x) = sin(x)/x. The formula given in Equation (3) covers all CBOC/TMBOC cases: k = +1 for CBOC(+) and TMBOC, k = –1 for CBOC(–), and k = 0 for CBOC(+/–), respectively. Equation (3) characterizes either the pilot channel’s PSD or the data channel’s PSD. In order to achieve the PSD of Equation (1), data and pilot channels should be combined. For example, if k = 0, any combination of data and pilot channels is possible in order to attain the PSD. If k ≠ 0, then the data channel should use in-phase combining (k = +1) and the pilot channel should use anti-phase combining (k = –1) or vice versa.

Now, if we take as a reference the PSD of CBOC(+/–) (which, incidentally, is also the PSD of Equation (1)), the spectral differences between the other CBOC/TMBOC modulations and CBOC(+/–) are quantized by the following equation:

(6)

Examples of spectral difference between CBOC(+/–) and each of the following modulations: CBOC(–), CBOC(+), and TMBOC(6,1,(N-M)/N) and each of the following modulations: CBOC(–), CBOC(+), and TMBOC(6,1,(N-M)/N), respectively, are shown in Figure 2. Clearly, these differences are very small.

Figure 2. Examples of PSD spectral differences (linear scale) between various CBOC/TMBOC implementations and CBOC(+/-) assuming an MBOC receiver.

Impact on System Performance

As mentioned before, pilot and data channels typically use different CBOC/TMBOC modulations, in order to achieve an overall PSD as described by Equation (1). Now, based on the derivations we have presented so far, the following questions can be addressed: Which are the most suitable modulations (among the four discussed here; namely, CBOC(+), CBOC(–), CBOC(+/–), and TMBOC) to be used for a pilot channel and for a data channel, respectively; and how will the differences in the PSDs affect the error probability of the decoded signal and the tracking performance of each channel?

Uncoded Error Probability and Fractional Out-of-Band Energy. Data and pilot channels are usually processed independently and then combined (for example, non-coherently) in order to perform the line-of-sight (LOS) signal delay estimation and the navigation data detection. Since different CBOC or TMBOC modulations can be used for the data and pilot channels, one question to be addressed here is what is the most suitable modulation type. Additionally, the carrier-to-noise-density ratio (C/N₀) deterioration when another modulation type is employed is also important. These two issues are addressed in this section.

One important spectral parameter that allows us to answer the question about error probability in the decoded data is the so-called fractional out-of-band energy (FOBE), which tells us about the fraction of the signal power remaining outside a certain double-sided bandwidth, B_w. FOBE is related to the power containment factor, used by some authors, via (1 – FOBE(B_w)). Clearly, FOBE depends on the signal modulation type. The higher FOBE is, the greater the deterioration of the signal energy we have after the receiver bandwidth limiting filters, and thus the higher error probability of the decoded signal we have. From the data-channel point of view, correctly decoding the navigation data is very important and therefore, low FOBE is the most important characteris
tic when choosing the modulation type. The bit error probability in decoding a binary signal, such as a BOC or MBOC signal, can be computed by taking into account the signal energy deterioration due to filtering. Using the basic formula for computing the bit error probability in decoding a 2-level signal (in the cases of BOC or TMBOC modulation) or a 4-level signal (in the case of CBOC modulation), we can compare the performance of various TMBOC and CBOC modulations in terms of error probability of the decoded data bits, as shown in Figure 3. Clearly, the error probability criterion is more important for a data channel than for a pilot channel. Sine-BOC(1,1) and BOC(6,1) modulations are included in the comparison of Figure 3 as benchmarks. A double-sided bandwidth of 24.552 MHz was considered here, following the choice in the Galileo SIS-ICD.

Figure 3. Detection error probability for CBOC/TMBOC-modulated signals with a 24.552 MHz double-sided bandwidth.

As seen in Figure 3, in terms of the error probability of the decoded signal, BOC(1,1) modulation gives the best results, followed closely by TMBOC(6,1,4/33). In order to achieve an error probability of 10-2, the CNR differences shown in Table 1 are needed for the different modulation types. From Table 1, it can be seen that, among CBOC modulations, the CBOC(+) modulation is the best option from the point of view of decoding the data, and, therefore, it makes it a suitable option for data channels, as chosen in the Galileo SIS-ICD. We remark that the huge CNR gap for BOC(6,1) at B_w = 8 MHz is due to the fact that the power containment of a BOC(6,1) signal is very poor at such a low bandwidth.

Gabor Bandwidth and Tracking Error Variance. Another important spectral parameter of interest in this analysis is the root-mean-square (RMS) or Gabor bandwidth. A larger RMS or Gabor bandwidth permits a higher accuracy against thermal noise and the tracking accuracy is approximately inversely proportional to the RMS bandwidth. The code-tracking error variance is an important parameter when trying to achieve accurate location estimates. Indeed, a Cramér-Rao lower bound (CRLB) on the tracking error variance has been derived by other researchers. Following the derivation for CRLB on the tracking error variance, we can also compare the performance of various CBOC and TMBOC modulations, as presented in Figure 4. Clearly, this criterion is more important for a pilot channel than for a data channel. A double-sided receiver bandwidth of 24.552 MHz was considered here.

Figure 4. Cramér-Rao lower bound on tracking error variance (in seconds2) for CBOC/TMBOC-modulated signals with a 24.552 MHz double-sided bandwidth.

In terms of the tracking error variance bound, which linearly decreases with the CNR (on a dB scale), the CNR differences between various modulations are shown in TablE 2 for a 4-Hz tracking-loop bandwidth. Clearly, from Table 2, CBOC modulations are better in terms of tracking error variance than TMBOC modulation, and, among the CBOC variants, CBOC(–) has the best performance. This justifies the fact that the Galileo SIS-ICD has chosen the CBOC(–) as the best option for pilot channels. We can also see in Table 2 that the bandwidth limitation has an important effect on the tracking error bounds, as expected. At low receiver bandwidth (such as 8 MHz), the differences between various modulations are rather small, while at high or infinite bandwidths, BOC(6,1) modulation is by far the best option, followed by CBOC(–) with a 1.69 dB gap in CNR (that is, CBOC(–) requires an additional 1.69 dB in order to achieve the same tracking error performance as BOC(6,1)).

Multipath Error Envelope. The typical procedure for evaluating the performance of a multipath-mitigation technique is via the multipath error envelope (MEE). The MEE curves are obtained for two extreme phase variations of a multipath signal with respect to the LOS component while varying the multipath (that is, second path) delays from 0 to 1.2 chips at maximum, since the multipath errors become less significant after that. The upper multipath error envelope can be obtained when the paths are in-phase (that is, 0° phase difference) and the lower multipath error envelope when the paths are out-of-phase (that is, 180° phase difference). In MEE analysis, several simplifying assumptions are usually made in order to distinguish the performance degradation caused by the multipath only. Such assumptions include zero additive white Gaussian noise, ideal infinite-length PRN codes, zero residual Doppler shift, and zero initial code-delay error.

The MEE curves are generated here for different variants of MBOC implementation. The multipath performance of these MBOC variants with a BOC(1,1)-modulated reference receiver is also presented. In the MEE generation, the second path amplitude was fixed at 3 dB lower than the LOS component. The MEE curves were generated for a 24.552 MHz double-sided bandwidth. The narrow early-minus-late (nEML) correlator with an early-late correlator spacing of 0.0833 chips was used here as a tool for evaluating the performance of the different MBOC variants in the presence of multipath. The nEML is based on the idea of narrowing the spacing between the early and late correlator pair, where the choice of correlator spacing depends on the receiver’s available front-end bandwidth along with the associated sampling frequency.

MEE curves are shown for all of the examined MBOC variants in Figure 5. It can be observed from the figure that CBOC(–) has the best multipath mitigation performance followed by the TMBOC(6,1,4/33) and CBOC(+) variants. A similar conclusion can be drawn when a BOC(1,1) reference receiver is used instead of the respective MBOC reference receiver. However, from Figure 5, it is obvious that there is a moderate performance degradation when a BOC(1,1) reference receiver is used instead of the respective MBOC version, as expected intuitively.

Figure 5. Multipath error envelope curves for a narrow early-minus-late correlator with a 24.552 MHz double-sided bandwidth.

Simulation Results in Multipath Fading Channel

Simulations have been carried out in closely spaced multipath scenarios for different MBOC variants with a finite front-end bandwidth. The simulation profile is summarized in Table 3. A Rayleigh fading channel model is used in the simulation, where the number of channel paths is fixed to two. The successive path separation is random between 0.02 and 0.35 chips. The channel paths are assumed to obey a decaying power delay profile (PDP).

The received signal duration is 0.8 seconds for each particular C/N₀ level. The tracking errors are computed after each N_cN_nc-milliseconds interval (in this case, N_cN_nc = 20 milliseconds). In the final statistics, the first 600 milliseconds are ignored in order to remove the initial error bias that may come from the delay difference between the received signal and the locally generated reference code. Therefore, for the above configuration, the left-over tracking errors after 600 milliseconds are mostly due to the effect of multipath only. We ran the simulations for 1,000 statistical points, for each C/N_{0 b> level. The RMS error (RMSE) of the delay estimates can be plotted in meters, by using the relationship RMSE_m = RMSE_chips•c•T_c, where c is the speed of light, T_c is the chip duration, and RMSE_chips is the RMSE in chips. An RMSE versus C/N₀ plot for the given multipath channel profile is shown in Figure 6.}

As seen in the figure, the CBOC(–) reference receiver has the best multipath mitigation performance under a good

C/N₀ (that is, 40 dB-Hz and higher) followed by the other two MBOC variants (CBOC(+) and TMBOC(6,1,4/33)), which exhibit almost similar performance. A similar conclusion can be drawn for the BOC(1,1) reference receiver, where the CBOC(–)-modulated transmitted signal with BOC(1,1) reference receiver showed the best multipath mitigation performance among all three of the studied MBOC variants. In Figure 6, we observe that the small performance deterioration caused by use of a BOC(1,1) reference receiver is visible only under good C/N₀ conditions (that is, 40 dB-Hz and higher).

Figure 6. Root-mean-square error versus carrier-to-noise-density ratio for different MBOC variants in a two-path fading channel with 24.552 MHz double-sided bandwidth.

Conclusions

This article discusses the spectral differences between CBOC and TMBOC modulations and their impact on system performance. The exact frequency-domain form of the PSD for CBOC and TMBOC waveforms has been shown and the impact on tracking error variance bounds and on the error probability of the demodulated signal has been discussed. In addition, the multipath mitigation performances of different MBOC variants were presented in terms of RMSE and multipath error envelopes. It was shown that the CBOC(–) variant is the best variant in terms of multipath mitigation and tracking error variance, while TMBOC behaves better than CBOC in terms of error probability of the demodulated data. We also showed that the spectral differences and the differences between CBOC and TMBOC variants in terms of the two considered performance criteria are rather small, especially when the receiver bandwidth is not very high, and, therefore, several variants of MBOC can indeed be used for design and research purposes.

Acknowledgments

The research leading to the results presented in this article received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement number 227890 (the Galileo-Ready Advanced Mass Market Receiver–GRAMMAR–project). This research work has also been supported by the Academy of Finland and by the Tampere Doctoral Programme in Information Science and Engineering. Particular thanks are also addressed to Stephan Sand from the German Aerospace Center (DLR), Institute of Communications and Navigation, for his useful comments.

Elena Simona Lohan has been an adjunct professor in the Department of Communications Engineering at Tampere University of Technology (TUT) in Hervanta, Finland, since 2007. She obtained her Ph.D. degree in wireless communications from TUT. She also graduated with an M.Sc. in electrical engineering from “Politehnica” University of Bucharest, and with a diplôme d’études approfondies in econometrics from Ecole Polytechnique, Paris. Lohan is currently leading the research activities in signal processing for wireless communications in the Department of Communications Engineering at TUT.

Mohammad Zahidul H. Bhuiyan is a researcher in the Department of Communications Engineering at TUT. His main research areas are multipath mitigation and software receiver design for satellite-based positioning applications.

Heikki Hurskainen received an M.Sc. degree in electrical engineering and a doctoral degree in computing and electrical engineering from TUT in 2005 and 2009, respectively. Currently, Hurskainen is a senior research scientist in TUT’s Department of Computer Systems where he works on satellite navigation research projects.

FURTHER READING

• Galileo and Modernized GPS Signal Definitions and Policies
European GNSS (Galileo) Open Service Signal In Space Interface Control Document, Ref: OS SIS ICD, Issue 1.1, published by the European Union, Directorate General Enterprise and Industry, European Commission, Brussels, Belgium, September 2010.

“U.S., EU Announce Final Design for GPS-Galileo Civil Signal.” Announcement issued by the United States Mission to the European Union, Brussels, Belgium, July 26, 2007.

Navstar GPS Space Segment/User Segment L1C Interfaces, Rev. A, Interface Specification, IS-GPS-800A, prepared by Science Applications International Corporation, El Segundo, California for the Global Positioning System Wing, Systems Engineering and Integration, Los Angeles Air Force Base, California, June 2010.

• Binary Offset Carrier Modulation
“Low Complexity Unambiguous Acquisition Methods for BOC-modulated CDMA Signals” by E.S. Lohan, A. Burian, and M. Renfors in International Journal of Satellite Communications and Networking, Vol. 26, No. 6, 2008, pp. 503–522, doi: 10.1002/sat.922.

“Binary-Offset-Carrier Modulation Techniques with Applications in Satellite Navigation Systems” by E.S. Lohan, A. Lakhzouri, and M. Renfors in Wireless Communications and Mobile Computing, Vol. 7, No. 6, 2007, pp. 767–779, doi: 10.1002/wcm.407.

“Overview of the GPS M Code Signal” by B.C. Barker, J.W. Betz, J.E. Clark, J.T. Correia, J.T. Gillis, S. Lazar, K.A. Rehborn, and J.R. Straton, III, in Proceedings of 2000: Navigating into the New Millennium, the 2000 National Technical Meeting of The Institute of Navigation, Anaheim, California, January 26–28, 2000, pp. 542–549.

“The Offset Carrier Modulation for GPS Modernization” by J.W. Betz, in Proceedings of Vision 2010: Present and Future, the 1999 National Technical Meeting of The Institute of Navigation and 19th Biennial Guidance Test Symposium, San Diego, California, January 25–27, 1999, pp. 639-648.

• Multiplexed Binary Offset Carrier Modulation Implementations and Comparisons
“Future Wave: L1C Signal Performance and Receiver Design” by T.A. Stansell, K.W. Hudnut, and R.G. Keegan in GPS World, Vol. 22, No. 4, April 2011, pp. 30–36,41.

“Analytical Performance of CBOC-modulated Galileo E1 Signal Using Sine BOC(1,1) Receiver for Mass-market Applications” by E.S. Lohan, in Proceedings of PLANS 2010, IEEE/ION Position Location and Navigation Symposium, Indian Wells, California, May 4–6, 2010, pp. 245–253, doi: 10.1109/PLANS.2010.5507207.

“MBOC and BOC(1,1) Performance Comparison” by N. Hoult, L.E. Aguado, and P. Xia in The Journal of Navigation, Vol. 61, No. 4, October 2008, pp. 613–627, doi: 10.1017/S0373463308004918.

“The MBOC Modulation: A Final Touch for the Galileo Frequency and Signal Plan” by J.A. Avila-Rodriguez, G.W. Hein, S. Wallner, J.L. Issler, L. Ries, L. Lestarquit, A. De Latour, J. Godet, F. Bastide, T. Pratt, and J. Owen in Inside GNSS, Vol. 2, No. 6, Se
ptember-October 2007, pp. 43–58.

“Two for One: Tracking Galileo CBOC Signal with TMBOC” by O. Julien, C. Macabiau, J.L. Issler, and L. Ries in Inside GNSS, Vol. 2, No. 3, Spring 2007, pp. 50–57.

“MBOC: The New Optimized Spreading Modulation Recommended for Galileo L1 OS and GPS L1C” by G.W. Hein, J.A. Avila-Rodriguez, S. Wallner, J.W. Betz, C.J. Hegarty, J.J. Rushanan, A.L. Kraay, A.R. Pratt, S. Lenahan, J. Owen, J.L. Issler, and T.A. Stansell in Inside GNSS, Vol. 1, No. 4, May-June 2006, pp. 57–65.

• Gabor Bandwidth and Cramér-Rao Bound
Spread Spectrum Systems for GNSS and Wireless Communications by J.K. Holmes, published by Artech House, Inc., Norwood, Massachusetts, 2007.

“Multipath Mitigation: How Good Can It Get with the New Signals?” by L.R. Weill in GPS World, Vol. 14, No. 6, June 2003, pp. 106–113.

“A Family of Split Spectrum GPS Civil Signals” by J.J. Spilker, Jr., E.H. Martin, and B.W. Parkinson, in Proceedings of ION GPS-98, the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, September 15–18, 1998, pp. 1905–1914.

• Narrow Early-Minus-Late Correlation
“Extended Theory of Early-Late Code Tracking for a Bandlimited GPS Receiver” by J.W. Betz and K.R. Kolodziejski in Navigation: Journal of the Institute of Navigation, Vol. 47, No. 3, 2000, pp. 211–226.

June 1, 2011
Innovation: Doppler-Aided Positioning
Improving Single-Frequency RTK in the Urban Enviornment

By Mojtaba Bahrami and Marek Ziebart

A look at how Doppler measurements can be used to smooth noisy code-based pseudoranges to improve the precision of autonomous positioning as well as to improve the availability of single-frequency real-time kinematic positioning, especially in urban environments.

INNOVATION INSIGHTS by Richard Langley

WHAT DO A GPS RECEIVER, a policeman’s speed gun, a weather radar, and some medical diagnostic equipment have in common? Give up? They all make use of the Doppler effect. First proposed in 1842 by the Austrian mathematician and physicist, Christian Doppler, it is the change in the perceived frequency of a wave when the transmitter and the receiver are in relative motion.

Doppler introduced the concept in an attempt to explain the shift in the color of light from certain binary stars. Three years later, the effect was tested for sound waves by the Dutch scientist Christophorus Buys Ballot. We have all heard the Doppler shift of a train whistle or a siren with their descending tones as the train or emergency vehicle passes us. Doctors use Doppler sonography — also known as Doppler ultrasound — to provide information about the flow of blood and the movement of inner areas of the body with the moving reflectors changing the received ultrasound frequencies. Similarly, some speed guns use the Doppler effect to measure the speed of vehicles or baseballs and Doppler weather radar measures the relative velocity of particles in the air.

