A performance assessment demonstrates the ability of a networked group of users to locate themselves and each other, navigate, and operate under adverse conditions in which an individual user would be impaired. The technique for robust GPS positioning in a dynamic sensor network uses a distributed GPS aperture and RF ranging signals among the network nodes.
By Dorota A. Grejner-Brzezinska, Charles Toth, Inder Jeet Gupta, Leilei Li, and Xiankun Wang
In situations where GPS signals are subject to potential degradations, users may operate together, using partial satellite signal information combined from multiple users. Thus, collectively, a network of GPS users (hereafter referred to as network nodes) may be able to receive sufficient satellite signals, augmented by inter-nodal ranging measurements and other sensors, such as inertial measurement unit (IMU), in order to form a joint position solution.
This methodology applies to numerous U.S. Department of Defense and civilian applications, including navigation of dismounted soldiers, emergency crews, on-the-fly formation of robots, or unmanned aerial vehicle (UAV) swarms collecting intelligence, disaster or environmental information, and so on, which heavily depend on availability of GPS signals. That availability may be degraded by a variety of factors such as loss of lock (for example, urban canyons and other confined and indoor environments), multipath, and interference/jamming. In such environments, using the traditional GPS receiver approach, individual or all users in the area may be denied the ability to navigate.
A network of GPS receivers can in these instances represent a spatially diverse distributed aperture, which may be capable of obtaining gain and interference mitigation. Further mitigation is possible if selected users (nodes) use an antenna array rather than a single-element antenna. In addition to the problem of distributed GPS aperture, RF ranging among network nodes and node geometry/connectivity forms another topic relevant to collaborative navigation. The challenge here is to select nodes, which can receive GPS signals reliably, further enhanced by the distributed GPS aperture, to serve as pseudo-satellites for the purpose of positioning the remaining nodes in the network.
Collaborative navigation follows from the multi-sensor navigation approach, developed over the past several years, where GPS augmentation was provided for each user individually by such sensors as IMUs, barometers, magnetometers, odometers, digital compasses, and so on, for applications ranging from pedestrian navigation to georegistration of remote sensing sensors in land-based and airborne platforms.
Collaborative Navigation
The key components of a collaborative network system are
inter-nodal ranging sub-system (each user can be considered as a node of a dynamic network);
optimization of dynamic network configuration;
time synchronization;
optimum distributed GPS aperture size for a given number of nodes;
communication sub-system; and
selection of master or anchor nodes.
Figure 1 illustrates the concept of collaborative navigation in a dynamic network environment. Sub-networks of users navigating jointly can be created ad hoc, as indicated by the circles. Some nodes (users) may be parts of different sub-networks.
FIGURE 1. Collaborative navigation concept.
In a larger network, the selection of a sub-network of nodes is an important issue, as in case of a large number of users in the entire network, computational and communication loads may not allow for the entire network to be treated as one entity. Still, information exchange among the sub-networks must be assured.
Conceptually, the sub-networks can consist of nodes of equal hierarchy or may contain master (anchor) nodes that normally have a better set of sensors and collect measurements from all client nodes to perform a collaborative navigation solution. Table 1 lists example sensors and techniques that can be used in collaborative navigation.
TABLE 1. Typical sensors for multi-sensor integration: observables and their characteristics, where X,Y,Z are the 3D coordinates, vx, vy, vz are the 3D velocities,
The concept of a master node is also crucial from the stand point of distributed GPS aperture, where it is mandatory to have master nodes responsible for combining the available GPS signals.
Master nodes or some selected nodes will need anti-jamming protection to be effective in challenged electromagnetic (EM) environments. These nodes may have stand-alone anti-jamming protection systems, or can use the signals received by antennas at various nodes for nulling the interfering signals.
Research Challenges
Finding a solution that renders navigation for every GPS user within the network is challenging. For example, within the network, some GPS nodes may have no access to any of the satellite signals, and others may have access to one or more satellite signals. Also, the satellite signals received collectively within the network of users may or may not have enough information to determine uniquely the configuration of the network.
A methodology to integrate sensory data for various nodes to find a joint navigation solution should take into account:
acquisition of reliable range measurements between nodes (including longer inter-nodal distances);
limitation of inter-nodal communication (RF signal strength);
assuring time synchronization between sensors and nodes; and
limiting computational burden for real time applications.
Distributed GPS Apertures
In the case of GPS signal degradation due to increased path loss and radio frequency interference (RFI), one can use an antenna array at the receiver site to increase the gain in the satellite signal direction as well as steer spatial nulls in the interfering signal directions. For a network of GPS users, one may be able to combine the signals received at various receivers (nodes) to achieve these goals (beam pointing and null steering); see Figure 2.
Figure 2. Distributed antenna array.
However, a network of GPS users represents a distributed antenna aperture with large (hundreds of wavelengths) inter-element spacing. This large thinned antenna aperture has some advantage and many drawbacks. The main advantage is increased spatial resolution which allows one to discriminate between signals sources with small angular separations. The main drawback is very high sidelobes (in fact, grating lobes) which manifest as grating nulls (sympathetic nulls) in null steering. The increased inter-element spacing will also lead to the loss of correlation between the signals received at various nodes. Thus, space-only processing will not be sufficient to increase SNR by combining the satellite signals received at various nodes. One has to account for the large delay between the signals received at various nodes.
Similarly, for adaptive null steering, one has to use space-time adaptive processing (STAP) for proper operation. These research challenges must be solved for distributed GPS aperture to become a reality:
Investigate the increase in SNR that can be obtained by employing distributed GPS apertures (accounting for inaccuracies in the inter-nodal ranging measurements).
Investigate the improvement in the signal-to-interference-plus-noise ratio (SINR) that can be obtained over the upper hemisphere when a distributed GPS aperture is used for adaptive null steering to suppress RFI in GPS receivers. Obtain an upper bound for inter-node distances.
Based on the results of the above two investigations, develop approaches for combined beam pointing and null steering using distributed GPS apertures.
Inter-Nodal Ranging Techniques
In a wireless sensor network, an RF signal can be used to measure ranges between the nodes in various modes. For example, WLAN observes the RF signal strength, and UWB measures the time of arrival, time difference of arrival, or the angle of arrival. There are known challenges, for example, signal fading, interference or multipath, to address for a RF-based technique to reliably serve as internodal ranging method.
Ranging Based on Optical Sensing. Inter-nodal range measurements can be also acquired by active and passive imaging sensors, such as laser and optical imaging sensors. Laser range finders that operate in the eye-safe spectrum range can provide direct range measurements, but the identification of the object is difficult. Thus, laser scanners are preferred, delivering 3D data at the sensor level. Using passive imagery, such as digital cameras, provides a 2D observation of the object space; more information is needed to recover 3D information; the most typical techniques is the use of stereo pairs or, more generally, multiple-image coverage. The laser has advantages over optical imagery as it preserves the 3D object shapes, though laser data is more subject to artifacts due to non-instantaneous image formation.
In general, regardless whether 2D or 3D imagery is used, the challenge is to recognize the landmark under various conditions, such as occlusions and rotation of the objects, when the appearance of the landmark alternates and the reference point on the landmark needs to be accurately identified, to compute the range to the reference point with sufficient accuracy.
Network Configuration
Nodes in the ad hoc network must be localized and ordered considering conditions, such as type of sensors on the node (grade of the IMU), anti-jamming capability, positional accuracy, accuracy of inter-nodal ranging technique, geometric configuration, computational cost requirements, and so on. There are two primary types of network configurations used in collaborative navigation: centralized and distributed.
Centralized configuration is based on the concept of server/master and client nodes.
Distributed configuration refers to the case where nodes in the network can be configured without a master node, that is, each node can be considered equal with respect to other nodes.
Sensor Integration
The selection of data integration method is an important task; it should focus on arriving at an optimal solution not only in terms of the accuracy but also taking the computational burden into account. The two primary options are centralized and decentralized extended Kalman filter (EKF).
Centralized filter (CF) represents globally optimal estimation accuracy for the implemented system models.
Decentralized filter (DF) is based on a collection of local filters whose solutions can be combined by a single master filter. DFs can be further categorized based on information-sharing principles and implementation modes.
Centralized, Decentralized EKF. These two methods can provide comparable results, with similar computational costs for networks up to 30 nodes. Figures 3–5 describe example architectures of centralized/decentralized EKF algorithms.