The beginning of the space age heralded a new application of the Doppler effect. By measuring the shift in the received frequency of the radio beacon signals transmitted by Sputnik I from a known location, scientists were able to determine the orbit of the satellite. And shortly thereafter, they determined that if the orbit of a satellite was known, then the position of a receiver could be determined from the shift. That realization led to the development of the United States Navy Navigation Satellite System, commonly known as Transit, with the first satellite being launched in 1961. Initially classified, the system was made available to civilians in 1967 and was widely used for navigation and precise positioning until it was shut down in 1996. The Soviet Union developed a similar system called Tsikada and a special military version called Parus. These systems are also assumed to be no longer in use — at least for navigation.

GPS and other global navigation satellite systems use the Doppler shift of the received carrier frequencies to determine the velocity of a moving receiver. Doppler-derived velocity is far more accurate than that obtained by simply differencing two position estimates. But GPS Doppler measurements can be used in other ways, too. In this month’s column, we look at how Doppler measurements can be used to smooth noisy code-based pseudoranges to improve the precision of autonomous positioning as well as to improve the availability of single-frequency real-time kinematic positioning, especially in urban environments.

Correction and Further Details

The first experimental Transit satellite was launched in 1959. A brief summary of subsequent launches follows:
- Transit 1A launched 17 September 1959 failed to reach orbit
- Transit 1B launched 13 April 1960 successfully
- Transit 2A launched 22 June 1960 successfully
- Transit 3A launched 30 November 1960 failed to reach orbit
- Transit 3B launched 22 February 1961 failed to deploy in correct orbit
- Transit 4A launched 29 June 1961 successfully
- Transit 4B launched 15 November 1961 successfully
- Transits 4A and 4B used the 150/400 MHz pair of frequencies and provided geodetically useful results.
- A series of Transit prototype and research satellites was launched between 1962 and 1964 with the first fully operational satellite, Transit 5-BN-2, launched on 5 December 1963.
- The first operational or Oscar-class Transit satellite, NNS O-1, was launched on 6 October 1964.
- The last pair of Transit satellites, NNS O-25 and O-31, was launched on 25 August 1988.
“Innovation” is a regular column that features discussions about recent advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering at the University of New Brunswick, who welcomes your comments and topic ideas. To contact him, email lang @ unb.ca.

Real-time kinematic (RTK) techniques enable centimeter-level, relative positioning. The technology requires expensive, dedicated, dual-frequency, geodetic-quality receivers. However, myriad industrial and engineering applications would benefit from small-size, cost-effective, single-frequency, low-power, and high-accuracy RTK satellite positioning. Can such a sensor be developed and will it deliver? If feasible, such an instrument would find many applications within urban environments — but here the barriers to success are higher. In this article, we show how some of the problems can be overcome.

Single-Frequency RTK

Low-cost single-frequency (L1) GPS receivers have attained mass-market status in the consumer industry. Notwithstanding current levels of maturity in GPS hardware and algorithms, these receivers still suffer from large positioning errors. Any positioning accuracy improvement for mass-market receivers is of great practical importance, especially for many applications demanding small size, cost-effectiveness, low power consumption, and highly accurate GPS positioning and navigation. Examples include mobile mapping technology; machine control; agriculture fertilization and yield monitoring; forestry; utility services; intelligent transportation systems; civil engineering projects; unmanned aerial vehicles; automated continuous monitoring of landslides, avalanches, ground subsidence, and river level; and monitoring deformation of built structures. Moreover, today an ever-increasing number of smartphones and handsets come equipped with a GPS receiver. In those devices, the increasing sophistication of end-user applications and refinement of map databases are continually tightening the accuracy requirements for GPS positioning.

For single-frequency users, the RTK method does appear to offer the promise of highly precise position estimates for stationary and moving receivers and can even be considered a candidate for integration within mobile handhelds. Moreover, the RTK approach is attractive because the potential of the existing national infrastructures such as Great Britain’s Ordnance Survey National GNSS Network-RTK (OSNet) infrastructure, as well as enabling technologies such as the Internet and the cellular networks, can be exploited to deliver RTK corrections and provide high-precision positioning and navigation.

The basic premise of relative (differential) positioning techniques such as RTK is that many of the sources of GNSS measurement errors including the frequency-dependent error (the ionospheric delay) are spatially correlated. By performing relative positioning between receivers, the correlated measurement errors are completely cancelled or greatly reduced, resulting in a significant increase in the positioning accuracy and precision.

Single-Frequency Challenges. Although RTK positioning is a well-established and routine technology, its effective implementation for low-cost, single-frequency L1 receivers poses many serious challenges, especially in difficult and degraded signal environments for GNSS such as urban canyons. The most serious challenge is the use of only the L1 frequency for carrier-phase integer ambiguity resolution and validation. Unfortunately, users with single-frequency capability do not have frequency diversity and many options in forming useful functions and combinations for pseudorange and carrier-phase observables. Moreover, observations from a single-frequency, low-cost receiver are typically “biased” due to the high level of multipath and/or receiver signal-tracking anomalies and also the low-cost patch antenna design that is typically used. In addition, in those receivers, measurements are typically contaminated with high levels of noise due to the low-cost hardware design compared to the high-end receivers. This makes the reliable fixing of the phase ambiguities to their correct integer values, for single-frequency users, a non-trivial problem. As a consequence, the reliability of single-frequency observations to resolve ambiguities on the fly in an operational environ
ment is relatively low compared to the use of dual-frequency observations from geodetic-quality receivers. Improving performance will be difficult, unless high-level noise and multipath can be dealt with effectively or unless ambiguity resolution techniques can be devised that are more robust and are less sensitive to the presence of biases and/or high levels of noise in the observations.

Traditionally, single-frequency RTK positioning requires long uninterrupted initialization times to obtain reliable results, and hence have a time-to-fix ambiguities constraint. Times of 10 to 25 minutes are common. Observations made at tens of continuous epochs are used to determine reliable estimates of the integer phase ambiguities. In addition, these continuous epochs must be free from cycle slips, loss of lock, and interruptions to the carrier-phase signals for enough satellites in view during the ambiguity fixing procedure. Otherwise, the ambiguity resolution will fail to fix the phase ambiguities to correct integer values. To overcome these drawbacks and be able to determine the integer phase ambiguities and thus the precise relative positions, observations made at only one epoch (single-epoch) can be used in resolving the integer phase ambiguities. This allows instantaneous RTK positioning and navigation for single-frequency users such that the problem of cycle slips, discontinuities, and loss of lock is eliminated. However, for single-frequency users, the fixing of the phase ambiguities to their correct integer values using a single epoch of observations is a non-trivial problem; indeed, it is considered the most challenging scenario for ambiguity resolution at the present time.

Instantaneous RTK positioning relies fundamentally upon the inversion of both carrier-phase measurements and code measurements (pseudoranges) and successful instantaneous ambiguity resolution. However, in this approach, the probability of fixing ambiguities to correct integer values is dominated by the relatively imprecise pseudorange measurements. This is more severe in urban areas and difficult environments where the level of noise and multipath on pseudoranges is high. This problem may be overcome partially by carrier smoothing of pseudoranges in the range/measurement domain using, for example, the Hatch filter. While carrier-phase tracking is continuous and free from cycle slips, the carrier smoothing of pseudoranges with an optimal smoothing filter window-width can effectively suppress receiver noise and short-term multipath noise on pseudoranges. However, the effectiveness of the conventional range-domain carrier-smoothing filters is limited in urban areas and difficult GNSS environments because carrier-phase measurements deteriorate easily and substantially due to blockages and foliage and suffer from phase discontinuities, cycle-slip contamination, and other measurement anomalies. This is illustrated in Figure 1. The figure shows that in a kinematic urban environment, frequent carrier-phase outages and anomalies occur, which cause frequent resets of the carrier-smoothing filter and hence carrier smoothing of pseudoranges suffers in robustness and effective continuous smoothing.

Figure 1. Satellite tracking and carrier-phase anomaly summary during the observation time-span. These data were collected in a dense urban environment in both static and kinematic mode. The superimposed red-points show epochs where carrier-phase observables are either missing or contaminated with cycle slips, loss of locks, and/or other measurement anomalies.

Doppler Frequency Shift. While carrier-phase tracking can be discontinuous in the presence of continuous pseudoranges, a receiver generates continuous Doppler-frequency-shift measurements. The Doppler measurements are immune to cycle slips. Moreover, the precision of the Doppler measurements is better than the precision of pseudoranges because the absolute multipath error of the Doppler observable is only a few centimeters. Thus, devising methods that utilize the precision of raw Doppler measurements to reduce the receiver noise and high-frequency multipath on pseudoranges may prove valuable especially in GNSS-challenged environments. Figure 2 shows an example of the availability and the precision of the receiver-generated Doppler measurements alongside the delta-range values derived from the C/A-code pseudoranges and from the L1 carrier-phase measurements. This figure also shows that frequent carrier-phase outages and anomalies occur while for every C/A-code pseudorange measurement there is a corresponding Doppler measurement available.

Figure 2. Plots of C/A-code-pseudorange-derived delta-ranges (top), L1 carrier-phase-derived delta-ranges (middle), and L1 raw receiver-generated Doppler shifts that are transformed into delta-ranges for the satellite PRN G18 during the observation time-span when it was tracked by the receiver (bottom).

Smoothing. A rich body of literature has been published exploring aspects of carrier smoothing of pseudoranges. One factor that has not received sufficient study in the literature is utilization of Doppler measurements to smooth pseudoranges and to investigate the influence of improved pseudorange accuracy on both positioning and the integer-ambiguity resolution. Utilizing the Doppler measurements to smooth pseudoranges could be a good example of an algorithm that maximally utilizes the information redundancy and diversity provided by a GPS/GNSS receiver to improve positioning accuracy. Moreover, utilizing the Doppler measurements does not require any hardware modifications to the receiver. In fact, receivers measure Doppler frequency shifts all the time as a by-product of satellite tracking.

GNSS Doppler Measurement Overview

The Doppler effect is the apparent change in the transmission frequency of the received signal and is experienced whenever there is any relative motion between the emitter and receiver of wave signals. Theoretically, the observed Doppler frequency shift, under Einstein’s Special Theory of Relativity, is approximately equal to the difference between the received and transmitted signal frequencies, which is approximately proportional to the receiver-satellite topocentric range rate.

Beat Frequency. However, the transmitted frequency is replicated locally in a GNSS receiver. Therefore, strictly speaking, the difference of the received frequency and the receiver locally generated replica of the transmitted frequency is the Doppler frequency shift that is also termed the beat frequency. If the receiver oscillator frequency is the same as the satellite oscillator frequency, the beat frequency represents the Doppler frequency shift due to the relative, line-of-sight motion between the satellite and the receiver. However, the receiver internal oscillator is far from being perfect and therefore, the receiver Doppler measurement output is the apparent Doppler frequency shift (that includes local oscillator effects). The Doppler frequency shift is also subject to satellite-oscillator frequency bias and other disturbing effects such as atmospheric effects on the signal propagation.

To estimate the range rate, a receiver typically forms an average of the delta-range by simply integrating the Doppler over a very short period of time (for example, 0.1 second) and then dividing it by the duration of the integration interval. Since the integration of frequency over time gives the phase of the signal over that time interval, the procedure continuously forms the carrier-phase observable that is the integrated Doppler over time. Therefore, Doppler frequency shift can also be estimated by time differencing carrier-phase measurements. The carrier-phase-derived Doppler is com
puted over a longer time span, leading to smoother Doppler measurements, whereas direct loop filter output is an instantaneous measure produced over a short time interval.

Doppler frequency shift is routinely used to determine the satellite or user velocity vector. Apart from velocity determination, it is worth mentioning that Doppler frequency shifts are also exploited for coarse GPS positioning. Moreover, the user velocity vector obtained from the raw Doppler frequency shift can be and has been applied by a number of researchers to instantaneous RTK applications to constrain the float solution and hence improve the integer-ambiguity-resolution success rates in kinematic surveying. In this article, a simple combination procedure of the noisy pseudorange measurements and the receiver-generated Doppler measurements is suggested and its benefits are examined.

Doppler-Smoothing Algorithm Description

Motivated both by the continual availability and the centimeter-level precision of receiver-generated (raw) Doppler measurements, even in urban canyons, a method has been introduced by the authors that utilizes the precision of raw Doppler measurements to reduce the receiver noise and high-frequency multipath on code pseudoranges. For more detail on the Doppler-smoothing technique, see Further Reading. The objective is to smooth the pseudoranges and push the accuracy of the code-based or both code- and carrier-based positioning applications in GNSS-challenged environments.

Previous work on Doppler-aided velocity/position algorithms is mainly in the position domain. In those approaches, the improvement in the quality of positioning is gained mainly by integrating the kinematic velocities and accelerations derived from the Doppler measurement in a loosely coupled extended Kalman filter or its variations such as the complementary Kalman filter. Essentially, these techniques utilize the well-known ability of the Kalman filter to use independent velocity estimates to reduce the noise of positioning solutions and improve positioning accuracy. The main difference among these position-domain filters is that different receiver dynamic models are used.

The proposed method combines centimeter-level precision receiver-generated Doppler measurements with pseudorange measurements in a combined pseudorange measurement that retains the significant information content of each.

Two-Stage Process. The proposed Doppler-smoothing process has two stages: (1) the prediction or initialization stage and (2) the filtering stage. In the prediction stage, a new estimated smoothed value of the pseudorange measurement for the Doppler-smoothing starting epoch is obtained. In this stage, for a fixed number of epochs, a set of estimated pseudoranges for the starting epoch is obtained from the subsequent pseudorange and Doppler measurements. The estimated pseudoranges are then averaged to obtain a good estimated starting point for the smoothing process. The number of epochs used in the prediction stage is the averaging window-width or Doppler-smoothing-filter length. In the filtering stage, the smoothed pseudorange profile is constructed using the estimated smoothed starting pseudorange and the integrated Doppler measurements over time. The Doppler-smoothing procedures outlined here can be performed successively epoch-by-epoch (that is, in a moving filter), where the estimated initial pseudorange (the averaged pseudorange) is updated from epoch to epoch. Alternatively, an efficient and elegant implementation of the measurement-domain Doppler-smoothing method is in terms of a Kalman filter, where it can run as a continuous process in the receiver from the first epoch (or in post-processing software, but then without the real-time advantage). This filter allows real-time operation of the Doppler-smoothing approach.

In the experiments described in this article, a short filter window-width is used. The larger the window width used in the averaging filter process, the more precise the averaged pseudorange becomes. However, this filter is also susceptible to the ionospheric divergence phenomenon because of the opposite signs of the ionospheric contribution in the pseudorange and Doppler observables. Therefore, the ionospheric divergence effect between pseudoranges and Doppler observables increases with averaging window-width and the introduced bias in the averaged pseudoranges become apparent for longer filter lengths.

Using the propagation of variance law, it can be shown that the precision of the delta-range calculated with the integrated Doppler measurements over time depends on both the Doppler-measurement epoch interval and the precision of the Doppler measurements, assuming that noise/errors on the measurements are uncorrelated.

Experimental Results

To validate the improvement in the performance and availability of single-frequency instantaneous RTK in urban areas, the proposed Doppler-aided instantaneous RTK technique has been investigated using actual GPS data collected in both static and kinematic pedestrian trials in central London. In this article, we only focus on the static results and the kinematic trial results are omitted. It is remarked, however, that the data collected in the static mode were post-processed in an epoch-by-epoch approach to simulate RTK processing.

In the static testing, GPS test data were collected with a measurement rate of 1 Hz. At the rover station, a consumer-grade receiver with a patch antenna was used. This is a single-frequency 16-channel receiver that, in addition to the C/A-code pseudoranges, is capable of logging carrier-phase measurements and raw Doppler measurements. Reference station data were obtained from the Ordnance Survey continuously operating GNSS network. Three nearby reference stations were selected that give different baseline lengths: Amersham (AMER) ≈ 38.3 kilometers away, Teddington (TEDD) ≈ 20.8 kilometers away, and Stratford (STRA) ≈ 7.1 kilometers away. In addition, a virtual reference station (VRS) was also generated in the vicinity (60 meters away) of the rover receiver.

Doppler-Smoothing. Before we present the improvement in the performance of instantaneous RTK positioning, the effect of the Doppler-smoothing of the pseudoranges in the measurement domain and comparison with carrier-phase smoothing of pseudoranges is given. To do this, we computed the C/A-code measurement errors or observed range deviations (the differences between the expected and measured pseudoranges) in the static mode (with surveyed known coordinates) using raw, Doppler-smoothed and carrier-smoothed pseudoranges. FIGURE 3a illustrates the effect of 100-second Hatch-filter carrier smoothing and FIGURE 3b shows a 100-second Doppler-smoothing of the pseudoranges for satellite PRN G28 (RINEX satellite designator) with medium-to-high elevation angle. The raw observed pseudorange deviations (in blue) are also given as reference. The quasi-sinusoidal oscillations are characteristic of multipath. Comparing the Doppler-smoothing in Figure 3b to the Hatch carrier-smoothing in Figure 3a, it can be seen that Doppler-smoothing of pseudoranges offers a modest improvement and is more robust and effective than that of the traditional Hatch filter in difficult environments.

Figure 3. Smoothed pseudorange errors (observed range deviations) using the traditional Hatch carrier-smoothing filter. Smoothing filter length in the experiments for both filters was set to 100 seconds. Satellite PRN G28 was chosen to represent a satellite at medium-to-high elevation angle.

Figure 3. Smoothed pseudorange errors (observed range deviations) using the Doppler-smoothing filter. Smoothing filter length in the experiments for both filters was set to 100 seconds. Satellite PRN G28 was chosen to represent a satellite at medium-to-high elevation angle.

Figure 4a illustrates carrier-phase Hatch-filter smoothing for low-elevation angle satellite PRN G18. In this figure, the Hatch carrier-smoothing filter reset is indicated. It can be seen that due to the frequent carrier-phase discontinuities and cycle slips, the smoothing has to be reset and restarted from the beginning and hardly reaches its full potential. In contrast, Doppler smoothing for PRN G18 shown in FIGURE 4b had few filter resets and managed effectively to smooth the very noisy pseudorange in some sections of the data.

Figure 4. Smoothed pseudorange errors (observed range deviations) and filter resets and filter length (window width) using the traditional Hatch carrier-smoothing filter. Smoothing filter length in the experiments for both filters was set to 100 seconds. Satellite PRN G18 was chosen to represent a satellite at low elevation angle as it rises from 10 to 30 degrees.