In Figure 3, all measurements collected at the nodes and the inter-nodal range measurements are processed by a single centralized EKF. Figures 4 and 5 illustrate the decentralized EKF with the primary difference between them being in the methods of applying the inter-nodal range measurements. The range measurements are integrated with the observations of each node by separate EKF per node in Figure 4, while Figure 5 applies the master filter to integrate the range measurements with the EKF results of all participating nodes.
To provide a preliminary performance evaluation of an example network operating in collaborative mode, simulated data sets and actual field data were used. Figure 6 illustrates the field test configuration, showing three types of nodes, whose trajectories were generated and analyzed.
FIGURE 6. Collaborative navigation field test configuration.
Nodes A1, A2, and A3 were equipped with GPS and tactical grade IMU, node B1 was equipped with GPS and a consumer grade IMU, and node C1 was equipped with a consumer grade IMU only. The following assumptions were used: all nodes were able to communicate; all sensor nodes were time-synchronized; nodal range measurements were simulated from GPS coordinates of all nodes; and the accuracy of GPS position solution was 1–2 meters/coordinate (1s); the accuracy of inter-nodal range measurements was 0.1meters (1s); all measurements were available at 1 Hz rate; the distances between nodes varied from 7 to 70 meters.
Individual Navigation Solution. To generate the navigation solution for specific nodes, either IMU or GPS measurements or both were used. Since the reference trajectory was known, the absolute value of the differences between the navigation solution (trajectory) and the reference trajectory (ground truth) were considered as the navigation solution error. Figure 7 illustrates the absolute position error for the sample of 60 seconds of simulated data, with a 30-second GPS outage for nodes A1, A2, A3 and B1 (node C1 is not shown, as its error in the end of the test period was substantially bigger than that of the remaining nodes. Table 2 shows the statistics of the errors of each individual node’s trajectory for different sensor configurations.
FIGURE 7. GPS/IMU positioning error for A1, A2, A3, B1 (includes a 30-second GPS outage.)
Collaborative Solution. In this example, collaborative navigation is implemented after acquiring the individual navigation solution of each node, which was estimated with the local sensor measurements. The collaborative navigation solution is formed by integrating the inter-nodal range measurements to other nodes in a decentralized Kalman filter, which is referred to as “loose coupling of inter-nodal range measurements.” The test results of different scenarios are listed in Table 3. For cases labeled “30-sec GPS outage,” the GPS outage is assumed at all nodes that are equipped with GPS. The results listed in Table 3 indicate a clear advantage of collaborative navigation for nodes with tactical and consumer grade IMUs, particularly during GPS outages. When GPS is available (see, for example, node A1) the individual and collaborative solutions are of comparable accuracy.
The next experiment used tight coupling of inter-nodal range measurements at each node’s EKF in order to calibrate observable IMU errors even during GPS outages. In addition, varying numbers of master nodes are considered in this example. The tested data set was 600 seconds long, with repeated simulated 60-second GPS gaps, separated by 10-second periods of signal availability. The inter-nodal ranges were ~20 meters.
Table 4 and Figure 8 summarize the navigation solution errors for collaborative solution of node C1 equipped with consumer grade IMU only, supported by varying quality other nodes. The error of the individual solution for this node in the end of the 600-second period reach nearly 250 kilometers (2D). Even for the case with a single anchor node (A1), the accuracy of the 2D solution is always better than 2 meters. Another 900-second experimental data with repeated GPS 60-second gaps on B1 node was analyzed with inter-nodal ranging up to 150 meters. Table 5 summarizes the results for C1 node.
FIGURE 8. Absolute error for IMU-only and collaborative navigation solutions of C1 (GPS outage.)
Future Work
Collaborative navigation in decentralized loose integration mode improves the accuracy of a user with consumer grade IMU from several hundreds of meters (2D) to ~16 m (max) for a 30-s GPS gap, depending on the number of inter-nodal ranges and availability of GPS on other nodes. For a platform with GPS and consumer grade IMU (node B1) the improvement is from a few tens of meters to below 10 m.
Better results were obtained when tight integration mode was applied, that is, inter-nodal range measurements were included directly in each EKF that handles measurement data collected by each individual node (architecture shown in Figure 4). For repeated 60-second GPS gaps, separated by 10-second signal availability, collaborative navigation maintains the accuracy at ~1–2 meter level for entire 600 s tested for nodes C1 and B1.
Even though the preliminary simulation results are promising, more extended dynamic models and operational scenarios should be tested. Moreover, it is necessary to test the decentralized scenarios 1 and 2 (Figures 4–5) and then compare them with the centralized integration model shown in Figure 3. Ad hoc network formation algorithm should be further investigated.
FIGURE 9. Absolute errors in collaborative navigation solutions of C1.
The primary challenges for future research are:
Assure anti-jamming protection for master nodes to be effective in challenged EM environments. These nodes can have stand alone anti-jamming protection system, or can use the signals received by antennas at various nodes for nulling the interfering signals.
Since network of GPS users, represents a distributed antenna aperture with large inter-element spacing, it can be used for nulling the interfering signals. However, the main challenge is to develop approaches for combined beam pointing and null steering using distributed GPS apertures.
Formulate a methodology to integrate sensory data for various nodes to obtain a joint navigation solution.
Obtain reliable range measurements between nodes (including longer inter-nodal distances).
Assess limitations of inter-nodal communication (RF signal strength).
Assure time synchronization between sensors and nodes.
Assess computational burden for the real time application.
Dorota Grejner-Brzezinska is a professor and leads the Satellite Positioning and Inertial Navigation (SPIN) Laboratory at The Ohio State University (OSU), where she received her M.S. and Ph.D. in geodetic science. Charles Toth is a senior research scientist at OSU’s Center for Mapping. He received a Ph.D. in electrical engineering and geoinformation sciences from the Technical University of Budapest, Hungary. Inder Jeet Gupta is a research professor in the Electrical and Computer Engineering Department of OSU. He received a Ph.D. in electrical engineering from OSU. Leilei Li is a visiting graduate student at SPIN Lab at OSU. Xiankun Wang is a Ph.D. candidate in geodetic science at OSU
Spectracom’s new 8-channel GPS constellation simulator, the Pendulum GSG-54, provides a wide-range of capabilities for in-line production testing of devices integrating GPS receivers due to its ease-of-operation and fast test cycles, according to the company. Its versatility also supports engineering organizations’ efforts for integrating GPS receivers into devices under development.
As more and more electronic devices integrate GPS receivers, manufacturers require instrumentation to fully test the GPS capabilities of each device on the manufacturing floor. According to Staffan Johansson, Spectracom product manager, “We understand the need for high-throughput manufacturing testing of GPS receivers. A multi-channel GPS simulator must be easy to use, yet powerful enough to confirm each device’s performance under a variety of real-world conditions.”
The Pendulum GSG-54 simulates the satellite signals detected by a GPS receiver. It comes in a bench-top chassis that is compact and portable. It offers built-in standards-based test scenarios that can be initiated or modified on the fly from the intuitive front panel interface, and offers a variety of connectivity options to control and reconfigure test parameters, Spectracom said.
The GSG-54 GPS constellation simulator builds on the features available from Spectracom’s GSG-L1 single-channel GPS signal generator that offers simple but fast assembly verification for functions such as antenna connectivity, receiver operation, or satellite signal identification. The GSG-54 provides for many more test cases due to its ability to simulate eight different satellite signals to test position accuracy, sensitivity to loss of satellite signals, timing accuracy, and dynamic range. It can simulate movements and user trajectories, multi-path scenarios and various other atmospheric conditions.
“Like our other products, the GSG-54 offers the lowest cost of ownership for manufacturers and development engineers by providing complete testing of multi-channel GPS performance with high throughput and ease-of-use without unnecessary complexity or expense,” said Lisa Withers, president and CEO of Spectracom.
By Bradford W. Parkinson and Stephen T. Powers, with Gaylord Green, Hugo Fruehauf, Brock Strom, Steve Gilbert, Walt Melton, Bill Huston, Ed Martin, James Spilker, Fran Natali, Joe Strada, Burt Glazer, Dick Schwartz, Len Jacobson, AJ Van Dierendonck, and others.
GPS Phase I program approval meant that the real work could begin. The conclusion of a two-part history, told by the people who made it.
By January 1974, the GPS program at the Joint Program Office (JPO) was well underway. With only about 30 officers, the workload was enormous. Fortunately, the Aerospace cadre of about 25 also made extraordinary contributions. In a flurry of activity, the team developed requests for proposals, made top-level specifications, and published initial interface control documents. The work of converting viewgraphs into real hardware, as many know, is an exacting and sometimes painful process.
Of course there were many challenges, but five of them, principally engineering, stand out as particularly daunting. These were:
Defining the specific details of the GPS CDMA signal structure;
Achieving rapid and accurate satellite orbit prediction;
Ensuring and demonstrating spacecraft longevity approaching ten years;
Developing a full family of GPS user equipment.
We discuss each challenge in detail, including the names of those most instrumental in meeting them. The first appearances of their names are highlighted, although if they appeared in Part 1 of this story (May 2010 issue), their names are not highlighted.
EARLY GPS MANPACK worn by JPO Army deputy Lt. Col. Paul Weber. This photo graced the cover of the first-ever GPS brochure! (Credit: Bradford W. Parkinson and Stephen T. Powers)
Challenge 1.Defining the specific details of the GPS CDMA signal structure (coherence, acquisition, spreading, communication protocol, structure, error correction, message structure, and so on).
The selection of the GPS signal structure was broadly confirmed with the tests that were run by program 621B at the White Sands Missile Range with the help of Joe Clifford, Bill Fees, and Larry Hagerman, all from the Aerospace Corporation.
While the fundamental decision to select CDMA had been made during the Lonely Halls meeting, a vast number of details had yet to be worked out. Fortunately, there were many earlier studies of the signal. Dr. Jim Spilker (then of Philco Ford), who had also written the major reference book on digital communications, authored one of the studies. Dr. Charles Cahn, Nat Natali, Burt Glazer, Ed Martin, and Dr. Robert Gold of Magnavox all made significant contributions. One of the most important details was the decision that the carrier, code, and data of the GPS signal would all be phase-coherent (Figure 1). As discussed later, this decision enabled much of the precision that we now see in advanced GPS receivers.
FIGURE 1. GPS signals were designed to be all aligned as transmitted, that is, coherent. (Courtesy Misra and Enge, Global Positioning System).
The exact Gold codes family had to be selected from the original family, since Dr. Gold’s technique did not include the natural Doppler shifts. The data message was integrated into both the civil (C/A ) and military (P/Y) signals through inversion of their codes every 20 milliseconds.
To work out the details of the data message, the JPO had a strong team including Major Mel Birnbaum, Col. Brock Strom, and Capt. Bob Rennard. Outside contractors making major contributions included Dr. Fran Natali, Dr. A. J. Van Dierendonck, and others. Van Dierendonck played a particularly effective role in helping define “GPS time.” This sounds rather mundane, but had some very interesting complexity. Jim Spilker recommended the 1023-bit message length to avoid a correlation problem associated with Doppler shifts (this recommendation was incorrectly attributed in the last issue).
The data stream came down at 50 bits per second. Through this tiny pipe of information, all the precision of GPS had to pass. It included the space-vehicle orbit-position information (ephemerides), system time, space-vehicle clock-prediction data, transmitter status information, and C/A signal handover time to the P/Y code. Also as a part of the message, ionospheric-propagation delay models were incorporated for the single-frequency user. Further, to aid rapid acquisition of new satellites just rising over the horizon, the ephemerides of all other satellites in the full constellation had to be included. Each digital word had to be defined in terms of scaling, bias offset, and precision in terms of the number of bits transmitted.
About 95 percent of the GPS message has endured with no changes needed at all. In a few cases, because the newer user equipment is more accurate, greater precision is desirable. It is a great tribute to the brilliant engineers and scientists who designed the signal structure in 1975 that it has endured for 35 years with so little need for modification.
Some of the JPO Heroes at a “dining-in,” a recognition dinner. From left, Major Mel Birnbaum (made many important contributions. He was famous for marathon code reviews that could last 18 hours straight. He hated to miss schedules!); Col. Don Henderson (later Maj. Gen.) second Air Force deputy; Major Ralph Tourino (later Maj. Gen.), Program Control; Lt. Col. Ken Juvette. director of procurement; and LCdr. Joe Strada, a key leader in the extensive test program. (Credit: Bradford W. Parkinson and Stephen T. Powers)Credit: Bradford W. Parkinson and Stephen T. Powers
Challenge 2. Developing space-hardened, long-life, atomic clocks (qualified for the upper Van Allen Belt, with 4- to 5-year lifetime requirement for individual clocks).
In 1966, both the Air Force and the Navy recognized that developing a precise, stable time-base for generating the one-way (passive) navigation ranging signal in the satellite was essential. Cesium atomic clocks had been invented, demonstrated, and offered for commercial sale by the middle of the 1950s, before the Space Age. The major commercial issues with these clocks were that they tended to be bulky, power-hungry, and not hardened against space radiation. To address that problem, rubidium atomic clocks, noteworthy for their small size and low power requirements, were developed. Still, the issues of mechanical and radiation hardening as well as temperature sensitivity had to be resolved before they could be used in space.
The 621B/Woodford/Nakamura study of 1964/66 called for atomic clocks in the satellites in at least seven places. The study advocated a technology program to space-harden existing clock technology. Unfortunately, the Air Force chose not to pursue a space atomic-clock technology program.
However, the Naval Research Laboratory (NRL) did institute a program in 1964. It pursued the technology for stable clocks with a series of satellites that have already been discussed. The first Timation satellite, launched in May 1967, carried a quartz clock. Not surprisingly, the frequency varied substantially with satellite temperature. The second Timation satellite also contained a quartz clock as well as a temperature controller and showed improved operation, but the results still fell short of those necessary for a GPS satellite. The third satellite in the series had not been launched before the Pentagon approved GPS development in December 1973. In any case, Timation 3 was designed to carry two slightly upgraded, off-the-shelf commercial rubidium clocks.
Qualification Model of the first GPS atomic clock, built by Rockwell International working directly with Efratom, a small German company. (Credit: Bradford W. Parkinson and Stephen T. Powers)
Based on the progress that NRL had made, during the Lonely Halls meeting the JPO decided to commit to atomic clocks in the first operational GPS satellites. This third Timation satellite was renamed NTS-I and came under the newly formed Joint Program Office for GPS. The satellite was launched on July 14, 1974, as a part of the GPS program. However, the ineffective attitude-stabilization system caused varying sun angles and hence, significantly varying temperatures, masking any careful evaluation of the rubidium performance.
The GPS space-based rubidium atomic clock technology was derived from a unit produced by Efratom, a small company initially based in Germany. The geniuses behind this creative device were Ernst Jechart and Gerhard Huebner.
By the summer of 1974, a satellite contractor, Rockwell International (RI), had been selected to build the GPS operational satellites. Included in the program direction by the JPO was a separate development of rubidium clocks for the satellites as an alternative to the NRL cesium clock effort, in case the NRL effort faltered. Hugo Fruehauf of Rockwell had independently discovered and contacted Efratom, the company that NRL was working with, although his interaction was totally independent of that of the NRL. In addition, Fruehauf’s relationship with Efratom was simplified because of his fluency in German, since Jechart did not speak English, and Efratom had just established an office in Southern California near the Rockwell developers. Figure 2, a page from the original Rockwell proposal, shows the excellent ground test data at both 1000 seconds and at 24 hours.
Figure 2. Test results for the Rockwell proposed GPS space-hardened prototype atomic (rubidium) clock, based on the Efratom commercial clocks. (Credit: Bradford W. Parkinson and Stephen T. Powers)
On realizing that the small Efratom company would be incapable of producing a radiation-hardened, space-qualified rubidium oscillator, RI’s GPS satellite program manager Richard Schwartz created a teaming relationship with them, which included his chief engineer, Hugo Fruehauf, plus Dale Ringer, Dr. Chuck Wheatley of Rockwell’s Autonetics Division, and Efratom’s Werner Weidemann. With heroic efforts, this team built a space-qualified clock in time for the first GPS launch in February 1978.
Meanwhile, the NRL-sponsored development of a cesium clock by FTS ran somewhat behind schedule. Their cesium clock was not available for the first three GPS satellite launches. The first NRL hardened clock was included on the fourth GPS satellite; unfortunately that unit failed after 12 hours of operation because of a power-supply problem. As a result, the only operating clocks on the first four GPS satellites were those developed by the Joint Program Office through its contractor Rockwell International. The decision to proceed to full-scale development for GPS, called DSARC 2, was made before any NRL-developed clocks had become operational.
That said, the NRL-sponsored FTS cesium clocks were available for later satellites, and performed extremely well. Later Block II GPS satellites carried two rubidium-frequency standards made by Rockwell and two cesium-frequency standards (primary source, Frequency and Time Systems; secondary sources, Kernco and Frequency Electronics Inc., on selected vehicles). Figure 3 summarizes the early clock program.