Figure 4. Smoothed pseudorange errors (observed range deviations) and filter resets and filter length (window width) using the Doppler-smoothing. Smoothing filter length in the experiments for both filters was set to 100 seconds. Satellite PRN G18 was chosen to represent a satellite at low elevation angle as it rises from 10 to 30 degrees.

Considering RTK in this analysis, we can demonstrate the increase in the success rate of the Doppler-aided integer ambiguity resolution (and hence the RTK availability) by comparison of the obtained integer ambiguity vectors from the conventional LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) ambiguity resolution method using Doppler-smoothed pseudoranges with those obtained without Doppler-aiding in post-processed mode. The performance of ambiguity resolution was evaluated based on the number of epochs where the ambiguity validation passed the discrimination/ratio test. The ambiguity validation ratio test was set to the fixed critical threshold of 2.5 in all the experiments. In addition to the ratio test, the fixed solutions obtained using the fixed integer ambiguity vectors that passed the ratio test were compared against the true position of the surveyed point to make sure that indeed the correct set of integer ambiguities were estimated.

The overall performance of the single-epoch single-frequency integer ambiguity resolution obtained by the conventional LAMBDA ambiguity resolution method without Doppler-aiding is shown in Figure 5 for baselines from 60 meters up to 38 kilometers in length. In comparison, the performance of the single-epoch single-frequency integer ambiguity resolution from the LAMBDA method using Doppler-smoothed pseudoranges are shown in Figure 6 for those baselines and they are compared with integer ambiguity resolution success rates of the conventional LAMBDA ambiguity resolution method without Doppler-aiding. Figure 6 shows that using Doppler-smoothed pseudoranges enhances the probability of identifying the correct set of integer ambiguities and hence increases the success rate of the integer ambiguity resolution process in instantaneous RTK, providing higher availability. This is more evident for shorter baselines. For long baselines, the residual of satellite-ephemeris error and atmospheric-delay residuals that do not cancel in double differencing potentially limits the effectiveness of the Doppler-smoothing approach. It is well understood that those residuals for long baselines strongly degrade the performance of ambiguity resolution. Relative kinematic positioning with single frequency mass-market receivers in urban areas using VRS has also shown improvement.

Figure 5. Single-epoch single-frequency integer ambiguity resolution success rate obtained by the conventional LAMBDA ambiguity resolution method without Doppler-aiding.

Figure 6. Plots of integer ambiguity resolution success rates: single-epoch single-frequency integer ambiguity resolution success rate obtained by the conventional LAMBDA ambiguity resolution method without Doppler-aiding (in blue) and using Doppler-smoothed pseudoranges (in green).

Conclusion

In urban areas, the proposed Doppler-smoothing technique is more robust and effective than traditional carrier smoothing of pseudoranges. Static and kinematic trials confirm this technique improves the accuracy of the pseudorange-based absolute and relative positioning in urban areas characteristically by the order of 40 to 50 percent.

Doppler-smoothed pseudoranges are then used to aid the integer ambiguity resolution process to enhance the probability of identifying the correct set of integer ambiguities. This approach shows modest improvement in the ambiguity resolution success rate in instantaneous RTK where the probability of fixing ambiguities to correct integer values is dominated by the relatively imprecise pseudorange measurements.

The importance of resolving the integer ambiguities correctly must be emphasized. Therefore, devising innovative and robust methods to maximize the success rate and hence reliability and availability of single-frequency, single-epoch integer ambiguity resolution in the presence of biased and noisy observations is of great practical importance especially in GNSS-challenged environments.

Acknowledgments

The study reported in this article was funded through a United Kingdom Engineering and Physical Sciences Research Council Engineering Doctorate studentship in collaboration with the Ordnance Survey. M. Bahrami would like to thank his industrial supervisor Chris Phillips from the Ordnance Survey for his continuous encouragement and support. Professor Paul Cross is acknowledged for his valuable comments. The Ordnance Survey is acknowledged for sponsoring the project and providing detailed GIS data.

Manufacturer

The data for the trial discussed in this article were obtained from a u-blox AG AEK-4T receiver with a u-blox ANN-MS-0-005 patch antenna.

Mojtaba Bahrami is a research fellow in the Space Geodesy and Navigation Laboratory (SGNL) at University College London (UCL). He holds an engineering doctorate in space geodesy and navigation from UCL.

Marek Ziebart is a professor of space geodesy at UCL. He is the director of SGNL and vice dean for research in the Faculty of Engineering Sciences at UCL.

FURTHER READING

• Carrier Smoothing of Pseudoranges

“Optimal Hatch Filter with an Adaptive Smoothing Window Width” by B. Park, K. Sohn, and C. Kee in Journal of Navigation, Vol. 61, 2008, pp. 435–454, doi: 10.1017/S0373463308004694.

“Optimal Recursive Least-Squares Filtering of GPS Pseudorange Measurements” by A. Q. Le and P. J. G. Teunissen in VI Hotine-Marussi Symposium on Theoretical and Computational Geodesy, Wuhan, China, May 29 – June 2, 2006, Vol. 132 of the International Association of Geodesy Symposia, Springer-Verlag, Berlin and Heidelberg, 2008, Part II, pp. 166–172, doi: 10.1007/978-3-540-74584-6_26.

“The Synergism of GPS Code and Carrier Measurements” by R. Hatch in Proceedings of the 3rdInternational Geodetic Symposium on Satellite Doppler Positioning, Las Cruces, New Mexico, February 8-12, 1982, Vol. 2, pp. 1213–1231.

• Combining Pseudoranges and Carrier-phase Measurements in the Position Domain

“Position Domain Filtering and Range Domain Filtering for Carrier-smoothed-code DGNSS: An Analytical Comparison” by H. Lee, C. Rizos, and G.-I. Jee in IEE Proceedings Radar, Sonar and Navigation, Vol. 152, No. 4, August 2005, pp. 271–276, doi:10.1049/ip-rsn:20059008.

“Complementary Kalman Filter for Smoothing GPS Position with GPS Velocity” by H. Leppakoski, J. Syrjarinne, and J. Takala in Proceedings of ION GPS/GNSS 2003, the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 9–
12, 2003, pp. 1201–1210.

“Precise Platform Positioning with a Single GPS Receiver” by S. B. Bisnath, T. Beran, and R. B. Langley in GPS World, Vol. 13, No. 4, April 2002, pp. 42–49.

“GPS Navigation: Combining Pseudorange with Continuous Carrier Phase Using a Kalman Filter” by P. Y. C. Hwang and R. G. Brown in Navigation, Journal of The Institute of Navigation, Vol. 37, No. 2, 1990, pp. 181–196.

• Doppler-derived Velocity Information and RTK Positioning

“Advantage of Velocity Measurements on Instantaneous RTK Positioning” by N. Kubo in GPS Solutions, Vol. 13, No. 4, 2009, pp. 271–280, doi: 10.1007/s10291-009-0120-9.

• Doppler Smoothing of Pseudoranges and RTK Positioning

Doppler-Aided Single-Frequency Real-Time Kinematic Satellite Positioning in the Urban Environment by M. Bahrami, Ph.D. dissertation, Space Geodesy and Navigation Laboratory, University College London, U.K., 2011.

“Instantaneous Doppler-Aided RTK Positioning with Single Frequency Receivers” by M. Bahrami and M. Ziebart in Proceedings of PLANS 2010, IEEE/ION Position Location and Navigation Symposium, Indian Wells, California, May 4–6, 2010, pp. 70–78, doi: 10.1109/PLANS.2010.5507202.

“Getting Back on the Sidewalk: Doppler-Aided Autonomous Positioning with Single-Frequency Mass Market Receivers in Urban Areas” by M. Bahrami in Proceedings of ION GNSS 2009, the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, 22–25 September 2009, pp. 1716–1725.

• Integer Ambiguity Resolution

“GPS Ambiguity Resolution and Validation: Methodologies, Trends and Issues” by D. Kim and R. B. Langley in Proceedings of the 7th GNSS Workshop – International Symposium on GPS/GNSS, Seoul, Korea, 30 November – 2 December 2000, Tutorial/Domestic Session, pp. 213–221.

The LAMBDA Method for Integer Ambiguity Estimation: Implementation Aspects by P. de Jong and C. Tiberius. Publications of the Delft Geodetic Computing Centre, No. 12, Delft University of Technology, Delft, The Netherlands, August 1996.

“A New Way to Fix Carrier-phase Ambiguities” by P.J.G. Teunissen, P.J. de Jonge, and C.C.J.M. Tiberius in GPS World, Vol. 6, No. 4, April 1995, pp. 58–61.

“The Least-Squares Ambiguity Decorrelation Adjustment: a Method for Fast GPS Integer Ambiguity Estimation” by P.J.G. Teunissen in Journal of Geodesy, Vol. 70, No. 1–2, 1995, pp. 65–82, doi: 10.1007/BF00863419.
May 1, 2011
Innovation: GLONASS

Developing Strategies for the Future

By Yuri Urlichich, Valeriy Subbotin, Grigory Stupak, Vyacheslav Dvorkin, Alexander Povalyaev, and Sergey Karutin

A team of authors from Russian Space Systems, a key developer of navigation and geospatial technologies in the Russian aerospace industry, describes the new L3 CDMA signal to be broadcast by GLONASS-K satellites and the progress to date in developing the SDCM augmentation system.

INNOVATION INSIGHTS by Richard Langley

IT’S NO LONGER JUST A GPS WORLD. Russia’s GLONASS, or Global′naya Navigatsionaya Sputnikova Sistema, will soon have a full complement of satellites in orbit providing positioning, navigation, and timing worldwide.

The Soviet Union began development of GLONASS in 1976 just a few years after work started on GPS. The first satellite was launched in 1982 and a fully populated constellation of 24 functioning satellites was achieved in early 1996. However, due to economic difficulties following the dismantling of the Soviet Union, by 2002 the constellation had dropped to as few as seven satellites. But the Russian economy improved, and restoration of GLONASS was given high priority by the Russian government. The satellite constellation was gradually rejuvenated using primarily a new modernized spacecraft, GLONASS-M. The new design offered many improvements, including better onboard electronics, a longer lifetime, an L2 civil signal, and an improved navigation message. The GLONASS-M spacecraft still used a pressurized, hermetically sealed cylinder for the electronics, as had the earlier versions. Today, 26 functional GLONASS-M satellites are on orbit, 22 of them in service and providing usable signals, with four more having reserve status. A full constellation of 24 satellites should be available later this year with launches of several GLONASS-M satellites and the latest variant, the GLONASS-K satellite.

GLONASS-K satellites are markedly different from their predecessors. They are lighter, use an unpressurized housing (similar to that of GPS satellites), have improved clock stability, and a longer, 10-year design life. They also include, for the first time, code-division-multiple-access (CDMA) signals accompanying the legacy frequency-division-multiple-access signals. There will be two versions: GLONASS-K1 will transmit a CDMA signal on a new L3 frequency, and GLONASS-K2, in addition, will feature CDMA signals on L1 and L2 frequencies. The first GLONASS-K1 satellite was launched on February 26 and is now undergoing tests.

GLONASS is being further improved with a satellite-based augmentation system. Called the System for Differential Correction and Monitoring or SDCM, it will use a ground network of monitoring stations and Luch geostationary communication satellites to transmit correction and integrity data using the GPS L1 frequency. The first of these satellites, Luch-5A, will be launched this year.

In this month’s column, a team of authors from Russian Space Systems, a key developer of navigation and geospatial technologies in the Russian aerospace industry, describes the new L3 CDMA signal to be broadcast by GLONASS-K satellites and the progress to date in developing the SDCM augmentation system.

The Russian Global Navigation Satellite System (GLONASS) is once again approaching full operation. As of March, 22 satellites are in service, providing nearly continuous global coverage. These satellites are modernized GLONASS or GLONASS-M satellites, transmitting the legacy frequency-domain-multiple-access (FDMA) navigation signals in the L1 and L2 frequency bands.

The structure of the navigation signals transmitted by the satellites determines the accuracy of the pseudorange measurements, which, in turn, affects a user’s position accuracy. Evolution of the GLONASS navigation signals is a top priority for the overall system development. A new version of the satellites, GLONASS-K, will broadcast a code-division-multiple-access (CDMA) signal in the L3 band for the first time in the system’s history. In addition to the change in signal parameters, new navigation information will be transmitted to users through this signal. Further GLONASS navigation signal development assumes that a new CDMA civil signal will also become available in the L1 and L2 bands.

The evolution of GNSS augmentation is also an important task in the development of satellite navigation in Russia. The Russian satellite-based augmentation system (SBAS), the System for Differential Correction and Monitoring (SDCM), is entering into the deployment phase and that is why some aspects of interoperability and compatibility with other SBASs become important. Taking into account the fact that satellite channels are the most efficient and universal tool to supply GNSS users with precise ephemeris and clock parameters and the positive experience of regional systems (such as the Quasi-Zenith Satellite System), we can see the potential for the development of a precise positioning service.

In this article, we will discuss plans for modernizing GLONASS, covering both the new signals and the augmentation service.

Navigation Signals

The main task for GLONASS development is an extension of the ensemble of navigation signals. This extension means that new CDMA signals in the L1, L2, and L3 bands will be added to the existing FDMA signals. The GLONASS satellites will keep broadcasting the legacy signals until the last receiver stops working.

The first phase in the implementation of CDMA technology on GLONASS-K satellites includes a new signal in the L3 band on a carrier frequency of 1202.025 MHz. The first GLONASS-K satellite was launched on February 26, 2011, and is undergoing tests. The ranging code chipping rate for the CDMA signal is 10.23 megachips per second with a period of 1 milliseconds. It is modulated onto the carrier using quadrature phase-shift keying (QPSK), with an in-phase data channel and a quadrature pilot channel. The signal spectrum is shown in Figure 1.

Figure 1. L3 CDMA signal spectrum (frequencies in MHz).

A block diagram of how the GLONASS L3 signal is formed is presented in Figure 2. The set of possible ranging codes consists of 31 truncated Kasami sequences. (Kasami sequences are binary sequences of length 2^m – 1 where m is an even integer. These sequences have good cross-correlation values approaching a theoretical lower bound. The Gold codes used in GPS are a special case of Kasami codes.) The full length of these sequences is 2¹⁴ – 1 = 16,383 symbols, but the ranging code is truncated to a length of N = 10,230 with a period of 1 milliseconds and with the following initial state (IS) in the generator (G) registers: G2 – IS = 00110100111000, G1 IS = n, G3 IS = n + 32. It these equations, n is the system number of the satellite in the orbit constellation. For these codes, inter-channel jamming is about –40 dB.

Figure 2. Formulation of L3 CDMA signal.

The navigation message symbols (NSs) are transmitted at a rate of 100 bits per second with half-rate convolution coding (CC) with a memory of 6. This means that the duration of an NS is 10 milliseconds and the duration of the CC symbols is 5 milliseconds. The CC switch (see Figure 2) should be in the lower position for the first half of each NS.

The pseudorandom sequence of the L3 data signal, PRS-D, is modulo-2 summed with a periodic 5-bit Barker code (BC = 00010) b
efore phase modulation. Barker code symbols have a duration of 1 millisecond and are synchronized with the pseudorandom code symbols. The pseudorandom sequence of the L3 pilot signal, PRS-P, is modulo-2 summed with a 10-bit Neuman-Hoffman code (NH = 0000110101). The Neuman-Hofman code symbols have a duration of 1 millisecond and are synchronized with the information symbols. The Barker and Neuman-Hoffman codes are used for CC synchronization in the L3 user’s receiver (see Further Reading for background details).

The navigation message superframe (2 minutes long) will consist of 8 navigation frames (NFs) for 24 regular satellites in the GLONASS first modernization stage and 10 NFs (lasting 2.5 minutes) for 30 satellites in the future. Each NF (15 seconds long) includes 5 strings (3 seconds each). Every NF has a full set of ephemerides for the current satellite and part of the system almanac for three satellites. The full system almanac is broadcast in one superframe. A time marker is located at the beginning of a string and given as a number of a string within the current day in the satellite time scale.

The GLONASS system and the satellites’ time scales are coordinated with the Russian national time scale, UTC(SU), which is periodically adjusted for a leap seconds. A special flag, A, is used in each frame to inform users about an anomalous fifth string of this frame. If А = 0, the fifth string will be normal with a 3-second duration; if А = 1, the fifth string will be either 2 seconds or 4 seconds. The correction value (+1 second or –1 second) is also transmitted in the special NF flag, KP. If KP = 11, the fifth string will be shorter due to a correction of –1 second; if KP = 01, it will be longer due to a correction of +1 second. A user should not use the short string. A string is lengthened by adding “0” to the normal string. This algorithm is implemented with the objective of simplifying the time scale correction process in user equipment.

Modulation and Multiplexing. There are intensive studies being carried out for developing new CDMA signals in the L1 and L2 bands in addition to the L3 signal described above. The main difficulties to be overcome in these studies are to ensure a low-power spectral density (PSD) of –238 dBW/m²/Hz in the 1610.6–1613.8 MHz radio astronomy band and the multiplexing of more than two signal components, providing a constant signal level.

The first task could be solved by using a modulation with a low PSD level in the radio astronomy band, such as a binary offset carrier (BOC) modulation with a subcarrier frequency of 5.115 MHz and a spreading code chipping rate of 2.5575 megachips per second (BOC(5, 2.5)) as shown in Figure 3.

Figure 3. BOC(5, 2.5) signal spectrum (frequencies in MHz).

There are two well-known methods of signal multiplexing — time multiplexing and amplitude equalizing. The time multiplexing technique is used for the GPS L2C signal, while the amplitude equalizing method is used for the composite BOC (CBOC) signals in the Galileo E1/L1 band and the alternative BOC (AltBOC) signals in E5a-E5b bands. This method has the disadvantage of about 10–16 percent loss of the transmitter power on the equalization. However, it has an advantage: simple user equipment architecture and, more importantly, the possibility of step-wise implementation of the multicomponent signal. The step-wise approach is compatible with older receivers. New user equipment will be able to track both old and new signal components, as well as a combined signal consisting of old and new components. Vector and phase diagrams for two-, four-, and six-component AltBOC signals are shown in Figure 4. Even with six components, losses are lower than about 16 percent, but it is possible to avoid any loss using time multiplexing. That is why the final decision about future GLONASS signals has not yet been made.

Figure 4. Vector and phase relationships for AltBOC signals with (a) 2-, (b) 4-, and (c) 6-components, with losses of 0, and about 15 and 16 percent respectively.