Figure 3. Earliest satellite-clock technology developments, culminating in the last row: four Rockwell satellites with Rockwell-developed rubidium clocks. (Credit: Bradford W. Parkinson and Stephen T. Powers)
In spite of NRL’s development difficulties, GPS users owe a debt to the lab for its pursuit of this technology. Clearly GPS would not have performed so well without space-hardened atomic clocks. It was the apparent NRL progress that strengthened the argument. The support of Ron Beard of NRL in this joint effort has been invaluable to the program over many years. More than 450 atomic frequency standards have now flown in space. By far the greatest user has been GPS.
Challenge 3.Achieving rapid and accurate satellite orbit prediction, to within a few meters of user ranging error (URE) after 90,000 miles of travel.
Since the GPS system architecture had upload stations only on U.S. soil, the satellites were out of sight for many hours, making accurate prediction of their orbits essential. To achieve the expected positioning accuracy, the orbit prediction had to contribute less than a few meters of ranging error after 90,000 miles of travel. Achieving this standard was a major challenge in the early days of GPS. Such a prediction must account for the complications of Earth pole wander, Earth tides, general and special relativity, the noon turn maneuver of the satellite, solar and Earth radiation, and the reference station’s location. Figure 4 gives an example of the problems of polar wander.With roughly a 400-day period, this effect had an amplitude of many tens of feet. While this wander has to be included in the GPS orbit-prediction model, fortunately GPS is the major technique to measure it.
Another, usually unrecognized feature is that the monitor stations only use the GPS signal for ranging. In other words, they are passive, rather than using the usual technique of that era, two-way ranging. The reference receivers were of a special design, developed by Jim Spilker’s company, STI. They successfully received the first signal from the Rockwell/ITT satellite (NDS-1) on March 5, 1978, after its launch on February 22, 1978.
Fortunately, the Transit program had pioneered precise orbit prediction and had taken these effects into account. Its Astro/Celeste program, developed by Bob Hill and Dick Anderle at the Naval Surface Weapons Center in Dahlgren, Virginia, batch-processed the measurements taken by the reference stations. Unfortunately, this processing would take too long to provide the most up-to-date predictions.
A new scheme was devised that included partial derivatives of prediction relative to reference-station measurements. A.J. Van Dierendonck applied his knowledge of filters to help lead development of these calculations, which allowed a modified (linearized) Kalman filter to be used for near-real-time optimal prediction. Bill Fees of Aerospace, Walt Melton of General Dynamics, and Sherm Francisco of IBM, among others, implemented these techniques. The initial master control and upload stations were located at Vandenberg Air Force Base, since moved to Schriever Air Force Station; a backup master control station has been re-established at Vandenberg.
Figure 4. Motion of the Earth’s spin axis must be included in the measurement parameters for GPS satellite location. The broadcast ephemeris is adjusted to include this effect, so the user need not make further adjustments. (Courtesy of International Earth Rotation and Reference Service). (Credit: Bradford W. Parkinson and Stephen T. Powers)
Challenge 4.Ensuring and demonstrating spacecraft longevity approaching 10 years (the issue was GPS affordability)
The issue was simply that sustaining a constellation of 24 satellites would be prohibitively expensive if the satellites did not have long lives. Again, the Air Force/621B study by Woodford and Nakamura in 1966 focused on the problem: “The most specific change in satellite technology is the increase of mean time before failure (MTBF). MTBFs on the order of 3 to 5 years can now be considered feasible.”
The problem is easily illustrated in Figure 5. The light blue line shows the trade-off between average satellite lifetime, L, and the required number of satellites per year for a 24-satellite constellation. GLONASS, the Russian system competing with GPS, has the experience shown in the upper white box. With satellite lifetimes averaging two to three years (or less), GLONASS has a corresponding requirement for eight to 12 satellite launches per year. Only a very wealthy country can sustain such a launch program.
Figure 5. The imperative for long satellite lifetimes. (Credit: Bradford W. Parkinson and Stephen T. Powers)
The red oblong illustrates the U.S. GPS experience, which requires only two to three launches per year. Also shown is the initial experience of GPS during Phase I. The first 10 GPS satellites reached an average age of 7.6 years, with #3 and #10 exceeding 9 years. This is an enormous credit to Rockwell International and in particular the program manager Richard Schwartz. He had excellent system engineering support from Andy Codik. The JPO satellite division was intially led by Major Gaylord Green and later by Maj. Doug Smith, with help from Capt. Jack Henry.
Three factors are key to long-lived satellites:
Designs with carefully selected redundancy (for example, clocks, power amplifiers),
Enforcing a rigorous part-selection program including the de-rating of parts (must be class S. or equivalent),
Testing as you fly and insisting on a detailed analysis of all failures.
Figure 5 also illustrates why the Timation clocks could not be used as prototypes for the GPS program. In general, their maximum lifetimes were approximately one year. Clearly their designs needed greater maturation.
The demonstrated lifetimes were essential to passing the next milestone, DSARC II, which allowed GPS to proceed to full-scale development.
Challenge 5.Developing a full family of GPS user equipment that capitalized on the digital signal (leading to inexpensive digital implementation) and spanned most fundamental military uses, as well as demonstrating civilian cost feasibility.
The last, but certainly equally difficult of these five engineering challenges, was the development of nine different types of GPS user equipment. Recognize that a major part of the challenge was to stuff the real-time digital software processing into the relatively primitive digital computers of that era. Table 1 summarizes the development of user equipment:
Data: Bradford W. Parkinson and Stephen T. Powers
All of the sets performed well within specification. They were characterized, however, by large size and heavy power demands. Magnavox, under the technical direction of Vito Calbi, produced the largest variety of user equipment. It was a subcontractor to General Dynamics, who reported directly to the JPO. At Aerospace, Frank Butterfield was a gifted contributor, particularly skilled at practical antenna design.
The Generalized Development Model (GDM) reciever, developed by Rockwell Collins Group, was the largest of the sets, created for a specific purpose: to demonstrate the ultimate jam resistance for GPS user equipment. It attained performance better than 100 db jamming-to-signals ratio (J./S) in actual flight test. The GDM receiver achieved this by integration with inertial components, directional antennas, and shading with the aircraft body. Such a receiver can fly directly over a 1 kW jammer at 4,000 feet and not be affected. The original GDM program manager at the USAF Avionics Lab was Maj. Roger Brandt.
The Rockwell Collins Generalized Development Receiver (GDM). This advanced receiver achieved more than 100 dB of anti-jam in actual flight tests. (Credit: Bradford W. Parkinson and Stephen T. Powers)
The single-channel manpacks were large and clumsy, but they operated very well. The payoff created by the CDMA signal is illustrated with the 12-channel, single-chip modern implementation, shown in the bottom picture. This contemporary chip’s accuracy is much better than any of the equipment produced during Phase I.
Developing test environment and analysis setup was almost as challenging as the user equipment. Lt. Col. Val Denninger, Maj. Darwin Abbey, and Lt. Cdr. Joe Strada led this very successful effort. While most testing took place at Yuma Proving Ground, test sites were also located in San Diego and elsewhere.
Left: 1978 single-channel (sequential) Manpacks, two types by Magnavox and Texas instruments. Batteries alone weighed much more than current military handsets. Right: The second JPO deputy, Col. Don Henderson (left), and Aerospace program manger Ed Lassiter (right). Bottom: A modern 12-channel (parallel) Atheros chip receiver with more capability. (Credit: Bradford W. Parkinson and Stephen T. Powers)
The Most Fundamental GPS Innovation
The CDMA (spread-spectrum or PRN) modulation used for passive ranging is clearly the most fundamental innovation of GPS. This signal enabled four-dimensional positioning for the user without requiring an atomic clock in the user equipment. The Russian GLONASS (the other, partially-operational global navigation satellite system) also used spread-spectrum passive ranging, but resorted to a frequency-separation scheme (FDMA, frequency-division multiple-access) that has proven inferior in actual use.
The innovative design of this CDMA signal has enabled all of today’s precision applications for GPS. It is currently common for inexpensive GPS receivers to simultaneously receive signals from more than 10 satellites, yet all of these signals are being broadcast on exactly the same frequency. In fact, the number of signals that can be received is virtually unlimited using the spread-spectrum CDMA approach. Using a routine processing algorithm, the user, receiving more than four signals, has an instantaneous position that is more accurate than that using four satellites alone. This robustness includes a technique to ensure integrity of the GPS solution. The method, called receiver-autonomous integrity monitoring (RAIM), isolates a rogue satellite that is not operating properly, to ensure integrity of the GPS solution.