There have been extensive studies on the definition of the ensemble of code sequences with a minimum level of interchannel jamming. It was found that the jamming level for random shifts does not depend on the code type, but rather depends on the number of symbols, N, in a period. Cross-correlation functions for Kasami 4095 and Weil 10230 codes are shown in Figures 5 and 6. (Kasami codes, as previously mentioned, are being used for the GLONASS L3 CDMA signal. Weil codes are prime length sequences constructed from the well-known Legendre sequences and are used for the GPS L1C signal.) For comparison, we show cross-correlation functions for random codes with equal lengths on the same figures. It is obvious that the histograms of predefined and random codes are close to being equal. Sidelobe dispersion levels are lower than 0.1 dB.

The results obtained from the studies allow us to draw a conclusion about the invariance of the stochastic characteristics of inter-channel interference using a code structure with a fixed length of N symbols. That is why it is possible to choose an ensemble of binary code sequences on the basis of generation simplicity.

Figure 5. Kasami and random code cross-correlation functions (4,095 symbols).

Figure 6. Weil and random code cross-correlation functions (10,230 symbols).

GLONASS Augmentation Development

SDCM has been under development since 2002. The main elements of the system, including the network of reference stations in Russia and abroad, the central processing facility (CPF), and the SDCM information distribution channel, have been designed.

Ground Stations. The SDCM uses 14 monitor stations in Russia and two in Antarctica at Russia’s Bellingshausen and Novolazarevskaya research stations. Eight more monitor stations will be added in Russia and several more outside Russia. The additional overseas stations may include sites in Latin America and the Asia-Pacific region.

Central Processing. Raw measurements (GLONASS and GPS L1 and L2 pseudorange and carrier-phase measurements) from the ground stations come to the SDCM CPF. The CPF calculates the precise satellite ephemerides and clocks, controls integrity, and generates the SBAS messages. The format of these messages is compliant with the international standard also used by the Wide Area Augmentation System (WAAS), the European Geostationary Navigation Overlay Service (EGNOS), and the Japanese Multi-functional Transport Satellite (MTSAT) Satellite-based Augmentation System (MSAS).

Format Limitations. The current SBAS format has a limited capability for broadcasting corrections for GLONASS and GPS satellites combined. There is space for only 51 satellites, insufficient for the current number of satellites on orbit. As a result, studies are looking into the efficiency of SDCM data broadcasting in an attempt to resolve this contradiction. The three main options are: use a dynamic satellite mask, use two CDMA signals, or provide an additional SBAS message.

Under the first option, SDCM satellites would only broadcast corrections and integrity data for those GLONASS and other GNSS satellites in view of users in the territory of the Russian Federation. For the second option, SDCM satellites would transmit two CDMA signals with independent sets of correc
tions and integrity data on each signal. The third option assumes that the SDCM data stream would have additional messages with information about satellites not included in the initial list of 51.

The first scenario is possible with the current version of the SBAS format. The other two options require some changes in the format of SBAS messages and international coordination. But the SDCM CPF is ready to operate in all of these modes.

Distribution. The main advantage of SBAS is its universal space channel to users. The SDCM orbit constellation will consist of three geostationary satellites from the multifunctional space relay system Luch (see Figure 7). Luch, which means “ray” or “beam” in Russian, will be used to relay communications between low Earth-orbiting spacecraft and ground facilities in Russia in a similar fashion to that of NASA’s Tracking and Data Relay Satellite System. The satellites will also include transponders for relaying SDCM signals from the CPF to users. The first satellite, Luch-5A, will be launched this year and will occupy an orbital slot at 16° west longitude. Luch-5B will be launched in 2012 to a slot at 95° east longitude. The full constellation will be deployed by 2014 with the launch of Luch-4 into a slot at 167° east longitude.

Figure 7. Multifunctional relay system Luch.

Wideband transponders (22 MHz) will be installed on board the Luch-5A and Luch-5B satellites. These transponders will transmit signals on a carrier frequency of 1575.42 MHz. As the SDCM service area is Russian territory, the main beam will be directed to the north with an angle of 7 degrees relative to the direction to the equator. The transmitted power will be 60 watts and will give a signal power level at the Earth’s surface roughly equal to that of GLONASS and GPS signals, about –158 dBW.

SDCM will also provide service through the Internet. A system website (www.sdcm.ru) already gives users information about real-time and a posteriori GLONASS and GPS monitoring (see Figure 8). An SDCM data-broadcasting ground system has been developed and is being tested now. It will help to verify SDCM data before the Luch satellites are launched. SDCM SBAS messages will be transmitted through the Internet in real time using the SISNeT (Signal in Space through the Internet) approach. The SISNeT protocol was developed for relaying EGNOS messages over the Internet.

Figure 8. SDCM website, www.sdcm.ru.(Click to enlarge.)

A set of experiments was carried out to evaluate SDCM performance. In one experiment, 130 hours of raw pseudorange data was processed to generate the results shown in Figure 9. The upper plot shows the positioning results of a stand-alone receiver working only with the GLONASS and GPS signals. The lower plot presents results of GLONASS/GPS/SDCM navigation. It is clear that the SDCM ephemeris and clock corrections improve user accuracy by more than a factor of two.

Figure 9. SDCM tests results; (a) without and (b) with SDCM corrections.

However, precise point positioning (PPP) technology, based on post-processing dual-frequency carrier-phase measurements with precise satellite ephemeris and clock data, expands the areas of practical use of satellite positioning without complex user ground infrastructure of reference stations and wireless communication channels. Studies have already demonstrated that decimeter-level PPP is possible using GLONASS data or GLONASS data in combination with GPS data. Tests are under way to deliver the precise satellite ephemeris and clock data over the Internet to allow real-time PPP. We can envisage that some time in the future, the ephemeris and clock data could be provided to users in real time using satellite signals.

Future SDCM Satellites. The first SDCM satellites will provide service over the main part of Russia, excluding northern regions. To cover those regions, the SDCM orbit constellation could be enlarged using satellites in circular, inclined geosynchronous orbit (GSO); inclined, elliptical geosynchronous orbit (IGSO); or Molniya-type highly elliptical orbit (HEO) with an orbital period of precisely one-half of a sidereal day.

A comparative availability analysis for satellites with different orbits shows that using four GSO/IGSO/HEO satellites in two planes allows a user anywhere in Russia to continuously receive a signal from two satellites with a minimum elevation angle of 5 degrees. If the elevation mask angle is 30 degrees, availability will fall to 0.9 for IGSO satellites and 0.8 for HEO satellites. An orbit constellation of GSO satellites provides an availability of 0.8 and 0.3 for 5- and 30-degree mask angles respectively.

It is important to point out that the development of satellite orbit and clock prediction technology allows us to consider the possibility of using GSO, IGSO, or HEO satellites for ranging signal broadcasting. In that case, the navigation message could include precise ephemerides and clock data for all GNSS satellites to provide the data for a PPP service as mentioned earlier.

Conclusion

GLONASS development is entering a new historical phase. New CDMA navigation signals and deployment of a national SBAS system will provide not only a new quality of navigation service, but the basis for a regional precise navigation system with an accuracy of a few decimeters for users in Russia and neighboring countries.

Acknowledgment

This article is based on the paper “GLONASS Developing Strategy” presented at ION GNSS 2010, the 23rd International Technical Meeting of The Institute of Navigation, Portland, Oregon, September 21–24, 2010.

Yuri Urlichich is the general director and general designer of the Joint Stock Company (JSC) Russian Space Systems, formerly the Russian Institute of Space Device Engineering, headquartered in Moscow. He is a GLONASS general designer, doctor of science, professor, and author of more than 150 papers and 20 patents.

Valeriy Subbotin is a first deputy general director and general designer of JSC Russian Space Systems and a doctor of science. He has worked in the space industry for more than 40 years and has published more than 45 papers.

Grigory Stupak is a deputy general director and general designer of JSC Russian Space Systems, a GLONASS deputy general designer, and a professor of Bauman Moscow State Technical University (BMSTU). He has worked in the space industry for 35 years and has published more than 150 papers.

Vyacheslav Dvorkin is a deputy general designer of JSC Russian Space Systems and a doctor of science. Dvorkin has been developing GLONASS, GNSS augmentations, and user equipment for more than 35 years. He is an author of 50 papers in the satellite navigation field.

Alexander Povalyaev is a deputy head of division in JSC Russian Space Systems and a professor of Moscow Aviation Institute. He has been developing methods and algorithms for processing GNSS carrier-phase measurements for 30 years and has published more than 40 papers.

Sergey Karutin is a deputy head of division in JSC Russian Space Systems and an assistant professor at BMSTU. Karutin has been on the GLONASS team since 1998, developing GNSS augmentations and user equipment. He received a Ph.D. degree in 2004.

FURTHER READING

• GLONASS Background and Use

“GPS, GLONASS, and More: Multiple Constellation Processing in the International GNSS Service” by T. Springer and R. Dach in GPS World, Vol. 21, No. 6, June 2010, pp. 48–58.

“The Future is Now: GPS + GLONASS + SBAS = GNSS” by L. Wanninger in GPS World, Vol. 19, No. 7, July 2008, pp. 42–48.

“GLONASS: Review and Update” by R.B. Langley in GPS World, Vol. 8, No. 7, July 1997, pp. 46–51.

• GLONASS Current and Future Signal Structures

GLONASS Interface Control Document, Edition 5.1, Russian Institute of Space Device Engineering, Moscow, 2008.

“The Spreading and Overlay Codes for the L1C Signal” by J.J. Rushanan in Navigation, Vol. 54, No. 1, Spring 2007, pp. 43–51.

Spread Spectrum Systems for GNSS and Wireless Communications by J.K. Holmes, Artech House, Inc., Norwood, Massachusetts, 2007.

“The Galileo Code and Others” by G.W. Hein, J.-A. Avila-Rodriguez, and S. Wallner in Inside GNSS, Vol. 1, No. 6, September 2006, pp. 62–74.

• System for Differential Correction and Monitoring

“Russian System for Differential Correction and Monitoring: A Concept, Present Status, and Prospects for Future” by S.V. Averin, V.V. Dvorkin, and S.N. Karutin in Proceedings of ION GNSS 2006, the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 26–29, 2006, pp. 3037–3044.

Minimum Operational Performance Standards for Global Positioning/Wide Area Augmentation System Airborne Equipment, RTCA/DO-229D, prepared by SC-159, RTCA Inc., Washington, D.C., December 13, 2006.

“Appendix B. Technical Specifications for the Global Navigation Satellite System (GNSS)” in Aeronautical Telecommunications: International Standards and Recommended Practices, Annex 10 to the Convention on International Civil Aviation, Vol. I. Radio Navigation Aids, (6th ed.), International Civil Aviation Organization, Montreal, Quebec, Canada, 2006.

• SISNeT

“Proposal of an Internet-Based EGNOS Receiver Architecture and Demonstration of the SISNeT Concept” by E. González, M. Toledo, A. Catalina, C. Barredo, F. Torán, and A. Salonico in Proceedings of ION GPS/GNSS 2003, the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 9-12, 2003, pp. 1628–1641.

• Precise Point Positioning

“An Evaluation of OmniStar XP and PPP as a Replacement for DGPS in Airborne Applications” by J.S. Booth, and R.N. Snow in Proceedings of ION GNSS 2009, the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, September 22–25, 2009, pp. 1188–1194.

“Precise Point Positioning for Real-Time Determination of Co-Seismic Crustal Motion” by P. Collins, J. Henton, Y. Mireault, P. Héroux, M. Schmidt, H. Dragert, and S. Bisnath in Proceedings of ION GNSS 2009, Savannah, Georgia, September 22–25, 2009, pp. 2479–2488.

“Orbits and Clocks for GLONASS Precise-Point-Positioning” by R. Píriz, D. Calle, A. Mozo, P. Navarro, D. Rodríguez, and G. Tobías in Proceedings of ION GNSS 2009, Savannah, Georgia, September 22–25, 2009, pp. 2415–2424.

“Study on Precise Point Positioning Based on Combined GPS and GLONASS” by X. Li, X. Zhang, and F. Guo in Proceedings of ION GNSS 2009, Savannah, Georgia, September 22–25, 2009, pp. 2449–2459.

April 1, 2011
Innovation: Realistic Randomization

A New Way to Test GNSS Receivers

By Alexander Mitelman

INNOVATION INSIGHTS by Richard Langley

GNSS RECEIVER TESTING SHOULD NEVER BE LEFT TO CHANCE. Or should it? There are two common approaches to testing GNSS receivers: synthetic and realistic. In synthetic testing, a signal simulator is programmed with specific satellite orbits, receiver positions, and signal propagation conditions such as atmospheric effects, signal blockage, and multipath. A disadvantage of such testing is that the models used to generate the synthetic signals are not always consistent with the behavior of receivers processing real GNSS signals. Realistic testing, on the other hand, endeavors to assess receiver performance directly using the signals actually transmitted by satellites. The signals may be recorded digitally and played back to receivers any number of times. While no modeling is used, the testing is specific to the particular observing scenario under which the data was recorded including the satellite geometry, atmospheric conditions, multipath behavior, and so on. To fully examine the performance of a receiver using data collected under a wide variety of scenarios would likely be prohibitive. So, neither testing approach is ideal. Is there a practical alternative? The roulette tables in Monte Carlo suggest an answer.

Both of the commonly used testing procedures lack a certain characteristic that would better assess receiver performance: randomness. What is needed is an approach that would easily provide a random selection of realistic observing conditions. Scientists and engineers often use repeated random samples when studying systems with a large number of inputs especially when those inputs have a high degree of uncertainty or variability. And mathematicians use such methods to obtain solutions when it is impossible or difficult to calculate an exact result as in the integration of some complicated functions. The approach is called the Monte Carlo method after the principality’s famous casino. Although the method had been used earlier, its name was introduced by physicists studying random neutron diffusion in fissile material at the Los Alamos National Laboratory during the Second World War.

In this month’s article, we look at an approach to GNSS receiver testing that uses realistic randomization of signal amplitudes based on histograms of carrier-to-noise-density ratios observed in real-world environments. It can be applied to any simulator scenario, independent of scenario details (position, date, time, motion trajectory, and so on), making it possible to control relevant parameters such as the number of satellites in view and the resulting dilution of precision independent of signal-strength distribution. The method is amenable to standardization and could help the industry to improve the testing methodology for positioning devices — to one that is more meaningfully related to real-world performance and user experience.

Virtually all GNSS receiver testing can be classified into one of two broad categories: synthetic or realistic. The former typically involves simulator-based trials, using a pre-defined collection of satellite orbits, receiver positions, and signal propagation models (ionosphere, multipath, and so on). Examples of this type of testing include the 3rd Generation Partnership Project (3GPP) mobile phone performance specifications for assisted GPS, as well as the “apples-to-apples” methodology described in an earlier GPS World article (see Further Reading).

The primary advantage of synthetic testing is that it is tightly controllable and completely repeatable; where a high degree of statistical confidence is required, the same scenario can be run many times until sufficient data has been collected. Also, this type of testing is inherently self-contained, and thus amenable to testing facilities with modest equipment and resources.

Synthetic approaches have significant limitations, however, particularly when it comes to predicting receiver performance in challenging real-world environments. Experience shows that tests in which signal levels are fixed at predetermined levels are not always predictive of actual receiver behavior. For example, a receiver’s coherent integration time could in principle be tuned to optimize acquisition at those levels, resulting in a device that passes the required tests but whose performance may degrade in other cases. More generally, it is useful to observe that the real world is full of randomness, whereas apart from intentional variations in receiver initialization, the primary source of randomness in most synthetic tests is simply thermal noise.

By comparison, most realistic testing approaches are designed to measure real-world performance directly. Examples include conventional drive testing and so-called “RF playback” systems, both of which have also been described in recent literature (see Further Reading). Here, no modeling or approximation is involved; the receiver or recording instrument is physically operated within the signal environment of interest, and its performance in that environment is observed directly. The accuracy and fidelity of such tests come with a price, however. All measurements of this type are inherently literal: the results of a given test are inseparably linked to the specific multipath profile, satellite geometry, atmospheric conditions, and antenna profile under which the raw data was gathered. In this respect, the direct approach resembles the synthetic methods outlined above — little randomness exists within the test setup to fully explore a given receiver’s performance space.

Designing a practical alternative to the existing GNSS tests, particularly one intended to be easy to standardize, represents a challenging balancing act. If a proposed test is too simple, it can be easily standardized, but it may fall well short of capturing the complexities of real-world signals. On the other hand, a test laden with many special corner cases, or one that requires users to deploy significant additional data storage or non-standard hardware, may yield realistic results for a wide variety of signal conditions, but it may also be impractically difficult to standardize.

With those constraints in mind, this article attempts to bridge the gap between the two approaches described above. It describes a novel method for generating synthetic scenarios in which the distribution of signal levels closely approximates that observed in real-world data sets, but with an element of randomness that can be leveraged to significantly expand testing coverage through Monte Carlo methods. Also, the test setup requires only modest data storage and is easily implemented on existing, widely deployed hardware, making it attractive as a potential candidate for standardization.

The approach consists of several steps. First, signal data is gathered in an environment of interest and used to generate a histogram of carrier-to-noise-density (C/N₀) ratios as reported by a reference receiver, paying particular attention to satellite masking to ensure that the probability of signal blockage is calculated accurately. The histogram is then combined with a randomized timing model to create a synthetic scenario for a conventional GNSS simulator, whose output is fed into the receiver(s) under test (RUTs). The performance of the RUTs in response to live and simulated signals is compared in order to validate the fidelity and usefulness of the histogram-based simulation. This hybrid approach combines the benefits of synthetic testing (repeatability, full control, and compactness) with those of live testing (realistic, non-static distribution of signal levels), while avoiding many of the drawbacks of each.

Histograms

The method explored in this article relies on cumulative histograms of C/N₀ values reported by a receiver in a homogeneous signal environment. This representation is compact and easy to implement with existing simulator-based test setups, and provides information that can be particularly useful in tuning acquisition algorithms.

Motivation and Theoretical Considerations. To motivate the proposed approach, consider an example histogram constructed from real-world data, gathered in an environment (urban canyon) where A-GPS would typically be required. This is shown in FIGURE 1, together with a representative histogram of a standard “coarse-time assistance” test case (as described in the 3GPP Technical Standard 34.171, Section 5.2.1) for comparison. (Note that the x-axis is actually discontinuous toward the left side of each plot: the “B” column designates blocked signals, and thus corresponds to C/N₀ = –∞.)

From the standpoint of signal distributions, it is evident that existing test standards may not always model the real world very accurately.