Another technique, called carrier tracking, is enabled with the coherence of the code and the carrier broadcast in this signal. When coupled with some form of differential GPS operation, the result is relative positioning accuracy that is unprecedented — frequently better than a millimeter. For example, surveyors can now routinely resolve three-dimensional position to this accuracy. Even common user equipment can make use of the coherence of the signal. The receiver accomplishes this by employing the so-called Hatch/Eschenbach filter that uses the reconstructed carrier signal to smooth the code-transition measurement that greatly decreases the noise of the raw code measurement.
The processing gain in the GPS CDMA signal has been enhanced by deep integration with inertial navigation components. This has enabled the demonstrations of very high interference rejection by such receivers. DaleKlein and Ed Copps of Intermetrics Corp. were major contributor
s to the integration of GPS with inertial measurement units for the Magnavox high-performance military receivers.
Side-Tone Ranging. The competing side-tone ranging signal structure offered by NRL in the 1970 Easton patent had a fundamental flaw. If the signals were broadcast at the same frequency, they would interfere with each other. On the other hand, if they were broadcast on different frequencies, the user equipment would require a separate analog front end and tracking loops for each signal. In addition, each channel would have its own time-delay bias that would probably vary with temperature of the user equipment. A study by Magnavox also noted that the side-tone ranging signal could be easily spoofed; it was not clear how to encrypt such a signal. The final problem was that the signal was fundamentally an analog type and would have not been able to take advantage of modern digital signal processing. As a result, the receivers would be more complex and expensive.
The Air Force 621B/Aerospace and Magnavox studied the CDMA signal structure extensively after the 621B Woodford/Nakamura study was completed in 1966. Bob Gold of Magnavox had, in 1967, invented the technique to select acquisition codes that were mathematically guaranteed to not look alike (were uncorrelated). Early in the program, the JPO hired Dr. Jim Spilker, a recognized worldwide authority on digital signal processing, to contribute to this effort. Another worldwide expert, Charlie Cahn of Magnavox, was also a major contributor to the signal design. As mentioned previously, the details of the signal required the efforts of many people.
By 1969, the CDMA signal was being used in many communication applications. Adapting this signal for navigation raised the questions that were posed in an earlier section. It is hard to believe today the issues surrounding its use had to be addressed in 1970. It is to the great credit of Program 621B that it built the receivers and ran the series of tests at White Sands Missile Range that had earlier resolved all the major issues surrounding the signal structure. This irrefutable evidence allowed the JPO team to confidently choose this signal during the Lonely Halls meeting in September 1973. Great credit must go to Bill Feess who worked tirelessly to complete the analysis that demonstrated 5-meter accuracy in those White Sands tests.
CDMA-Enabled Applications
The distinction between the Timation side-tone ranging and the 621B CDMA signal is critical to understanding the origins of GPS. The Air Force CDMA signal was different in essential and fundamental ways from the Easton side-tone ranging modulation. Three examples of precise three-dimensional applications, not achievable with side-tone ranging, illustrate the subsequent success of the 621B digital CDMA signal.
Aircraft Blind Landing. In 1992, the Federal Aviation Administration (FAA) sponsored Stanford’s development and demonstration of the first Category III (blind landing) system in a commercial aircraft; the effort was led by Clark Cohen and developed by a group of Stanford students under the supervision of Brad Parkinson. The only sensor for both position and attitude was GPS. The carrier-tracking receiver was a derivative of a Trimble receiver; it relied on the CDMA signal structure for both accuracy and integrity. (See Figure 6.)
Figure 6. Results of first blind landing tests using GPS alone, 110 landings with a commercial Boeing 737. (Credit: Bradford W. Parkinson and Stephen T. Powers)
Robotic Farm Tractor. Using similar technology, a different group of Stanford students in the same lab demonstrated the first precision GPS-controlled robotic farm tracker. Again, the capability was enabled by the GPS CDMA signal. The John Deere Company sponsored this effort, which has now expanded into a worldwide market of more than $400 million per year.
Robotic farm tractor developed at Stanford with support from John Deere company. Student leader Mike O’Connor and colleague Tom BeLl shown. Tracking test at 5 meters/second, with worst error around 3 inches! Now a $400M/year market. (Credit: Bradford W. Parkinson and Stephen T. Powers)
Earth Crustal Monitoring. A third example of the power of the CDMA signal is precise survey, focused on Earth movement and crustal tracking (Figure 7). The original GPS surveying receivers were pioneered by PhilWard at Texas Instruments and Charlie Trimble at Trimble Navigation, among others.
Figure 7. Continuous observation of earth crustal motion with a precision of better than a millimeter: distributed slip on Kilauea volcano, Hawaii. (Credit: Bradford W. Parkinson and Stephen T. Powers)
Summary. Many technologies came together to make GPS operational, none more revolutionary than the signal structure demonstrated by 621B at White Sands, and selected by Parkinson during the Lonely Halls meeting. Virtually all high-precision uses of GPS depend on the characteristics of this signal.
Credit: Bradford W. Parkinson and Stephen T. Powers
More on GPS Origins
The fundamental basis for the GPS design was clearly the Woodford/Nakamura and subsequent studies undertaken by 621B, not the system outlined by NRL in the Easton patent. More than 500 million current users have overwhelmingly confirmed the value of the selected technique using a minimum of four-satellite passive ranges and the CDMA signal. If each GPS user had to employ an atomic clock, the price of most GPS receivers would be prohibitive. The value of a four-dimensional solution for users has also been irrefutable. Had GPS followed the blueprint of the NRL patent, it is reasonable to say that almost all system uses, military as well as civilian, would have been fatally compromised. Further, had the Easton side-tone ranging signal been selected, broadcasting 30 satellites on the same frequency, as GPS does today, would have created an undecipherable electromagnetic jumble.
Summarizing Easton’s Patent. We earlier mentioned the NRL/Easton patent for the Timation design. It is important to summarize that invention and its relationship to the actual GPS design. A few people have written that Roger Easton “invented” GPS. As stated, Easton did have a competing concept that he had developed at NRL. In October 1970, four years after the completion of the secret, seminal system study by Woodford and Nakamura, Easton applied for a patent, “Navigation System Using Satellites and Passive Ranging Techniques,” that was granted on January 29, 1974 (U.S. 3,789,409). A careful reading of the patent, available on the web, reveals the following:
The technique described by Easton clearly calls for a synchronized “extremely stable oscillator” at the user station. Elsewhere he states: “would typically be controlled by an atomic clock.” This less-capable method of navigating was examined in the Woodford/Nakamura study, four years before Easton’s patent application, and is definitely not the technique chosen by GPS.
The patent advocates the use of a passive ranging technique, whose description occupies most of the patent, with multiple frequency tones, not the CDMA technique of GPS that had already been studied by 621B. Before the patent was issued, 621B had already built prototype GPS CDMA receivers, flown them at the White Sands range, and demonstrated three-dimensional accuracies of about 5 meters. The Easton passive-ranging technique, commonly called side-tone ranging (STR), had been included in a 621B analysis of alternatives. STR was rejected because of poor resistance to interference or spoofing, and the inab
ility to broadcast all satellites at the same frequency without destructive self-interference.
Both the description and the accompanying diagram in the patent clearly refer to two-dimensional navigation, using lines of position. To extend this to three or four dimensions was not mentioned. Such extension would probably only be possible if the satellites all broadcast on different frequencies, which would have made extremely high-precision positioning (as attained by the actual GPS design) infeasible.
Thus, it is correct to state that the Easton patent did not, in any way, represent the actual GPS design in at least these three fundamental aspects.
Further Transit Contribution. In 1974, after the first phase of GPS had been approved, the Transit program requested funds to upgrade the Transit signal structure to the same passive ranging technique (CDMA) being planned for GPS. The program’s purpose was to use Transit signals to track Trident missile testing launches in broad ocean areas. Air Force Col. Bradford Parkinson (director of the GPS Program), Dr. James Spilker (Stanford Telecommunications Inc.), and Jack Klobuchar (Air Force Cambridge Research Laboratory) responded with a technique for substituting GPS signals, with a translated frequency relayed to the ground to track those missile tests.
After three Pentagon briefings on the proposed alternative technique, Dr. Bob Cooper of the DoD concluded that the GPS signal would be used. Included was a decision to add two more satellites to the Phase I development of GPS to accommodate the Trident launch window. As a result, $66 million was transferred from the Navy to the USAF GPS program. The benefit to the fledgling GPS program was enormous. This greatly expanded the test time for GPS, and also reduced the risk, since no spare satellites had been approved for the program. While the Trident program was somewhat unhappy with the loss of funds and control, it immediately unleashed the creativity of Johns Hopkins University Applied Physics Laboratory and successfully met the Trident missile test tracking requirements.
GPS JPO Innovations
GPS was the first DoD program directed to be managed as a Joint Service Development Program. This new approach, conceived by Dr. Currie, led the GPS program to be designated a JPO or Joint Program Office. As a result, there were deputy program managers assigned from the Navy (Cdr. Bill Huston), Army (Lt. Col. Paul Weber), Marine Corps (Lt. Col. Jack Barry), and Defense Mapping Agency (Paul Frey), as well as the customary Air Force deputy (initially Lt. Col. Steve Gilbert, later Lt. Col. Don Henderson). Rather than use these well-qualified people from other services simply as liaisons, they were each assigned specific programmatic responsibilities.
At the first major program review at Andrews Air Force Base, Parkinson called the convening general’s attention to the fact that he was leading a joint program, and with the general’s indulgence he had invited his deputies from the other services to attend. Since attendance by other services at Air Force program reviews was unheard of, this drew a gasp from the roughly 200 Air Force officers attending. The JPO approach truly broke new ground in intra-service cooperation.
At the JPO. Frank Butterfield of Aerospace, Col. Parkinson, and Cdr. Bill Huston, deputy JPO director from the U.S. Navy, in the early 1970s. A model of a Phase I GPS satellite stands on the table between the latter two. (Credit: Bradford W. Parkinson and Stephen T. Powers)
Parkinson had entreated the Federal Aviation Administration to also send a deputy. The public response by the FAA deputy administrator for development was: “We don’t want GPS, we don’t need GPS, and if it is ever deployed, we will never use it.” Throughout this period, Glen Gilbert (sometimes called “the father of air traffic control”) was a strong and early advocate for FAA use of GPS. It took many years for the FAA to accept his views. Obviously times change; the current relationship between the FAA and the GPS Program Office is excellent, fostered by Col. Dave Madden and his FAA counterpart Leo Eldredge.
JPO as Prime Contractor. The JPO cadre served as the prime or integrating activity for the whole program. Gen. Schultz almost fired Parkinson when he proposed this. The general had expected him to hire a separate commercial integrating contractor. After Parkinson explained that the major interfaces between the three segments — satellite, ground control, and user equipment — were the signals, Gen. Schultz acceded to the plan. This pioneering aspect was critical because it ensured that all aspects of the system would be under the direct purview and control of the JPO.
Award and Incentive Fees. The use of innovative procurement awards for the contractors was very new in DoD in 1974. Beginning with the satellite contract, the JPO made extensive use of new forms of positive rewards for the contractor, including incentives for on-orbit performance. Gaylord Green pioneered this activity with skills developed as a project officer in the Advanced Ballistic ReEntry Systems Program (ABRES) program office. Incentives were applied to virtually all the other contracts as well, and seemed to have a very positive effect.
Normally the Space and Missile Systems Organization (SAMSO) procurement office, which was independent of the JPO, would have been reluctant to approve such radical new ideas. Fortunately, Parkinson carpooled with another colonel who was head of SAMSO procurement and a breath of fresh air. This attitude was exemplified by a sign at eye level as you left the procurement director’s office: “Nothing would be done at all if a man waited until he could do it so well that no one could find fault with it.” (It turns out this came from remarks by Cardinal John Henry Newman.) With that attitude, the SAMSO office approved almost all of the JPO’s “wild” procurement innovations. Many of these innovations are now routine.
Changes. The Air Force provided a high-level spec for the satellite that defined the signal structure, the power on the ground, the frequencies, the orbit, and the amount of weight the booster could put into that orbit at apogee. The JPO left it up to the contractor to design a satellite that could meet those requirements. The key point is the JPO never changed the requirements, which kept GPS on course with minimum cost increases for the devlopment.
Refurbished Atlas F Booster. Today, up to half the cost of a satellite on-orbit is the cost of the booster to place it there. While the costs were perhaps not proportionally so large in 1977, they still could consume large pieces of a program’s budget. Luckily, the United States had mothballed much of its liquid-fuel ballistic missile force during that period. The JPO chose to use refurbished Atlas Fs as boosters, saving many millions of dollars. Some have suggested this idea originated with NRL. While NRL may have also been using them, both Parkinson and Green came from the ABRES program where refurbished Atlas Fs were already employed. Thus, the decision made in the Lonely Halls meeting was based on knowledge the JPO already had, which included additional steps the ABRES had taken to improve the reliability of the booster. (See Figure 8).
Figure 8. Refurbished Atlas-F booster characteristics. Col. Parkinson and Maj. Green brought this concept from previous use on the USAF ABRES program. (Credit: Bradford W. Parkinson and Stephen T. Powers)
A Motto. Emblazoned on a prominent wall in the JPO was a sign that read:
“The mission of this Program Office is to
Drop 5 bombs in the same hole
and build a cheap set that navigates
and don’t you forget it!”
By distilling the JPO mission into one succinct motto, the program intended to provide a guide for all its actions. If a decision fundamentally helped achieve that mission, it was probably the right one.
The Political Battlefield. Political battles in the Pentagon are often brutal and unforgiving. The fundamental reason is that the budget is always viewed as a zero-sum game. One program’s money comes at another program’s expense. GPS was a system that sprang from the space development community (“the Space Weenies”) and had virtually no champions from the operational components. Unlike current DoD satellite programs, there were no explicit formal requirements for the new system and hence little official status. Parkinson spent many trips to the operating forces to explain the value of precision weapon delivery. Between skepticism and deafness, GPS survival was always extremely uncertain. The Air Force generally opposed its deployment, even after the extensive tests of 1978–80 had clearly demonstrated that GPS was, by far, the best blind-bombing system ever conceived.
Fortunately, there were some key supporters of GPS who overcame that resistance. They were affectionately called the GPS Mafia. The most important member of this unchartered group was Malcolm Currie, whose efforts were discussed earlier. His powerful number-three position at the Pentagon gave him the authority to force funding decisions on the uniformed military. At least one general officer was extremely upset with Parkinson over his relationship with Dr. Currie, and gave him a public tongue-lashing over the issue during a chance encounter in a Pentagon corridor. Dr. Johnny Foster, whom Mal Currie replaced, was another early supporter of the program.
USAF Col. Steve Gilbert, the original deputy program manager for GPS in Los Angeles, was a tireless, heroic contributor. Later on he played a critical role, fighting the battles within the Pentagon as the Air Force Program Element Monitor (PEM). His next position was as the GPS representative in the Office of the Secretary of Defense. While there, Steve fought back repeated challenges that would have canceled GPS in the early 1980s. Without his efforts, GPS almost certainly would never have happened.
Other members of the GPS Mafia were Lt. Col. Paul Martin (the original GPS Program Element Monitor), Brig. Gen. Hank Stelling (RDS in Pentagon), and Cols. Brent Brentnall and Emmitt DeAvies (DDR&E representatives).
The users of GPS owe all of these supporters a real vote of thanks. As the Duke of Wellington said about the battle of Waterloo, “It was a near-run thing.”
Fortunately, GPS supporters prevailed, and the two Iraq wars have made all branches of the military believers in the value of the system, although they sometimes regard it as magic. A combat Army colonel in Iraq was reportedly asked what he thought of satellite systems to help him fight. His response:
“I don’t need any (expletive) space systems. My GPS and my Iridium comm give us everything we need.”
GPS really is a stealth utility.
Thoughts on the Future
There are now many additional or improved satellite systems on the horizon. American GPS has heretofore only offered a single, clear navigation signal for civil users. That is rapidly changing. Two more frequencies and a number of additional signals will be available from the next two generations of U.S. satellites. Other countries are also working hard to follow the GPS lead. Figure 9 depicts some of these new systems.
Figure 9. Upgrades of GPS (only current operational civil signal; next generation, four new civil signals at two new frequencies), GLONASS (next generation, four new civil signals at two new frequencies) and new international navigation satellite systems (Galileo, four new civil signals to appear at two new frequencies; finally, Compass) are on the near horizon. The plethora of signals will enable improved accuracy and integrity. This will lead to new applications. (Credit: Bradford W. Parkinson and Stephen T. Powers)
An international common navigation signal called L1C has been accepted and almost completely defined. It will broadcast on the same 1575 MHz frequency as the current GPS civil signal. It will be of the same type (CDMA) as the original GPS signal, although it will have significant enhancements to increase precision and accuracy. If the engineering is done properly, this signal should be interchangeable for all GNSS systems that support civilian use. The positioning, navigation, and timing (PNT) community will benefit enormously by having all of these signals available. Again, the key enabling decision was the CDMA signal structure defined by 621B and tested at White Sands.