FIGURE 1a. Example histogram of a real-world urban canyon, the San Francisco financial district;.

Figure 1b. Example histograms of 3GPP TS 34.171 “coarse-time assistance” test case).

The histogram is useful in other ways as well. Since the data set is normalized (the sum of all bin heights is 1.0), it represents a proper probability mass function (PMF) of signal levels for the environment in question. As such, several potentially useful parameters can be extracted directly from the plot: the probability of a given signal being blocked (simply the height of the leftmost bin); upper and lower limits of observed signal levels (the heights of the leftmost and rightmost non-zero bins, respectively, excluding the “blocked” bin); and the center of mass, defined here as

(1)

where y[n] is the height of the nth bin (dimensionless), x[n] is the corresponding C/N₀ value (in dB-Hz), and x[“B”] = –∞ by definition.

Finally, representing environmental data as a PMF enables one additional theoretical calculation. The design of the 3GPP “coarse-time assistance” test case illustrated above assumes that a receiver will be able to acquire the one relatively strong signal (the so-called “lead space vehicle (SV)” at -142 dBm) using only the assistance provided, and will subsequently use information derivable from the acquired signal (such as the approximate local clock offset) to find the rest of the satellites and compute a fix. Suppose that for a given receiver, the threshold for acquisition of such a lead signal given coarse assistance is P_i (expressed in dB-Hz). Then the probability of finding a lead satellite on a given acquisition attempt can be estimated directly from the histogram:

(2)

where is the average number of satellites in view over the course of the data set. A similar combinatorial calculation can be made for the conditional probability of finding at least three “follower” satellites (that is, those whose signals are above the receiver’s threshold for acquisition when a lead satellite is already available).

The product of these two values represents the approximate probability that a receiver will be able to get a fix in a given signal environment, expressed solely as a function of the receiver’s design parameters and the histogram itself. When combined with empirical data on acquisition yield from a large number of start attempts in an environment of interest, this calculation provides a useful way of checking whether a particular histogram properly captures the essential features of that environment. This validation may prove especially useful during future standardization efforts.

Application to Acquisition Tuning. In addition to the calculations based on the parameters discussed above, histograms also provide useful information for designing acquisition algorithms, as follows.

Conventionally, the acquisition problem for GNSS is framed as a search over a three-dimensional space: SV pseudorandom noise code, Doppler frequency offset, and code phase. But in weak signal environments, a fourth parameter, dwell time – the predetection integration period, plays a significant role in determining acquisition performance. Regardless of how a given receiver’s acquisition algorithm is designed, dwell time (or, equivalently, search depth) and the associated signal detection threshold represent a compromise between acquisition speed and performance (specifically, the probabilities of false lock and missed detection on a given search). To this end, any acquisition routine designed to adjust its default search depth as a function of extant environmental conditions may be optimized by making use of the a priori signal level PMF provided by the corresponding histogram(s).

Data Collection

The hardware used to collect reference data for histogram generation is simple, but care must be taken to ensure that the data is processed correctly. The basic setup is shown in FIGURE 2.

Figure 2. Data collection setup with a reference receiver generating NMEA 0183 sentences or in-phase and quadrature (I/Q) raw data and one or more test receivers performing multiple time-to-first-fix (TTFF) measurements.

It is important to note that the individual components in the data-collection setup are deliberately drawn here as generic receivers, to emphasize that the procedure itself is fundamentally generic. Indeed, as noted below, future efforts toward standardizing this testing methodology will require that it generate sensible results for a wide variety of RUTs, ideally from different manufacturers. Thus, the intention is that multiple receivers should eventually be used for the time-to-first-fix (TTFF) measurements at bottom right in the figure. For simplicity, however, a single test receiver is considered in this article.

Procedure. The experiment begins with a test walk or drive through an environment of interest. Since an open sky environment is unlikely to present a significant challenge to almost any modern receiver, a moderately difficult urban canyon route through the narrow alleyways of Stockholm’s Gamla Stan (Old Town) was chosen for the initial results presented in this article. The route, approximately 5 kilometers long, is shown in FIGURE 3 (top). For the TTFF trials gathered along this route, assisted starts with coarse-time aiding (±2 seconds) were used to generate a large number of start attempts during the walk, ensuring reasonable statistical significance in the results (115 attempts in approximately 60 minutes, including randomized idle intervals between successive starts).

Once the data collection is complete, the reference data set is processed with a current almanac and an assumed elevation angle mask (typically 5 degrees) to produce an individual histogram for each satellite in view, along with a cumulative histogram for the entire set, as shown in Figure 3 (bottom). The masking calculation is particularly important in properly classifying which non-reported C/N₀ values should be ignored because the satellite in question is below the elevation angle mask at that location and time, and which should be counted as blocked signals.

Figure 3a. Data collection, Gamla Stan (Old Town), Stockholm (route and street view).

Figure 4. Fluctuation timing models (top: “Multi SV” variant; bottom: “Indiv SV” variant).

In addition to proper accounting for satellite masking, the raw source data should also be manually trimmed to ensure that all data points used to build the histogram are taken homogeneously from the environment in question. Thus the file used to generate the histogram in Figure 3 was truncated to exclude the section of “open sky” conditions between the start of the file and the southeast corner of the test area, and similarly between the exit from the test area and the end of the file.

Finally, the resulting histogram is combined with a randomized timing model to create a simulator scenario, which is used to re-test the same RUTs shown in Figure 2.

Reference Receiver Considerations. The accuracy of the data collection described above is fundamentally limited by the performance of the reference receiver in several ways.

First, the default output format for GNSS data in many receivers is that of the National Marine Electronics Association (NMEA) 0183 standard (the histograms presented in this article were derived from NMEA data). This is imperfect in that the NMEA standard non-proprietary GSV sentence requires C/N₀ values to be quantized to the nearest whole dB-Hz, which introduces small rounding errors to the bin heights in the histograms. (In this study, this effect was addressed by applying a uniformly distributed ±0.5 dB-Hz dither to all values in the corresponding simulated scenario, as discussed below.) If finer-grained histogram plots are required, an alternative data format must be used instead.

Second, many receivers produce data outputs at 1 Hz, limiting the ability to model temporal variations in C/N₀ to frequencies less than 0.5 Hz, owing to simple Nyquist considerations. While the raw data for this study was obtained at walking speeds (1 to 2 meters per second), and thus unlikely to significantly misrepresent rapid C/N₀ fading, studies done at higher speeds (such as test drives) may require a reference receiver capable of producing C/N₀ measurements at a higher rate.

A third limitation is the sensitivity of the reference receiver. Ideally, the reference device would be able to track all signals present during data gathering regardless of signal strength, and would instantaneously reacquire any blocked signals as soon as they became visible again. Such a receiver would fully explore the space of all available signals present in the test environment. Unfortunately, no receiver is infinitely sensitive, so a conventional commercial-grade high sensitivity receiver was used in this context. Thus the resulting histogram is, at best, a reasonable but imperfect approximation of the true signal environment.

Finally, a potentially significant error source may be introduced if the net effects of the reference receiver’s noise figure plus implementation loss (NF+IL) are not properly accounted for in preparing the histograms. (If an active antenna is used, the NF of the antenna’s low-noise amplifier essentially determines the first term.) The effect of incorrectly modeling these losses is that the entire histogram, with the exception of the “blocked” column, is shifted sideways by a constant offset.

The correction applied to the histogram to account for this effect must be verified prior to further acquisition testing. This can be done by generating a simulator scenario from the histogram of interest, as described below, and recording a sufficiently long continuous data set using this scenario and the reference receiver. A corresponding histogram is then built from the reference receiver’s output, as before, and compared to the histogram of the original source data. The amplitude of the “blocked” column and the center of mass are two simple metrics to check; a more general way of comparing histograms is the two-sided Kolmogorov-Smirnov test (see “Results”).

Timing Models

The histograms described in the preceding section specify the amplitude distribution of satellite signals in a given environment, but they contain no information about the temporal characteristics of those signals. This section briefly describes the timing models used in the current study, as well as alternatives that may merit further investigation.

In real-world conditions, the temporal characteristics of a given satellite signal depend on many factors, including the physical features of the test environment, multipath fading, and the velocity of the user during data collection. Various timing models can be used to simulate those temporal characteristics in laboratory scenarios.

Perhaps the simplest model is one in which signal levels are changed at fixed intervals. This is trivial to implement on the simulator side, but it is clearly unlikely to resemble the real-world conditions mentioned above. A second alternative would be to generate timing intervals based on the Allan (or two-sample) variance of individual C/N₀ readings observed during data collection as a measure of the stability of the readings. While this is more physically realistic than an arbitrarily chosen interval as described above, it is still a fixed interval. These observations suggest that a timing model including some measure of randomness may represent a more realistic approach.

One statistical function commonly used for real-world modeling of discrete events (radioactive decay, customers arriving at a restaurant, and so on) is the Poisson arrival process. This process is completely described with a single non-negative parameter, λ, which characterizes the rate at which random events occur. Equivalently, the time between successive events in such a process is itself a random variable described by the exponential probability distribution function:

(3 )

The resulting inter-event timings described by this function are strictly non-negative, which is at least physically reasonable, and directly controllable by varying the timing parameter λ. For simplicity, then, the Poisson/exponential timing model was chosen as an initial attempt at temporal modeling, and used to generate the results presented in this article.

Two variants of the Poisson/exponential timing model are considered. In the first, defined herein as the “Multi SV” case, a single thread determines the timing of fluctuation events, and the power levels of one or more satellites are adjusted at each event. In the second variant, defined as the “Indiv SV” case, each simulator channel receives its own individual timing thread, and all fluctuation events are interleaved in constructing the timing file for the simulator. These two variants are shown schematically in FIGURE 4.

Figure 4. Fluctuation timing models (top: “Multi SV” variant; bottom: “Indiv SV” variant).

Constructing Scenarios

Once a target histogram is available, it is necessary to generate random signal amplitudes for use with a simulator scenario. This is done by means of a technique known as the probability integral transform (PIT). This approach uses the c
umulative distribution function (or, in the discrete case considered here, a modified formulation based on the cumulative mass function) of a probability distribution to transform a sequence of uniformly distributed random numbers into a sequence whose distribution matches the target function.

Finally, the random signal levels generated by the PIT process are assigned to individual simulator channels according to a set of timed events as described in the preceding section, completing the randomized scenario to be used for testing.

Results

Given a simulator scenario constructed as described above, the RUTs originally included in the data collection campaign are again used to conduct acquisition tests, this time driven from the simulator.

To validate that a particular fluctuating scenario properly represents the live data, it is necessary to quantify two things: how well a generated histogram matches the source data, and how well a receiver’s acquisition performance under simulated signals matches its behavior in the field. At first these may appear to be two qualitatively different problems, but a mathematical tool known as the two-sided Kolmogorov-Smirnov (K-S) test can be used for both tasks.

Validation of Experimental Setup. As a first step toward validating that the C/N₀ profile of the simulated signals matches that of the reference data, TABLE 1 gives the values of the two-sided K-S test statistic, D (a measure of the greatest discrepancy between a sample and the reference distribution), for histograms generated with the reference receiver for the two timing-thread models described above and several values of the Poisson/exponential parameter, λ. The reference cumulative mass function (CMF) for each test was derived from the histogram generated for the raw (empirically collected) data set.

These results illustrate good agreement (D < 0.05) between the overall signal distribution profile in the empirical data set and that in each of the six simulated fluctuating scenarios.

As a further check, TABLE 2 shows the same K-S statistic for the histogram generated from the “Multi SV” timing model as a function of several NF+IL values. As before, the reference CMF comes from the raw (empirically collected) data set, and the same reference receiver was used to generate data from the simulator scenario. Evidently, an NF+IL value of 4 dB gives good agreement between empirical and simulated data sets.

Validation of Receiver Performance. Finally, TTFF tests with the simulated scenarios described above are conducted with the same receiver(s) used in the original data gathering session. Here, the K-S test is used to compare the live and simulated TTFF results rather than signal distributions. An example result, illustrating cumulative distribution functions of TTFF, is shown in FIGURE 5 for the live data set collected during the original data gathering session, alongside three results from the “Multi SV” fluctuating model, generated with NF+IL = 4 dB and several different values of the Poisson/exponential timing parameter, λ. While agreement with live data is not exact for any of the simulated scenarios, the λ^-1 = 3.0 seconds case appears to correspond reasonably well (D < 0.10).

FIGURE 5 Time-to-first-fix cumulative distribution functions from live and simulated data (“Multi SV” variant with NF+IL = 4 dB).

Conclusions and Future Work

This article has introduced a novel approach to testing GNSS receivers based on histograms of C/N₀ values observed in real-world environments.

Much additional work remains. For the proposed method to be amenable to standardization, it is obviously necessary to gather data from many additional environments. Indeed, it appears likely that no one histogram will encapsulate all environments of a particular type (such as urban canyons), so significant additional experimentation and data collection will be required here. Also, as mentioned at the beginning of the article, the proposed method will need to be tested with multiple receivers to verify that a particular result is not unique to any specific brand or architecture. Finally, higher rate C/N₀ source data may also be necessary to capture the rapid fades that may be encountered in dynamic scenarios, such as drive tests, and the fluctuation timing models will need to be revisited once such data becomes available.

Acknowledgments

The author gratefully acknowledges the assistance of Jakob Almqvist, David Karlsson, James Tidd, and Christer Weinigel in conducting the experiments described in this article. Thanks also to Ronald Walken for valuable insights on the accurate treatment of the source environment in calculating target histograms. This article is based on the paper “Fluctuation: A Novel Approach to GNSS Receiver Testing” presented at ION GNSS 2010.

Alexander Mitelman is the GNSS research manager at Cambridge Silicon Radio, headquartered in Cambridge, U.K. He earned his S.B. degree from the Massachusetts Institute of Technology and M.S. and Ph.D. degrees from Stanford University, all in electrical engineering. His research interests include signal-quality monitoring and the development of algorithms and testing methodologies for GNSS.

FURTHER READING

• GNSS Receiver Testing in General
GPS Receiver Testing, Application Note by Agilent Technologies. Available online at http://cp.literature.agilent.com/litweb/pdf/5990-4943EN.pdf.

• Synthetic GNSS Receiver Testing
“Apples to Apples: Standardized Testing for High-Sensitivity Receivers” by A. Mitelman, P.-L. Normark, M. Reidevall, and S. Strickland in GPS World, Vol. 19, No. 1, January 2008, pp. 16–33.

Universal Mobile Telecommunications System (UMTS); Terminal conformance specification; Assisted Global Positioning System (A-GPS); Frequency Division Duplex (FDD), 3GPP Technical Specification 34.171, Release 7, Version 7.0.1, July 2007, published by the European Telecommunications Standards Institute, Sophia Antipolis, France. Available online at http://www.3gpp.org/.

• Realistic GNSS Receiver Testing
“Record, Replay, Rewind: Testing GNSS Receivers with Record and Playback Techniques” by D.A. Hall in GPS World, Vol. 21, No. 10, October 2010, pp. 28–34.

“Proper GPS/GNSS Receiver Testing” by E. Vinande, B. Weinstein, and D. Akos in Proceedings of ION GNSS 2009, the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, September 22–25, 2009, pp. 2251–2258.

“Advanced GPS Hybrid Simulator Architecture” by A. Brown and N. Gerein in Proceedings of The Institute of Navigation 57th Annual Meeting/CIGTF 20th Guidance Test Symposium, Albuquerque, New Mexico, June 11–13, 2001, pp. 564–571.

• Receiver Noise
“Measuring GNSS Signal Strength: What is the Difference Between SNR and C/N₀?” by A. Joseph in Inside GNSS, Vol. 5, No. 8, November/December 2010, pp. 20–25.

“GPS Receiver System Noise” by R.B. Langley in GPS World, Vol. 8, No. 6, June 1997, pp. 40–45.

Global Positioning System: Theory and Applications, Vol. I, edited by B.W. Parkinson and J.J. Spliker Jr., published by the American Institute of Aeronautics and Astronautics, Inc., Washington, D.C., 1996.

• Test Statistics
“The Probability Integral Transform and Related Results” by J. Agnus in SIAM Review (a publication of the Society for Industrial and Applied Mathematics), Vol. 36, No. 4, December 1994, pp. 652–654, doi:10.1137/1036146

“Kolmogorov-Smirnov Test” by T.W. Kirkman on the College of Saint Benedict and Saint John’s University Statistics to Use website: http://www.physics.csbsju.edu/stats/KS-test.html.

• NMEA 0183
NMEA 0183, The Standard for Interfacing Marine Electronic Devices, Ver. 4.00, published by the National Marine Electronics Association, Severna Park, Maryland, November 2008.

“NMEA 0183: A GPS Receiver Interface Standard” by R.B. Langley in GPS World, Vol. 6, No. 7, July 1995, pp. 54–57.

Unofficial online NMEA 0183 descriptions: NMEA data; NMEA Revealed by E.S. Raymond, Ver. 2.3, March 2010.

March 1, 2011
Innovation: GNSS and the Ionosphere

What’s in Store for the Next Solar Maximum?

By Anna B.O. Jensen and Cathryn Mitchell

Although the sun can become disturbed at any time, solar activity is correlated with the approximately 11-year cycle of spots on the sun’s surface. We are just coming out of a minimum in the solar cycle and headed for the next maximum, predicted to occur around the middle of 2013. How significantly will GNSS users be affected? In this month’s column, two ionosphere experts tell us what might be in store.

INNOVATION INSIGHTS by Richard Langley

“HERE COMES THE SUN / here comes the sun / And I say / it’s all right.”

Is it? Of course, George Harrison was referring to the welcome return of the sun after a long dreary English winter. But can GNSS users sing the same refrain?

The signals from global navigation satellites must transit the ionosphere on their way to receivers on or near the Earth’s surface. The passage exacts a toll in the form of an added delay of the pseudorandom-noise-code signals and an advance of the phase of the signals’ carriers, due to the presence of the ionosphere’s free electrons. These perturbations must be ameliorated in some way to achieve high accuracy in GNSS positioning, navigation, and timing applications.

Where do the ionosphere’s electrons come from? For the most part, they are valence electrons, stripped from upper atmosphere atoms and molecules by the extreme ultraviolet light continuously emitted by the sun. On the Earth’s night-side, the electrons and the ionized atoms and molecules tend to recombine. This ionization and recombination process, along with the interactions of the particles with the Earth’s magnetic field, governs the density of the electrons at a particular location and time. The ionosphere is also affected by the solar wind, and its associated magnetic field, but the cocoon established by the Earth’s magnetic field (the magnetosphere) tends to deflect the solar wind so that it usually has little influence on the ionosphere.

Normally, the sun is quiescent: its electromagnetic and particle radiation is fairly constant, and its effects on the ionosphere benign. The delay in GNSS code observations and the advance in phase observations can be readily estimated and removed from the observations using a variety of models and methods. However, the sun can become disturbed, giving rise to occasional violent outbursts with large increases in electromagnetic and particle radiation. These outbursts can radically change the distribution of the electrons in the ionosphere, reducing the effectives of some amelioration methods. The electron density variability can become so rapid that a GNSS receiver can lose lock on satellite signals. And an increase in the sun’s radio emissions can become so large as to drown out GNSS signals on the sunlight side of the Earth.

Although the sun can become disturbed at any time, solar activity is correlated with the approximately 11-year cycle of spots on the sun’s surface. We are just coming out of a minimum in the solar cycle and headed for the next maximum, predicted to occur around the middle of 2013. How significantly will GNSS users be affected? In this month’s column, two ionosphere experts tell us what might be in store.

GNSS satellite signals are affected by the space environment and the Earth’s atmosphere as they travel from satellites at an altitude of about 20,000 kilometers above the surface of the Earth to receivers located at, or close to, the surface.

In the upper part of the Earth’s atmosphere, the ionosphere, which is located from about 80 to 1,000 kilometers above the surface of the Earth, satellite signals are affected by the free electrons stripped from atoms and molecules by ionization. The signals are refracted by this plasma, which changes their speed of travel. The effect is mainly a function of the number of free electrons present, the electron density.

In the lower parts of Earth’s atmosphere, in the troposphere and the stratosphere — where the atoms and molecules are electrically neutral — the satellite signals experience additional refraction. Here the effect is a function of pressure, temperature, and humidity. The effect of the troposphere and stratosphere is often just referred to as the “tropospheric effect” in GNSS positioning as it is in the troposphere where most of the neutral atmosphere refraction occurs.

The ionospheric and tropospheric effects on satellite signals must be accounted for in the GNSS positioning process in order to obtain reliable and accurate position solutions. In this article, we look at the ionospheric effect on satellite signals. Although the variation in signal speed is the largest direct ionospheric effect on the GNSS satellite signals, scintillation is another important effect. Scintillation occurs when irregularities in the electron density of the ionosphere cause rapid changes in the phase and amplitude of the transmitted signals. These changes might cause a GNSS receiver to lose lock on a satellite signal. This means in practice that satellite signals are lost, or signal tracking can be rather difficult, during scintillation events. However, we restrict our article to the subject of the propagation speed of the signals and do not consider scintillation further.

In the following, we review characteristics of the ionospheric effect on GNSS satellite signals as well as the predictions of increased ionospheric activity for the coming years and the consequences for GNSS users.

Signals

The ionosphere as a whole is electrically neutral, but it contains a significant number of free electrons and ions. The negatively charged free electrons affect the electromagnetic satellite signals in various ways. Most important is the signal delay affecting code (pseudorange) measurements, also called the “ionospheric delay” (and the associated advance of carrier-phase measurements), which is caused by a change in the refractive index along the signal path. The refractive index changes continuously as a function of the composition of the transmission media all the way from the satellites to the GNSS receivers.

For the majority of the signal path — that is, from the satellite at an altitude of about 20,000 kilometers down to approximately 1,000 kilometers above the surface of the Earth — the change in the refractive index is usually sufficiently small to ignore when the GNSS satellite signals are used for positioning at the surface of the Earth (although, at times, the region above the ionosphere — the plasmasphere — can affect GNSS signals). We therefore use the approximation that the first part of the signal path is in a vacuum where the propagation of GNSS satellite signals is not affected.

Then, when the signals enter the ionosphere, we must consider the signal delay, and even though the density of electrons is largest at an altitude around 300 kilometers, we must consider the total number of electrons experienced by a satellite signal all the way through the ionosphere.

The size of the so-called first order effect of the signal delay, d, given in meters, can be modeled by the expression in Equation (1),

(1)

where f is the GNSS signal frequency, for instance 1.57542 x 10⁹ Hz for the GPS L1 frequency. The constant 40.3 is derived from the values of the electron charge, the electron mass, and the permittivity of free space. Finally, TEC is an abbreviation for total electron content and this value is given by integrating the number of free electrons along the signal path in a cross section of one square meter.

It turns out that the “delay” affecting carrier-phase measurements has exactly the same magnitude as the signal delay but is negative. In other words, the phase is advanced.

In practice, for single-frequency receivers, it is not possible to obtain the actual number of electrons along the signal path for every satellite signal, and we therefore need other models to predict or estimate the electron density or the signal delay.

A large number of models and methods for estimating the ionospheric signal delay have been developed. A comparison of some of them is given in a paper by Allain and Mitchell (see Further Reading). The most widely used model is probably the Klobuchar model, named after John Klobuchar, its developer. Coefficients for the Klobuchar model are determined by the GPS control segment and distributed with the GPS navigation message to GPS receivers where the coefficients are inserted into the model equation and used by receivers for estimation of the signal delay caused by the ionosphere.

Dispersion. The ionosphere is dispersive for radio waves, which means that the GNSS ionospheric signal delay is a function of the frequency of the signal. If pseudorange measurements from more than one frequency are available, for instance from dual-frequency GPS receivers, this can be used for enhanced modeling of the ionospheric effect by using combinations of the measurements made on both frequencies.

The basic expression for estimation of the ionospheric delay for dual-frequency code-based positioning is shown in Equation (2),

(2)

where d is the ionosphere delay, P denotes pseudorange, and f denotes frequency. The subscript notation L1 and L2 refers to the GPS L1 and L2 frequencies, respectively.

For high-accuracy carrier-phase-based positioning, an ionosphere-free combination of carrier-phase observations of the L1 and L2 frequencies is often used to reduce the effect of the ionospheric phase advance in the positioning process.

Estimating the ionosphere delay with Equation (2) for code observations or utilizing the ionosphere-free combination of the phase observations compensates for the first order ionospheric effect. This is the major part of the effect, but higher order effects are present, and the size of the residual higher order effects is increased (up to some centimeters) when the ionospheric activity is increasing.

For high-accuracy applications, the difference in the time of transmission and reception of the satellite signals of the various frequencies also must be considered as the signals on various frequencies are not transmitted from the satellites (nor received at a GNSS receiver) at exactly the same time epochs. These differences are normally referred to as the satellite and receiver differential code biases.

It is important also to note in this context that the noise level on the pseudorange corrected for the ionosphere and on the ionosphere-free carrier-phase observation is increased compared to using the pure single-frequency observations for positioning, but nevertheless these first-order approaches are used successfully in most software and receiver firmware for dual-frequency positioning.

Further developments of ionosphere-free combinations will evolve in the future as the new GPS L5 frequency and the new Galileo and GLONASS frequencies become fully available for multi-frequency ionosphere-free combinations. These more advanced combinations have the potential to further reduce the residual effect of the ionospheric delay in the positioning process.

Summing up, the GNSS signal delay caused by the ionosphere is a function of the electron density of the ionosphere. But what is driving the variation in electron density, and how do we know if it is changing?

Solar Activity and Sunspots

Equation (1) shows that the ionospheric signal delay is a direct function of the total electron content. The number of free electrons in the ionosphere is not constant; it varies significantly with time and space. The number of free electrons is driven by the ionization and recombination processes of the ionosphere, and these processes are in turn driven mainly by extreme ultraviolet radiation from the sun. Radiation from other cosmic sources also has an influence but it is minor compared to the effect of the solar radiation. There are also significant short-term (minutes to hours) changes caused by wave activity from the neutral atmosphere. The ionosphere itself is embedded in the neutral atmosphere — at these altitudes this is known as the thermosphere. The thermosphere is in constant movement due to waves and tides that are generated in situ or ascending from the underlying atmosphere. This thermosphere activity affects the ionosphere and causes some of the short-term variability in the electron density. However, the term “ionospheric activity” generally refers to the variability in electron density as driven by solar activity.

The fact that ionospheric activity is mainly driven by solar activity implies that the temporal variation of the electron content of the ionosphere follows a daily cycle, with the largest TEC values in the early afternoon local time, when the effect of the solar radiation has reached a maximum. Consequently, we see the lowest activity late at night just before sunrise.

There is also a geographic variability in the electron content with the highest electron density in the equatorial region and the lowest density in the high latitude regions. The latter, however, is affected by a larger variability, correlated with auroral activity.

The geographic variation of TEC is illustrated with a global ionosphere map from the Center for Orbit Determination in Europe (CODE) shown in Figure 1. Global ionosphere maps are generated at CODE on a daily basis, and the maps are available on the CODE website (see Further Reading).

Figure 1. Global ionosphere map for November 22, 2010, at 14:00 UTC. (Map generated by CODE, University of Bern.)

The TEC is provided in TEC units (TECU), where one TECU equals 1016 electrons per meter squared.

The sun also emits a constant flow of charged particles called the solar wind. The particles, mostly electrons and protons with energies between about 10 and 100 kilo-electron-volts, travel at an average speed of about 450 kilometers per second, but varying from 200 to 900 kilometers per second depending on solar activity. Although the Earth’s magnetosphere deflects most of the solar wind, the interplanetary magnetic field, which is associated with the solar wind, can cause disturbances in the geomagnetic field. When this happens, particles of the solar wind enter the geomagnetic field and cause increased ionization in the ionosphere. The solar wind therefore also has a large influence on the variability of ionospheric activity. Also, sudden eruptions of the sun such as solar flares and coronal mass ejections (CMEs) cause increased ionization and thereby a larger ionospheric variability.

Figure 2 shows a CME blast and subsequent impact at the Earth.

Figure 2. Coronal mass ejection (CME) and subsequent impact at the Earth. The left part of the illustration is composed of an image from NASA’s Solar Dynamics Observatory spacecraft superimposed on an image from the Solar and Heliospheric Observatory spacecraft jointly operated by NASA and the European Space Agency. The CME cloud arrives at the Earth about two to four days later and is shown being mostly deflected around the Earth’s magnetosphere. The blue paths emanating from the Earth’s poles represent some of its magnetic field lines. (Image: NASA/Goddard Space Flight Center.)

Solar activity and the quantity of emissions from the sun are highly correlated with the number of sunspots on its surface. A sunspot looks like a dark spot because the temperature in a sunspot is lower than that in its surroundings. The generation of sunspots is not well understood, but it is related to anomalies in the solar magnetic field. What is well known, however, is the history of the number of sunspots, because these have been observed since the early 1600s.

The number of sunspots generally follows a cycle of about 11 years. During the last few years (2007–2009), we have experienced a time period with a low number of sunspots. In fact, there were many days in a row without any sunspots visible (see Figure 3). During the next three to four years, the number of sunspots is expected to increase, and this will be followed by a decrease until we reach a new period of low solar activity in 2019–2020.

Figure 3. Images of the sun taken by the Solar and Heliospheric Observatory spacecraft. On the left is an image taken on March 27, 2001, at the peak of the last sunspot cycle. The daily sunspot count was 241. On the right is an image taken on December 15, 2008, near the minimum of the last sunspot cycle, showing no sunspots. (Image: Solar and Heliospheric Observatory)

Numerous investigations of time series of sunspot numbers have been carried out, and even though the cycles generally last 11 years, cycles of 9 and 13 years’ duration have been observed. Also, the cycles vary with respect to the maximum number of sunspots observed during a cycle, and various “cycles of cycles” appear to be present with respect to the strength of the sunspot cycles. For instance, a cycle with a period of about 420 years has been identified in the historic listings of sunspot numbers combined with other observations contributing to the knowledge of solar activity. A very low number of sunspots was observed for a number of years between 1645 and 1715 when the sun was especially calm. This period is often referred to as the Maunder Minimum after the solar astronomer Edward W. Maunder. If the theory of the 420-year cycle is correct, then we will see a period with lower solar activity and fewer sunspot numbers by the end of this century.

But let’s turn our attention to the previous and current sunspot cycles referred to as cycles number 23 and 24 (The 1755–1766 cycle is traditionally numbered “1.”). A new cycle begins with the first observed high-latitude, reversed-polarity sunspot. Reversed polarity means a sunspot with opposite magnetic polarity compared to sunspots from the previous solar cycle. Sunspots from the new and previous cycles initially coexist. Eventually, only the new-cycle sunspots are present. Cycle 24 began on January 4, 2008, when the first reversed-polarity sunspot appeared.

Analyses of observations of solar activity show that the density of the solar wind increases with increasing sunspot number. Also, with a large sunspot number, solar flares and CMEs happen more frequently. Ionospheric storm activity is more common when the sunspot number is high, and this activity increases the variability in ionospheric delays. This all adds up to an increased number of free electrons in the ionosphere and a larger variability, which provides a larger and more variable signal delay for all types of GNSS-based positioning, navigation, and timing during periods with high sunspot numbers.

We know that the sunspot number is expected to increase during the next three to four years. What can be expected and what can we do to minimize the effects of the increased ionospheric activity on positioning, navigation, and timing applications?

The Last Solar High

As mentioned earlier, the current solar cycle is referred to as cycle 24. During the last solar cycle, cycle 23, the GNSS community was alert and aware of what could happen, and therefore many events were observed and analyzed. Among the most well-known events is a sequence of storms during October and November 2003, commonly referred to as the Halloween Storms. The most extreme was the storm on October 30, 2003, which resulted from a CME on October 29 at 20:49 UTC, which subsequently impacted Earth’s magnetic field at 16:20 UTC on October 30 and produced a great geomagnetic storm, which lasted for many hours.

Effects on GPS positioning of this storm have been documented by the GNSS research group of the Royal Observatory of Belgium, where kinematic analyses of data from 36 GNSS stations in Europe showed position errors of more than 10 centimeters in the horizontal and up to 26 centimeters in the vertical between 21:00 and 22:00 UTC on October 30. The position errors were largest for locations in northern Europe including Sweden and Norway. The data analysis was carried out using high-quality carrier-phase data, and the processing was based on using an ionosphere-free linear combination of observations from the L1 and L2 frequencies, whereby the first-order effect of the ionosphere is removed from the results. The position errors are thus caused by mainly higher order ionospheric effects.

For navigation-grade GPS positioning, a U.S. National Atmospheric and Oceanic Administration technical memorandum (see Further Reading) reported that the Wide Area Augmentation System (WAAS) vertical error limit of 50 meters was exceeded for a period of about 11 hours on October 30, 2003. This means that, in practice, WAAS was not available for precision aircraft approaches during that time. The European Geostationary Navigation Overlay Service (EGNOS) was not transmitting during the storm, but simulations carried out later by ESA showed that the boundary regions of the EGNOS coverage area would have been especially affected by a reduction in service availability of about 20–60 percent during that day. The simulations also showed, however, that in the center of the EGNOS coverage area (in the vicinity of northern Italy), the effect would have been much smaller with a reduction in service availability of only 5–6 percent over the day.

Such large storms are also often accompanied by displays of aurora (aurora borealis and aurora australis) at lower latitudes than normal. Figure 4 shows full-sky aurora observed near Fredericton, New Brunswick, Canada (46 degrees north latitude) on October 31, 2003

Figure 4. Photo of red and green auroras observed near Fredericton, New Brunswick, Canada (46 degrees north latitude) early on October 31, 2003. (Courtesy of Richard and Marg Langley.)

During a storm event on November 20, 2003, auroral activity was visible at mid-latitudes over most of North America as far south as Florida and in southern Europe including Italy and Greece.

Eruptions of the sun, often occurring in connection with high sunspot numbers, can have other effects besides the influence on GNSS-based positioning, navigation, and timing. Power-grid blackouts are known to have happened because of geomagnetic storms in connection with the sunspot peaks of both cycles 22 and 23 in 1989 and in 2003, respectively. For instance, the southern part of Sweden experienced a power blackout for several hours during the evening of October 30, 2003.

Also, orbiting satellites can experience problems with the increased radiation and solar wind density. Solar panels are, for instance,
susceptible to increased aging. And many types of satellite communication can be affected by increased ionospheric activity, not only GNSS satellite signals. Signals used for satellite phones, satellite TV, and so on can be affected.

Another phenomenon that can affect GNSS positioning is solar radio storms (also referred to as solar radio bursts) caused by events on the sun, often a solar flare, which creates radio waves that are emitted from the solar atmosphere and can propagate to the Earth where they cause an increased noise level in radio signals. Solar radio storms can cover a wide range of frequencies, including the frequencies used for GNSS. One such storm occurring on December 6, 2006, did affect GNSS positioning. With an increased noise level on the satellite signals, GNSS performance is reduced. If the noise level becomes too large, as a consequence of, for instance, a solar radio storm, GNSS receivers will lose lock on the GNSS signals, whereby positioning performance is further reduced or positioning might even be impossible. Solar radio storms are expected to happen more frequently during the peak of a solar cycle, but the event in December 2006 happened during a period with low solar activity, highlighting the fact that GNSS performance can be affected at any time, even when the sunspot number is low.

Predictions for the Next Solar High

Many predictions for the present solar cycle have been made. Because of the very long period with low solar activity during 2007–2009, some predictions expected a sudden outburst of activity and a very large cycle maximum, while other predictions foretold another increase in solar activity might not occur for many years.

However, with a general increase in the number of sunspots during 2010, it looks like we are now well into solar cycle number 24. Things can still change, but the current predictions say the maximum of the current solar cycle will be lower than the maximum of the last cycle encountered in 2001.

Predictions of sunspot numbers are based on history, logged information on sunspot numbers, and on observations of related geomagnetic activity.

The latest prediction for the current cycle as generated by NASA is shown in Figure 5.

Figure 5. Sunspot cycle 23 and predictions for cycle 24 from NASA’s Marshall Space Flight Center. (Image: NASA)

The curves in Figure 5 show the observed smoothed sunspot number, with smoothing over a period of a year or so, and the predicted value for the remainder of cycle number 24. The dotted lines indicate the observed or expected range of the monthly-averaged sunspot numbers. The plot is updated every month as new data is obtained.

The current prediction for cycle 24 gives a smoothed sunspot number maximum of about 59 in June/July of 2013. This peak is much lower than that of the previous cycle. We are currently two years into cycle 24 and the predicted size continues to fall. According to forecasters, predicting the behavior of a sunspot cycle is fairly reliable once the cycle is well under way (about three years after the minimum in sunspot number occurs). Prior to that time, the predictions are less reliable but nonetheless equally as important.