We will mention one CDMA-enabled application with a large market potential. This is the use of multiple GNSSs (up to 50 satellites) in automobiles for lane guidance and car separation. During times of low visibility, freeways are notorious for multi-vehicle collisions. We believe the technology will be in hand to greatly reduce these tragedies. The new application would involve cooperative navigation with cars in the vicinity all tied together in a communication grid. GPS-measured velocity is almost a forgotten aspect of the system, yet it can be accurate to much better than 0.1 meters per second. If two cars in the vicinity of each other can know both relative position and relative velocity, collision probabilities can be easily assessed and avoidance actions quickly and automatically recommended.
This is just a glimpse of the future. We believe many other new or improved applications will be enabled by future deployments.
Summary
Just as a building is not invented, GPS was not the product of any single invention. GPS as a system was an innovation enabled by many antecedent technologies and concepts. Some were brand new in application, or had to be adapted to their role in GPS, for example the CDMA signal technique. In making those system selections, the final design was the product of the entire JPO team, whose roots went back to many of the greatest institutional sources of innovation in the country.
The two most critical foundations were:
The comprehensive study done by Jim Woodford and Hideyoshi Nakamura for USAF/621B in 1964/66, exploring virtually all alternative ranging techniques from satellites, both active and passive, and calling for atomic clocks in the satellites. In particular, the four-dimensional 621B concept of using “four in view” was analyzed and became the bedrock of the GPS design, ensuring that the user could make do with a simple crystal clock.
The selection and demonstration of the CDMA passive ranging signal by 621B at White Sands. These tests confirmed four-satellite, single-frequency operation and proved that such operation obviates the need for an atomic clock in each GPS user set.
These directly led to the systems architecture decisions made in the Lonely Halls meeting. Also essential were finding workable solutions to the five critical challenges:
Defining the specific details of the GPS CDMA signal structure
Achieving rapid and accurate satellite orbit prediction
Ensuring and demonstrating spacecraft longevity
Developing a full family of GPS user equipment.
In tracing the origins, the first navigation satellite program, the Transit program of APL, should be singled out. Working under contract to the Navy’s Nuclear Submarine Program, APL pioneered the dual-frequency technique to calibrate ionospheric delay errors as well as the painstaking development of an accurate orbit-prediction program. Both early efforts were essential to the ultimate success of GPS.
Also important was NRL’s push to harden frequency standards for use in satellites. While the JPO rejected Easton’s navigation technique, NRL’s apparent clock progress, by 1973, convinced the decisionmakers at the Lonely Halls meeting to commit to including atomic clocks in the first prototype, Rockwell-built GPS satellites. While it is ironic that no clock with NRL heritage was operational on the first four GPS satellites, the NRL’s persistence finally paid off with the introduction of its cesium beam clocks on an equal footing with the Efratom/Rockwell-designed rubidium clocks later, during GPS Phase II.
Throughout this article, many of the contributors to the early definition, development, and testing of GPS have been named. Certainly many others have also been inadvertently left out. In closing we would like to sincerely thank the scores of engineers who assembled the first-of-a-kind demonstration system.
As a stealth utility, one pervasive accolade is that GPS is now taken for granted. People throughout the world now expect to know exactly where they are and what time it is.
By Bradford W. Parkinson and Stephen T. Powers, with Gaylord Green, Hugo Fruehauf, Brock Strom, Steve Gilbert, Walt Melton, Bill Huston, Ed Martin, James Spilker, Fran Natali, Joe Strada, Burt Glazer, Dick Schwartz, Tom Stansell, and others
The original system study, the key innovations, and the forgotten heroes of the world’s first — and still greatest — global navigation satellite system. True history, told by the people who made it. Part One of a Two-Part Special Feature.
The stealth utility: over the past 30 years, a new entity has steadily and stealthily crept into the fabric of worldwide society, creating capabilities and dependencies that did not exist before. This utility is known as the Global Positioning System, or GPS. With more than a billion GPS receivers in use, this stunning achievement has truly revolutionized the way the world functions in the 21st century. Virtually every cell-phone system relies on GPS for timing. Almost every ship and aircraft carries multiple GPS receivers to provide positioning information. Other applications span military targeting, transportation, object tracking, and resource identification. Today, the loss of GPS signals would have catastrophic consequences.
How did GPS come into being? What technologies were essential to its success? Who developed those technologies? Recently a number of GPS histories have appeared that are very inaccurate on these subjects. Our purpose in writing this account is to set the record straight, and in so doing to give credit to many of the original developers of GPS whose contributions have somehow been forgotten. Throughout this article you will find their names highlighted. Space does not permit us to name the many other individuals who deserve enormous credit for the subsequent refinement and invention of new GPS applications.
Figure 1 gives a summary view of the history of U.S. satellite-based navigation, particularly GPS. Details of the Russian GLONASS and the European Galileo systems are not included as they arrived later, and generally mimicked the GPS development albeit with their own, locally developed detailed designs.
Figure 1. The eras of satellite navigation. (Credit: Bradford W. Parkinson and Stephen T. Powers)Dr. Richard Kershner, who led the development of Transit. On his left, young Col. Bradford Parkinson, who led the development of GPS. (Credit: Bradford W. Parkinson and Stephen T. Powers)
This history focuses on the period up to about 1980, when GPS was approved for full-scale development. Between that time and the date that GPS was declared fully operational, April 27, 1995, many additional contributions were made. The system withstood several early attempts by the Air Force to cancel it entirely. Fortunately, those attempts did not succeed, and the Air Force now fully embraces GPS as an essential part of virtually every weapon system in the inventory.
We call this a tribute to the almost-forgotten people whose intellectual labor and skill initially developed GPS. As we unveil this story, we will point out the original — and critical — system study, the 1966 Woodford/Nakamura Report, that became the essential blueprint for GPS. Many people are unaware of this study since, in its original form, it was classified U.S. Department of Defense (DoD) Secret. It was not declassified until August 1979, more than a year after the first launch of a GPS operational satellite in February 1978.
We also intend to describe and justify the key innovation that enabled the system. This keystone technology is the GPS code-division multiple-access (CDMA) signal. While CDMA was necessary for GPS success, it was by no means sufficient.
We will also define and describe the five major original challenges that had to be met to achieve the success that GPS now enjoys; that will come in the second installment of this history, to appear in next month’s issue.
Mathematician Bill Guier (l) and physicist George Weiffenbach (r), told APL Research Center director Frank T. McClure (c), about their success using Doppler tracking for satellites. “McClure’s brain started going into fast forward,” remembered John Dassoulas. “Knowing the navigational challenges the U.S. Navy faced, McClure said, ‘Well, if you can find out where the satellite is, you ought to be able to turn that problem upside down and find out where you are.’” (Credit: Bradford W. Parkinson and Stephen T. Powers)
GPS Predecessors: Transit
On October 4, 1957, the entire world was amazed by the launch of Russia’s Sputnik satellite. The American public greeted this event with both apprehension and curiosity. Both the Army and Navy had been quietly working on satellite projects for some years. In an attempt to catch up, the United States had a spectacular failed launch when the Naval Research Laboratory’s (NRL’s) TV-3 crashed on December 6, 1957. On January 31, 1958, the United States Army launched a grapefruit-sized satellite, Explorer 1. The NRL then achieved success with the launch of TV-4, renamed Vanguard-1, on March 27, 1958.
In 1958, the Applied Physics Laboratory (APL) of Johns Hopkins University employed an extremely competent team of engineers and scientists. Two of those scientists, Drs. William Guier and GeorgeWeiffenbach, began to study the orbits of the new Sputnik satellites. The satellites were broadcasting a continuous tone signal. Their velocity relative to the ground created a Doppler shift of that signal that was unique. After some innovative work, Guier and Weiffenbach discovered they could determine the Sputnik’s orbit with a single pass of the vehicle.
At that point Frank McClure of APL made a very creative suggestion: Why not turn the problem upside down? Using a known satellite position, a navigator could determine his location anywhere in the world after receiving and processing the satellite signal for 15 minutes. His insight became the basis for the Navy’s Transit satellite program, also known as the Navy Navigation Satellite System (Figure 2).