Even though the maximum of the current solar cycle is expected to be lower than the last peak, it is important for GNSS users to be aware of the effects to be expected during the coming years.

Consequences for GNSS Users

As discussed earlier in this article, GNSS users experience a general satellite signal delay caused by the ionosphere. This signal delay is always present but varies in size. The delay is generally well modeled by most receivers and software to an extent that makes GNSS useable for all of the purposes we know today.

During enhanced ionospheric activity, GNSS users can experience residual ionospheric effects, which can cause reduced positioning, navigation, and timing performance. In such cases, dual-frequency receivers might improve the situation because of the enhanced possibilities for handling the ionospheric effect with dual-frequency data.

During enhanced ionospheric or geomagnetic storm activity caused by sudden eruptions of the sun, increased ionospheric variability will occur. Apart from causing an increased ionospheric signal delay, and thereby increased residual effects in the positioning process, this will also cause increased scintillation effects. These might cause GNSS receivers to lose lock on some or all GNSS satellite signals, reducing performance of the GNSS receiver. In the few very worst cases, GNSS-based positioning, navigation, and timing might not be possible at all for a short interval of time during very high ionospheric activity.

These worst-case scenarios are more prone to happen close to the peak of a solar cycle, which we will meet next during 2013–2014.

However, it is worth noting that for the next peak of the solar cycle, we are much better prepared for the consequences than during the last cycle. GNSS software and receiver technology has been improved to better resist the challenges of increased ionospheric activity during this solar cycle. The improvements are based on experiences gained during the last solar cycles and are to the benefit of many GNSS users. For example, users of wide area augmentation systems such as WAAS and EGNOS have correction and integrity information available, which can be a great help in identifying time epochs when positioning and navigation solutions might not be trustable because of increased ionospheric activity. The integrity information is transmitted from geostationary satellites, and during time periods with extremely high ionospheric activity, the signals with integrity information might be disrupted. This should, however, be detected by the GNSS receiver, so warning messages will be displayed for navigators.

High-accuracy real-time kinematic (RTK) positioning is today often carried out with RTK correction data from a service provider generated using a network of reference stations. Here, indications of increased ionospheric activity can be detected by the software operated by the service provider, and warnings can be distributed to the RTK users.

Warning systems have been improved, and a number of sites on the Internet provide information on current and predicted ionospheric activity (see Further Reading).

Also, in the future, GNSS users will be able to benefit from the increased number of GNSS frequencies available. These frequencies open up opportunities for new and improved methods for correction of the ionospheric delay to the benefit of users who will experience more stable and reliable GNSS performance.

Summary and Conclusion

In this article we have reviewed the ionospheric effects on GNSS satellite signals, how these can be modeled and mitigated, and how they are related to solar activity and the number of sunspots. We have also described how sudden eruptions of the sun can cause increased ionospheric activity and how these events are often correlated with a high sunspot number. Some examples of consequences for GNSS users during the last solar high have been provided, and we have evaluated the predictions for the next solar high and possible consequences for GNSS users.

We are heading towards a period of increased solar activity. GNSS users must expect more disturbances compared to what we have seen for the last four to five years. The peak of the current solar cycle is expected to be lower than the last peak, and therefore consequences for GNSS users should also be less significant. Most of the time GNSS will work very well. But we will likely see a few days with major effects, and since the number of GNSS users is increasing, the overall consequences might also be more severe, not because the ionospheric activity is worse, but simply because more people will be affected.

ANNA B.O. JENSEN is the owner of AJ Geomatics in Copenhagen and a part-time associate professor of the National Space Institute at the Technical University of Denmark (DTU Space). She has a Ph.D. from the University of Copenhagen with co-supervision from the University of Calgary, and has worked in research and development within GNSS and geodesy for more than 15 years. Her current research interests include ionospheric modeling, high accuracy positioning, and navigation in the Arctic.

CATHRYN MITCHELL is a professor in the Department of Electronic and Electrical Engineering at the University of Bath in the United Kingdom and heads the INVERT Centre, which studies inverse problems and tomography over a range of scientific fields, including navigation, space science, and medical imaging. She has a Ph.D. from the University of Wales in Aberystwyth. Mitchell has a particular interest in the use of GNSS measurements to characterize and map the ionosphere.

FURTHER READING

• Introduction to the Ionosphere and Its Effects on GNSS
“The Perfect Solar Storm” by D.N. Baker and J.L. Green in Sky & Telescope, Vol. 121, No. 2, February 2011, pp. 28–34.

Severe Space Weather Events–Understanding Societal and Economic Impacts: A Workshop Report by the National Research Council Committee on the Societal and Economic Impacts of Severe Space Weather Events, published by National Academies Press, Washington, D.C., 2008; available on line: http://www.nap.edu/openbook.php?record_id=12507.

“A Beginner’s Guide to Space Weather and GPS” by P.M. Kintner, Jr., October 31, 2006; available on line: http://gps.ece.cornell.edu/SpaceWeatherIntro_ed2_10-31-06_ed.pdf.

“Combating the Perfect Storm: Improving Marine Differential GPS Accuracy with a Wide-Area Network” by S. Skone, R. Yousuf, and A. Coster in GPS World, Vol. 15, No. 10, October 2004, pp. 31–38.

“Space Weather: Monitoring the Ionosphere with GPS” by A. Coster, J. Foster, and P. Erickson in GPS World, Vol. 14, No. 5, May 2003, pp. 42–49.

The High-Latitude Ionosphere and its Effects on Radio Propagation by R.D. Hunsucker and J.K. Hargreaves, published by Cambridge University Press, Cambridge, U.K., 2002.

“GPS, the Ionosphere, and the Solar Maximum” by R.B. Langley in GPS World, Vol. 11, No. 7, July 2000, pp. 44–49.

• The Effects of the Halloween Storms on GNSS
“Impact of the Halloween 2003 Ionospheric Storm on Kinematic GPS Positioning in Europe” by N. Bergeot, C. Bruyninx, P. Defraigne, S. Pireaux, J. Legrand, E. Pottiaux, and Q. Baire in GPS Solutions, Online First, 2010, doi: 10.1007/s10291-010-0181-9.

“Assessment of EGNOS Performance Under Worst-Case Ionospheric Conditions (Solar Storm of October/November 2003)” by C. Montefusco, J. Ventura-Traveset, B. Arbesser-Rastburg, F. Froment, D. Flament, E. Tapias, S. Radicella, and R. Leitinger in EGNOS – The European Geostationary Navigation Overlay System – A Cornerstone of Galileo, ESA SP-1303, published by the European Space Agency Publications Division, Noorwijk, The Netherlands, 2006, pp. 259–268.

Halloween Space Weather Storms of 2003 by M. Weaver, W. Murtagh, C. Balch, D. Biesecker, L. Combs, M. Crown, K. Doggett, J. Kunches, H. Singer, and D. Zezula, NOAA Technical Memorandum OAR SEC-88, published by the Space Environment Center, National Oceanic and Atmospheric Administration, Office of Oceanic and Atmospheric Research, Boulder, Colorado, June 2004; available on line: http://www.swpc.noaa.gov/Services/HalloweenStorms_assessment.pdf

• Ionospheric Models and Corrections
“Ionospheric Delay Corrections for Single-Frequency GPS Receivers over Europe Using Tomographic Mapping” by D.J. Allain and C.N. Mitchell in GPS Solutions, Vol. 13, No. 2, 2009, pp. 141–151, doi: 10.1007/s10291-008-0107-y.

“Good, Better, Best: Expanding the Wide Area Augmentation System” by T.R. Schempp in GPS World, Vol. 19, No. 1, January 2008, pp. 62–67.

“Ionospheric Time-Delay Algorithm for Single-Frequency GPS Users” by J.A. Klobuchar in IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-23, No. 3, May 1987, pp. 325–331, doi: 10.1109/TAES.1987.310829.

“Global Ionosphere Maps Produced by CODE” on the website of the Astronomical Institute of the University of Bern, Bern, Switzerland: http://aiuws.unibe.ch/ionosphere/.

• Solar Cycle and Solar Weather Predictions:
“Solar Weather Event Modelling and Prediction” by M. Messerotti, F. Zuccarello, S.L. Guglielmino, V. Bothmer, J. Lilensten, G. Noci, M. Storini, and H. Lundstedt in Space Science Reviews, Vol. 147, 2009, pp. 121–185, doi: 10.1007/s11214-009-9574-x.

“Predicting Solar Cycle 24 and Beyond” by M.A. Clilverd, E. Clarke, T. Ulich, H. Rishbeth, and M.J. Jarvis in Space Weather, Vol. 4, S09005, 2006, doi: 10.1029/2005SW000207.

• Current Space Weather and Warnings
European Space Agency Space Weather Web Server, http://www.esa-spaceweather.net/spweather/current_sw/index.html

National Weather Service Space Weather Prediction Center, http://www.swpc.noaa.gov/

Swedish Institute of Space Physics (Institutet för rymdfysik) “Today’s and Recent Space Weather,” http://www.lund.irf.se/HeliosHome/spwfo.html

SpaceWeather.com – News and Information About the Sun-Earth Environment, http://www.spaceweather.com/

February 1, 2011
Innovation: The Distress Alerting Satellite System
Taking the Search out of Search and Rescue

By David W. Affens, Roy Dreibelbis, James E. Mentall, and George Theodorakos

In 1997, a Canadian government study determined that an improved search and rescue system would be one based on medium-Earth orbit satellites, which can provide full global coverage, can determine beacon location, and would need fewer ground stations. This month’s column examines the architecture of the GPS-based Distress Alerting Satellite System and takes a look at early test results.

INNOVATION INSIGHTS by Richard Langley

IT IS NOT COMMONLY KNOWN that the GPS satellites carry more than just navigation payloads. Beginning with the launch of the sixth Block I satellite in 1980, GPS satellites have carried sensors for the detection of nuclear weapons detonations to help monitor compliance with the Non-Proliferation Treaty. The payload is known as the Nuclear Detonation (NUDET) Detection System (NDS) and is jointly supported by the U.S. Air Force and the Department of Energy.

And now a third task is being assigned to the GPS satellites — that of search and rescue. Since the mid-1980s, a combination of low Earth orbit (LEO) and geostationary orbit (GEO) satellites have been used to detect and locate radio beacons activated by mariners, aviators, and others in distress virtually anywhere in the world and at any time. Some 28,000 lives have been saved worldwide since the search and rescue satellite-aided tracking, or SARSAT, system was implemented.

But the current system has some drawbacks. LEO satellites can determine a beacon’s position using the Doppler effect but their field-of-view is limited and one of them may not be in range when a beacon is activated. Furthermore, a large number of ground stations is needed to relay data from these satellites to search and rescue authorities. GEO satellites, on the other hand, have a large field of view (although missing parts of the Arctic and Antarctic), but they cannot position a beacon unless its signal contains location information provided by an integral satellite navigation receiver.

In 1997, a Canadian government study determined that a better SARSAT system would be one based on medium Earth orbit (MEO) satellites. A MEO system can provide full global coverage, determine beacon location, and do this with fewer ground stations. GPS was identified as the ideal MEO constellation.
And so was born the Distress Alerting Satellite System (DASS) that will become fully operational on Block III satellites. But already nine GPS satellites are hosting prototype hardware that is being used for proof-of-concept testing.

In this month’s column, we examine the architecture of DASS (including its relationship with the NDS), and take a look at some of the very positive test results already obtained — results that support the claim that DASS will take the search out of search and rescue.

NASA, which pioneered the technology used for the satellite-aided search and rescue capability that has saved thousands of lives worldwide since its inception nearly three decades ago, has developed new technology that will more quickly identify the locations of people in distress and reduce the risk to rescuers.

The Search and Rescue (SAR) Mission Office at the NASA Goddard Space Flight Center, in collaboration with several government agencies, has developed a next-generation satellite-aided search and rescue system, called the Distress Alerting Satellite System (DASS). NASA, the National Oceanic and Atmospheric Administration (NOAA), the U.S. Air Force, the U.S. Coast Guard, and other agencies are now completing the development and testing of the new system and expect to make it operational in the coming years after a complete constellation of DASS-equipped satellites is launched.

When completed, DASS will be able to almost instantaneously detect and locate distress signals generated by emergency beacons installed on aircraft and maritime vessels or carried by individuals, greatly enhancing the international community’s ability to rescue people in distress, This improved capability is made possible because the satellite-based instruments used to relay the emergency signals will be installed on the GPS satellites.

A recent satellite-aided rescue started on June 10, 2010, when 16-year-old Abby Sunderland on her 40-foot (12.2-meter) sailboat “Wild Eyes” encountered heavy seas approximately 2,000 miles (3,200 kilometers) west of Australia in the Indian Ocean. Her sailboat was dismasted and an emergency situation resulted. Ms. Sunderland activated her two emergency beacons whose signals were picked up by orbiting satellites. Using coordinates derived from the signals, a search plane spotted Ms. Sunderland the next day, and a day later she was rescued by a fishing boat directed to the scene. This highly publicized event is one of thousands of successful rescues made possible by years of NASA research and development.

Background

The beginnings of satellite-aided search and rescue date back to 1970, when a plane carrying two U.S congressmen crashed in a remote region of Alaska. A massive search and rescue effort was mounted, but to this day, no trace of them or their aircraft has ever been found. At the time, search for missing aircraft was conducted by search aircraft flying over thousands of square kilometers hoping to sight the missing aircraft. As a result of this tragedy, Congress recognized this inefficient search method and passed an amendment to the Occupational Safety and Health Act of 1970 requiring most aircraft flying in the United States to carry emergency locator beacons (ELTs) to provide a local homing capability. NASA then developed the technology to detect and locate an ELT from ground stations using the beacon signal relayed by satellites to provide more global coverage. This concept evolved into a highly successful international search and rescue system called COSPAS-SARSAT (COSPAS is an acronym for the Russian words “Cosmicheskaya Sistema Poiska Avariynyh Sudov,” which translates to “Space System for the Search of Vessels in Distress;” SARSAT is an acronym for Search and Rescue Satellite-Aided Tracking). Established by Canada, France, the United States, and the former Soviet Union in 1979, the system has 43 participating countries and has been instrumental in saving more than 28,000 lives worldwide, including 6,400 in the U.S. — all as a result of NASA’s innovations.

Since this auspicious beginning, NASA has continued to perform SAR research and development as a member of the National Search and Rescue Committee, and supports the National Search and Rescue Plan through an interagency memorandum of understanding with the Coast Guard, the Air Force, and NOAA. NOAA is responsible for operation of the U.S. portion of current COSPAS-SARSAT system that relies on SAR payloads on weather satellites in low-earth and geostationary orbits. As shown in Figure 1, the satellites relay distress signals from emergency beacons to a network of ground stations and ultimately to the U.S. Mission Control Center (USMCC) operated by NOAA. The USMCC distributes the alerts to the appropriate search and rescue authorities: the U.S. Air Force or the Coast Guard. The Air Force coordinates search and rescue for the mainland U.S. SAR region and operates the Air Force Rescue Coordination Center. The Coast Guard performs maritime search and rescue and oversees the U.S. national SAR policy.

FIGURE 1. Overall concept of search and rescue system. (Image: Cospas-Sarsat)

Beacons

Three types of distress emergency locator beacons are in use that are compatible with the COSPAS-SARSAT system:
- EPIRBs (emergency position-indicating radio beacons) designed for maritime use.
- ELTs (emergency locator transmitters) for use on aircraft.
- PLBs (personal locator beacons) for personal use. These can be used by persons engaged in high-risk activities such as mountain climbing and backcountry skiing.
Originally, emergency locator beacons transmitted an analog signal on two frequencies: 121.5 MHz and 243 MHz in the civil and military aeronautical communications bands, respectively, so that they would be audible over aircraft radios. Later, a signal that was encoded with a digital message and transmitted at 406 MHz was added. Since February 1, 2009, only the 406-MHz-encoded signals are relayed by satellites supporting the international COSPAS-SARSAT system. Therefore, older beacons that only transmit the 121.5/243-MHz signals are now only detectable by ground-based receivers and aircraft overflying a crash site.

The 406-MHz beacons transmit an approximately half-second message, or burst, approximately every 50 seconds, beginning 50 seconds after being activated. The actual time of burst transmission is dithered in time so that no two beacons will have all of their bursts coincident. A 406-MHz beacon may also have an integral global navigation satellite system (GNSS) receiver. Such a beacon uses the GNSS receiver to attempt to determine its location for inclusion in the transmitted digital message. In this way, the beacon will be located once it is detected by a low-Earth-orbit (LEO) or geostationary orbit (GEO) satellite.

Distress messages contain information such as:
- The beacon’s country of origin.
- A unique 15-digit hexadecimal beacon ID.
- Location, when equipped with an integrated GNSS receiver.
- Whether or not the beacon contains a 121.5-MHz homing signal.
Room for Improvement

SARSAT first became operational in the mid-1980s. The current system uses instruments placed on LEO and GEO weather satellites to detect and locate mariners, aviators, and recreational enthusiasts in distress almost anywhere in the world at anytime and in almost any condition. Previously, dedicated Russian LEO satellites were also implemented but the use of these satellites was discontinued in 2007.

Although it has proven its effectiveness, as evidenced by the number of persons rescued over the system’s lifetime, the current capability does have limitations. LEO spacecraft orbit the Earth 14 times a day and use the Doppler effect with satellite orbital ephemeris data to calculate the position of a beacon. However, a satellite may not be in a position to pick up a distress signal the moment a user activates the beacon. Time is critical in responding to an emergency situation. Unfortunately, delays of two hours or longer are possible, especially near the equator.

LEO spacecraft carry two instruments: a Search and Rescue Repeater (SARR) supplied by the Canadian Department of National Defence, and a Search and Rescue Processor (SARP) provided by the French Centre National d’Etudes Spatiales (CNES). The SARR is a pure repeater, which relays the beacon signal to a local ground station where the data is analyzed to obtain a location. The SARP processes the received beacon signal by measuring the Doppler shift as a function of time, and decoding the digital message included in the 406-MHz signal. This information is stored until it can be transmitted to a ground station using the SARR’s downlink transmitter. Under most conditions beacon locations can be determined to within a radius of 5 kilometers.

Geostationary weather satellites, on the other hand, orbit above the Earth in a fixed location over the equator. Although they do provide continuous visibility of much of the Earth, they cannot independently locate a beacon unless it contains a GNSS receiver that determines its position and includes it in the beacon’s digital message. Currently, not all beacons contain integral GNSS receivers. Furthermore, even if a beacon contains a GNSS receiver, the navigation signal may be obstructed by terrain or thick foliage.

The next-generation system, DASS, overcomes these limitations and will improve accuracy and response time to provide an even more capable life-saving system.

Distress Alerting Satellite System

A 1997 Canadian government study of possible alternative satellite systems for SARSAT, including commercial sources, determined that the ideal system is based on medium Earth orbit (MEO) satellites. A MEO system will be able to provide superior global detection and location data with fewer ground stations than the existing COSPAS-SARSAT system. The GPS constellation was identified as an ideal MEO platform.

The concept of the DASS system is straightforward. Three or more antennas track different GPS satellites equipped with search and rescue repeaters that receive the distress signal and retransmit the signal to the ground. Since each satellite is in a different orbit, each received signal has a different Doppler-shifted arrival frequency and time of arrival. Knowing the position and orbit of each satellite, it is possible to determine the position of the distress beacon.

Future improvement in location accuracy is made possible by one of the strengths of the DASS space segment. That is, the DASS location algorithm optimizes location accuracy utilizing time and frequency measurements of beacon signals that were not designed for that purpose. The DASS space segment allows for the beacon signal to be modified in the future, enhancing the performance of this type of location process.

Other advantages of DASS over the existing system are fairly obvious. Reception of the emergency signal is immediate. Locations can be determined after receiving a single beacon burst since it does not rely on measuring the Doppler shift over time to determine position, as in the current LEO system. A full constellation of DASS-equipped GPS satellites in orbit will ensure that four or more satellites are in view of the transmitting emergency beacon anywhere in the world while requiring fewer ground stations.

Another key strength of the DASS system is the promise of SARSAT transponders on each satellite in the large and well-managed GPS constellation. There are at least 24 GPS active satellites in orbit at any given time (currently, 31 are active). When the GPS constellation is fully populated by satellites with DASS transponders, it will provide global coverage for satellite-supported search and rescue and provide capabilities for rapid detection and location of distress beacons.

Efforts are ongoing to integrate a satellite beacon repeater instrument, to be provided by the Canadian government, onto the GPS Block III B and C satellites to provide the DASS space segment for operational use.

DASS Development

DASS development will proceed in phases referred to as the definition and development, proof of concept, demonstration and evaluation, initial operating capability, and final operating capability. The proof of concept (POC) phase was completed in January 2009. The POC testing and results are summarized in this article. At the time of this writing, preparations are ongoing to initiate the demonstration and evaluation phase.

Definition and Development. In 2000, as part of the definition and development phase, the NASA GSFC SAR Mission Office began discussions with the Department of Energy’s Sandia National Laboratories (SNL) to determine if it would be feasible to add a SAR repeater function to a Department of Energy (DOE) instrument on GPS satellites. Sandia representatives thought it possible, and NASA agreed to fund a study to determine if, with minor modification, one could include a search and rescue repeater function to their instrument. The SNL feasibility study concluded that the GPS DOE package could, with minor modifications, perform the SAR mission. The study also determined that accurate locations could be calculated after a single beacon transmission and improved with each subsequent beacon transmission. Based on this information, NASA, with the cooperation of the U.S. Air Force Space Command and SNL, proceeded with the development of the new space-based search and rescue system, which was named the Distress Alerting Satellite System.

Proof of Concept. In 2003, a memorandum of agreement (MOA) between NASA, NOAA, the Air Force, the Coast Guard, and the Department of Energy tasked NASA to perform a POC program for DASS. The MOA included the development of a POC space segment and a prototype ground station to perform post-launch checkout, performance testing, and implementation planning of an operational DASS system. It stressed the need for DASS, gave authority to each participating agency to participate in the POC demonstration, and defined the roles of each.

The Air Force Space Command approved the addition of modified equipment on GPS satellites. The DASS POC space segment operates as a subcomponent of GPS Block IIR and IIF satellites. Nine GPS Block IIR satellites carry experimental DASS payloads, and all 12 IIF satellites are scheduled to. Therefore, the final POC space segment will consist of 21 DASS-equipped GPS satellites. Each payload receives 406-MHz SAR signals on an extant GPS UHF antenna and relays the signals at a GPS S-band frequency on a second extant antenna.

It is important to note that the performance of the DASS POC space segment will be exceeded by the performance of the operational space segment being designed specifically for DASS and planned for launch on GPS Block III satellites.

A prototype DASS ground station (Figure 2) was funded by NASA and installed at GSFC. The DASS prototype ground system consists of four antennas, four receivers, and the workstations and servers necessary to process the received data, command and control the operation of the ground station, and display and analyze the results. The antennas are located on the corners of the roof of a building connected by fiber-optic cable to signal processing equipment located in another building two kilometers away.

FIGURE 2. Prototype ground station at NASA GSFC. (Images: NASA)

Proof of Concept Testing

The overall objectives of the POC tests were to demonstrate the effectiveness of the DASS concept and to define its technical and operational characteristics. The primary technical objective was to demonstrate the system’s ability to detect and locate 406-MHz emergency beacons under various controlled conditions. This is the most important measure of the system’s ability to perform as expected.

The specific objectives of the DASS POC demonstration were to
- Confirm the expected performance of the DASS concept.
- Determine if new or enhanced requirements needed to be established.
- Define preliminary performance levels that will be used to establish the scope and content of the next phase of development, referred to as the demonstration and evaluation phase.
Therefore, during POC testing, performance measurements were taken for the probability of detection, probability of location, and location accuracy, defined as follows.
- Probability of detection is the probability of detecting the transmission of a 406-MHz beacon and recovering a valid beacon message from any available satellite.
- Probability of location is the probability of obtaining a location solution within a given time after beacon activation, independently of any encoded position data in the 406-MHz beacon message.
- Location accuracy is the distance from the location solution obtained within 5 minutes after beacon activation, to the actual beacon location. The required performance is specified as the probability that a given solution is within a given distance of the actual location.
It is important to note that the predicted performance of DASS assumes a full constellation of DASS-equipped GPS satellites. In fact, one of the key strengths of DASS is the promise of DASS transponders on each satellite in the GPS constellation. When a full constellation is equipped with DASS transponders, there will typically be between seven and 13 GPS satellites visible at the NASA ground station. Thus, it will be possible to schedule the ground-station antennas to receive data from the best satellites in terms of geometry, signal strength, processing capability, and other factors.

However, at the time of the POC testing, there were only eight GPS satellites equipped with DASS transponders. A maximum of three DASS-equipped GPS satellites were visible at the same time at the NASA ground station (above a 15-degree elevation angle), and there were times when only one DASS-equipped GPS satellite was visible. Thus, it was impossible to optimize satellite selection since there was never an opportunity to select from an excess of satellites that a full constellation would provide.

In particular, satellite geometry and its effect on performance is never as optimal as what would be obtained from a full constellation of GPS satellites. To predict the results of a full constellation using the results from a severely reduced constellation, a calculation based on “dilution of precision” was used.

Dilution of precision (DOP) or geometric dilution of precision, to be specific, is used to describe the geometric strength of satellite configuration on GPS accuracy. When visible satellites are close together in the sky, the geometry is said to be weak and the DOP value is high; when far apart, the geometry is strong and the DOP value is low. Thus a low DOP value gives rise to a better GPS positional accuracy due to the wider angular separation between the satellites used to calculate a beacon’s position.

Location accuracy results can be scaled to reflect the true DOP that would be obtained by a satellite constellation of 24 GPS satellites. The DOP error caused by uncertainty in time and frequency measurements is used for scaling. The DOP of the satellites actually used to calculate a location solution, denoted by ftDOP_ACT, is always bigger than the DOP that would have been available from a constellation of 24 GPS satellites, ftDOP₂₄. The raw location errors need to be multiplied by the ratio ftDOP₂₄ / ftDOP_ACT to reflect the results that would have been obtained if all 24 satellites were present.

The raw average location error, err_avg, is given by the following:

err(b) = err(lat(b),lon(b))= distance from the known location to (lat(b),lon(b))

err_avg(b₀) = err(lat_avg(b₀),lon_avg(b₀))

where Ω(b₀) is the set of seven or fewer consecutive burst locations within 5 minutes, starting with burst b₀.

The scaled location error is the location error scaled by the DOP ratio:

Since DOP changes little over 5 minutes, the error of the average is approximately

where ftDOP_ACT(b) is the time-frequency DOP of burst b calculated with either three or four satellite geometries depending on
the number of measurements used in the location calculation.

Test Source

A custom-designed beacon simulator was used to generate the transmissions of multiple COSPAS-SARSAT 406-MHz beacons over an extended period of time. To represent expected operational realism in the tests, the beacon simulator was used to transmit beacons at the limits of the five major beacon parameters specified by COSPAS-SARSAT as well as the nominal values. The five major beacon parameters are transmit power, modulation index, bit rate, un-modulated carrier duration, and modulation rise and fall times (see TABLE 1).

Table 1. Cospas-Sarsat beacon specifications. (Data: Cospas-Sarsat)

During POC testing, five beacons were transmitted using three scenarios: maximum beacon parameter values, minimum beacon parameter values, and variable power. The parameter values changed in each test scenario and are highlighted in TABLE 2. Beacon detection and location performance is measured for periods when there are three or more satellites visible at the same time, and for durations sufficient to collect a statistically significant amount of data.

Table 2. Beacon parameter values for each test scenario. (Data: Authors)

Two characteristics of the test source that affect system performance are the beacon antenna pattern and ground mask. To simulate beacons, the beacon simulator has a monopole antenna with the gain pattern shown in Figure 3. There is a substantial reduction in the transmitted signal at high-elevation angles (above 60°). DASS-equipped GPS satellites are often at high-elevation angles during a typical day. As expected, the effect of the pattern on test results can clearly be seen upon close inspection of the data. However, the beacon antenna pattern is an unavoidable reality and is, therefore, fully represented in the data used to generate the results presented here. Additionally, there were significant ground obstructions of the beacon signal in certain directions. The effect of beacon antenna pattern is fully included in the results presented in this article, but ground mask is taken into account by limiting satellite visibility to an elevation cut-off angle of 15 degrees.

FIGURE 3. Beacon simulator transmit antenna gain pattern.

POC Test Results

In this section, we discuss the POC test results in terms of probability of detection, probability of location, and location accuracy.

Probability of Detection. As previously mentioned, probability of detection is the probability of detecting the transmission of a 406-MHz beacon and recovering a valid beacon message from any available satellite. The requirement is that 95 percent of individual transmitted messages are detected.

Test results are given in TABLE 3 and show that the probability of detection is approximately 99 percent for all scenarios, even though only three satellites were in view at a time. Obviously, the probability of detection is dependent on the number of available satellites and performance would improve with continuous coverage by four or more satellites.

Table 3. Probability of detection test results. (Data: Authors)

Probability of Location. Again, the probability of location is the probability of obtaining a location solution within a given time after beacon activation, independently of any encoded position data in the 406-MHz beacon message. The requirement is that the probability of calculating a beacon location is 98 percent within 5 minutes.

Since the probability of location is dependent on the number of visible satellites, our performance was limited by the reduced constellation of DASS-equipped satellites. Results from periods of three-satellite coverage were 85 percent within 5 minutes, 92 percent within 10 minutes, and 94 percent within 15 minutes.

Again, the probability of location is dependent on the number of visible satellites, and performance would improve with continuous coverage by four or more satellites. To investigate the possible improvement with enhanced satellite coverage, we reduced the minimum satellite elevation angle from 15 to 10 degrees. This allowed a fourth satellite to become visible for a limited time at very low elevation angles. Even though the signal quality from such a satellite was poor, the probability of location during this period of four-satellite coverage improved as follows: 91 percent within 5 minutes, 96 percent within 10 minutes, and 97 percent within 15 minutes.

As can be seen from these results, even adding a satellite with a very low elevation-angle pass significantly improves performance. The expectation is that having a full constellation of satellites available would improve performance even more. Furthermore, the increase in satellite performance expected in the operational system will also improve probabilities of detection and location.

Location Accuracy. Recall that location accuracy is measured as the percentage of location solutions obtained within five minutes after beacon activation that are within five kilometers of the actual beacon location.

The requirement is to obtain 95 percent of the locations to within 5 kilometers of the actual location and 98 percent within 10 kilometers within five minutes after beacon activation.

As mentioned earlier, the requirements included in the performance specification assume a constellation of 24 DASS-equipped GPS satellites. POC testing was done with a system that had only eight DASS-equipped GPS satellites available. However, location errors can be scaled to reflect what the DOP would be if the satellite constellation contained all 24 GPS satellites. Therefore, it is the scaled results that can be used to determine whether performance will meet the requirement.

TABLE 4, therefore, presents the location accuracy results as measured, and after being scaled by DOP.

Table 4. Location accuracy for 5-minute periods. (Data: Authors)

Another important performance metric for DASS is location accuracy obtained after a single beacon burst is received. Even though there is not currently a requirement for single burst location accuracy, it is a very desirable feature of DASS since an emergency situation does not guarantee that more than a single burst will be received. Single burst location accuracy was, therefore, measured with the results shown in TABLE 5. Once again, the results are scaled by DOP values to remove the effect of non-optimal satellite geometry.

Table 5. Single burst location accuracy. (Data: Authors)

More insight into this performance can be gained by examining the single burst location accuracy distribution as a function of distance error, as shown in TABLE 6. It can be seen that, for these beacons, computed locations are within 9 kilometers of the actual location 95 percent of the time. Again, the expectation is that having a full constellation of satellites available would improve this performance. For instance, having more satellites to choose from might allow the system to select data from satellites with stronger or less noisy links.

Table 6. Single burst location accuracy by distance error. (Data authors)

Conclusion

The promise of search and rescue instruments on each satellite in the large and well-managed GPS constellation will provide a significant advancement in the capabilities of the already highly successful COSPAS-SARSAT system. The new system will provide global coverage for satellite-supported search and rescue and provide capabilities for rapid detection and location of distress beacons while requiring fewer ground stations.

The DASS POC system has validated, by test, the predictions made by analysis during the definition and development phase. The DASS POC testing has demonstrated reliable detection and accurate location of beacons within five minutes of activation. Accurate locations are also produced after even a single burst of a newly activated beacon, which is a desirable feature of DASS, since an emergency situation does not guarantee that more than a single burst will be received.

The performance obtained using a reduced constellation of satellites equipped with a modified, existing instrument not only demonstrates the existing capability, but also confirms the improvements to come with the operational system. In fact, the success of DASS is being emulated by the European Union in the design of their future Galileo GNSS constellation and the Russians in an upgraded GLONASS GNSS constellation, all of which will be interoperable by international agreement.

DASS will contribute to NASA’s goal of taking the search out of search and rescue. Achieving this goal will not only improve the chances of rescuing people in distress quickly, which is critical to their survival; it will also reduce the risk to rescuers who often put themselves in dangerous situations to affect a rescue. That is why the motto of the Search and Rescue Office is “Saving more lives, reducing risks to search personnel, and saving resources.”

David W. Affens is the manager of the NASA Search and Rescue (SAR) Mission Office at the Goddard Space Flight Center (GSFC) in Greenbelt, Maryland, where he began working in 1990. He holds a degree in electronic engineering. Before joining NASA, he worked in various aspects of submarine warfare and intelligence gathering for the U.S. Navy over a span of 21 years.

Roy Dreibelbis is a consultant who has worked in rescue-related jobs since 1957, including helicopter rescue missions in Vietnam. As an officer in the U.S. Air Force, he was the director of Inland SAR at rescue headquarters for the coterminous 48 states, was commander of the 33rd Air Rescue Squadron, and served as deputy chief of staff for rescue operations at rescue headquarters from 1979 until 1981. Upon retirement from the Air Force, he was employed by the State of Louisiana as flight operations director and chief pilot. In 1987, he accepted employment with contractors in the District of Columbia area that supported NASA and NOAA SARSAT activities.

James E. Mentall is the NASA/GSFC Search and Rescue Instrument Manager. He has a Ph.D. in physics and has spent more than 42 years of his professional life at GSFC. For 15 of those years, he has been responsible for the integration and test of the Search and Rescue Repeater and the Search and Rescue Processor on the NOAA Polar-orbiting Operational Weather Satellites. He has also served as the deputy mission manager for the Search and Rescue Mission Office and played a significant role in the procurement of the DASS antenna system and ground station.

George Theodorakos is the chief staff engineer for MEI Technologies, Inc. He received his B.S. summa cum laude and M.S. degrees in electrical engineering from the University of Maryland, College Park, Maryland, in 1978 and 1987, respectively. Since 2002, in his role as chief staff engineer at MEI, he has provided technical management support to the Search and Rescue Mission Office at GSFC.

FURTHER READING

• Distress Alerting Satellite System (DASS)
“Distress Alerting Satellite System (DASS)” on the NASA Search and Rescue Mission Office website, Goddard Space Flight Center, Greenbelt, Maryland.

• Search and Rescue Satellite-Aided Tracking (SARSAT)
“Search and Rescue,” Chapter 6 in Review of the Space Communications Program of NASA’s Space Operations Mission Directorate by the Committee to Review NASA’s Space Communications Program, Aeronautics and Space Engineering Board, Division on Engineering and Physical Sciences, National Research Council, published by the National Academies Press, Washington, D.C., 2007.

National Search and Rescue Plan of the United States, authored on behalf of the National Search and Rescue Committee by the United States Coast Guard, Washington, D.C.

• Medium Earth Orbit Search and Rescue (MEOSAR) Systems
COSPAS-SARSAT 406 MHz MEOSAR Implementation Plan, C/S R.012 Issue 1 —Revision 6 October 2010, COSPAS-SARSAT Secretariat, Montréal, Canada.

“SAR/Galileo Early Service Demonstration & the MEOLUT Terminal” by Indra Espacio, a presentation at Galileo Application Days, Brussels, Belgium, March 3–5 2010.

“Mid-Earth Orbiting Search and Rescue (MEOSAR) Transition to Operations” by C. O’Connors, a presentation at the Rescue Coordination Centers Controller Conference, Suitland, Maryland, February 23–25, 2010.

“Overview of MEOSAR System Status” by J. King, a presentation at BMW-2009, Beacon Manufacturers Workshop, St. Pete Beach, May 8, 2009.

“MEOSAR to the Rescue” by J. King in Channels, the EMS SATCOM Quarterly, published by EMS Technologies, Inc., January 31, 2007.

• Nuclear Detonation (NUDET) Detection System
“Detecting Nuclear Detonations with GPS” by P.R. Higbie and N.K. Blocker in GPS World, Vol. 5, No. 2, February 1994, pp. 48–50.
January 1, 2011