This pioneering system was developed under the leadership of Dr. Dick Kershner, head of the Space Department of APL. Transit’s main purpose was to provide position updates to the United States submarine ballistic-missile force then under development. These submarines were a major deterrent during the Cold War. Transit was first tested in 1960, and by 1964 the system was fully operational. Under Kershner, APL rapidly mastered the art of building long-life satellites. In fact, two of the vehicles continued operation for more than 20 years.
Figure 2. The Transit birdcage of operational orbits. (Credit: Bradford W. Parkinson and Stephen T. Powers)
Transit was a relatively small satellite that initially used solar power and gravity-gradient stabilization (Figure 3). It provided a position fix every few hours; fixes took 10 to 16 minutes of exposure of the submarine’s antenna on the surface. It achieved 25-meter accuracy, but only in two dimensions. Further, if the user was moving, accurate velocity measurement was critical: a 1-knot error would produce a 0.2-nautical mile position error.
All Navy ships could use the system, and in 1967 Transit was offered to the civilian community by Vice President Hubert Humphrey. Magnavox became the principal developer of civil user sets with Tom Stansell as an early expert in the technology.
Contributions to GPS. The Transit program developed a technique essential for GPS: the use of two frequencies to calibrate the time delay of the radio signal induced by the ionosphere. This dual-frequency technique was incorporated into GPS to attain the highest positioning accuracy. In addition, Transit also pio
neered the accurate prediction of satellite orbits, another essential GPS technology. Orbit prediction will be highlighted later, as one of the five fundamental challenges that faced GPS system designers.
In 1974, Transit made a further contribution to GPS development that we discuss in that approximate timeframe.
Figure 3. A Transit satellite showing the gravity-gradient boom that kept the antennas pointing at the earth. (Credit: Bradford W. Parkinson and Stephen T. Powers):
Program 621B
As early as 1962, Dr. Ivan Getting, president of the Aerospace Corporation, saw the need for a new satellite-based navigation system. He envisioned a more accurate positioning system that would be available in three dimensions, 24 hours a day, seven days a week. He had direct access to the highest levels of the Pentagon and was a tireless advocate for his vision.
Getting’s energy and foresight in the early 1960s were essential to gaining Air Force support to study system alternatives. As a result, the Air Force formed a new satellite navigation program that was later named 621B. Getting’s efforts were recognized in 2002 when he shared the Charles Stark Draper Prize of the National Academy of Engineering with Bradford Parkinson.
By 1962, engineers at Aerospace, under Air Force sponsorship, were heavily immersed in studying the system aspects of a new navigational satellite system. From 1964 to 1966, Aerospace carried out an extensive, formal system study whose principal authors were James Woodford and HideyoshiNakamura, both highly regarded space-systems engineers.
Their work was summarized as a DoD secret briefing in August 1966. As a result of the classification, it was unavailable to anyone outside the project until 13 years later, in 1979, when it was finally declassified (figure 4).
The Woodford/Nakamura Report was a complete system study that examined these issues:
capabilities and limitations of then-current DoD navigation systems;
tactical applications and utility of improved positioning accuracy;
comprehensive analysis of alternative system configurations and techniques for positioning, using satellites.
The report concluded with a set of recommendations for advanced technology development for navigation satellite programs.
Figure 4. Front page of the seminal GPS system study performed from 1964 to 1966 by USAF 621B Program. Originally classified secret, it was not declassified until after the initial GPS satellite had been launched. This was the essential foundation to the GPS System design. (Credit: Bradford W. Parkinson and Stephen T. Powers)
The detailed analysis of possible passive navigation techniques was extremely important. It pointed out that the most capable passive-ranging design, called triple delta rho, would eliminate the need for an extremely stable clock in the user equipment and would provide three-dimensional positioning. (In this article we use clock, oscillator, and frequency standard interchangeably. The timing community makes some distinctions among these words, but for purposes of this history the distinctions are not particularly important.) This later was selected as the fundamental GPS system concept of ranging to four satellites simultaneously.
Key conclusions of the 1966 study advocated:
passive ranging from the satellites (the issue was which ranging signal to use)
atomic clocks in space, and a technology program to develop space hardened atomic clocks
further system studies as well as experimental demonstrations.
Since the full survey of alternative system configurations was extremely important in selecting an optimum system configuration, we reproduce the summary in figure 5. Note that the “Computation Performed by User” is split into two columns. Focus on the columns of the one-way passive ranging techniques with the red outline. Inside, there are two “user boxes,” one with A and one with X. The A shows the user needs an atomic clock. The X shows the user needs only a crystal clock. The option later selected for GPS is designated as G. This technique is the 3Δρ (triple delta rho, or four satellites) that eliminated the need for the user atomic clock, and provided three-dimensional positioning (really four-dimensional since it also captured time).
In October 1970, more than four years after the completion of this study, Roger Easton of NRL applied for a patent on the two-satellite, ρ-ρ technique (option N) that required an atomic clock for the user and was only two-dimensional. The patent (U.S. 3,789,409) was granted in 1974, a year after the three-dimensional design of the GPS system had already been defined in the Lonely Halls Pentagon meeting to be described later.
Figure 5. Summary of the alternative satellite-based navigation techniques from the1964–66 USAF/621B study. The most capable option, circled in green, became the basis for the White Sands prototyping and testing, and then evolved into GPS. NRL applied for a patent on the less capable technique (red line) four years after the Woodford/Nakamura Study was completed. (Credit: Bradford W. Parkinson and Stephen T. Powers)Credit: Bradford W. Parkinson and Stephen T. Powers
More 621B Studies. From 1966 to 1972, program 621B continued with trade-off studies including: signal modulation, user data processing techniques, orbital configuration, orbital prediction, receiver accuracy, error analysis, system cost, and comprehensive estimates of the tactical mission benefits. More than 90 reports completed by USAF/Aerospace during this period remain available in the Aerospace Corporation library.
PRN or CDMA Signal Structure. Of these studies, the most important were those aimed at selecting the best passive ranging technique for the navigation signal. By 1967, it appeared that the best technique was a variation of a new communications modulation known as CDMA. Pioneering this signal were several outstanding scientists, Dr. Fran Natali and Dr. Jim Spilker (both of Philco-Ford), and Dr. Charlie Cahn (of Magnavox).
Credit: Bradford W. Parkinson and Stephen T. Powers
This signal has many names. In addition to CDMA, it is sometimes called spread spectrum, since the energy of the signal was spread over a wide range of radio frequencies. It is also sometimes called PRN or pseudorandom noise because the encoded (and repeated) sequence appears to be random transitions of +1 and -1.
The name code-division is used because each satellite is assigned its own coded signal. Each was a binary (digital) sequence selected to be uncorrelated with other signals and also uncorrelated with time shifts of the signal itself. The expected, powerful advantage of this technique was that all satellites would broadcast on exactly the same frequency. It would clearly lend itself to digital signal processing. Furthermore, and very important, any time-shifts induced by the receiver for the various satellite signals would be effectively eliminated.
However, several significant questions concerning CDMA still needed resolution. These included:
Could such a signal be easily acquired in the face of time uncertainty and Doppler shifts?
Was there a technique to encrypt the military signal so that unauthorized users could not gain access?
How would the c
odes be easily selected to avoid a false lock and also allow additional satellites to be added without interfering with existing satellite signals?
Would the anticipated complexity of the receiver drive costs to unacceptable levels?
Was the signal resistant to accidental or deliberate interference?
Could this signal accommodate communication capability for satellite location, satellite clock correction, and other parameters?
Fortunately, in 1967 a technique for selecting orthogonal codes was invented by an accomplished applied mathematician, Dr. Robert Gold of the Magnavox Corp. Naturally these are now known as the Gold codes. His solution resolved the third CDMA issue stated above.
White Sands Tests. To address the remaining issues, the 621B program developed two prototype versions of CDMA navigation receivers (Magnavox and Hazeltine) for testing at the White Sands Missile Range (WSMR). For these initial 1971 tests, 621B arranged four transmitters in a configuration known as the inverted range. (Interestingly, the more capable receiver was the MX-450 that was only on loan from Magnavox.) These transmitters broadcast CDMA signals from locations that were similar to a satellite configuration except that they were broadcast from the ground. For the simulation of satellite geometry, a balloon-based transmitter was also included for the aircraft-landing tests. Al Gillogly of Aerospace spent many hours installing and troubleshooting the test configuration.
Al Gillogly, Aerospace engineer (left), setting up the critical tests of prototype GPS receivers at WSMR in 1970. (Credit: Bradford W. Parkinson and Stephen T. Powers)
By 1972, program 621B had successfully proven the effectiveness and accuracy of the CDMA signal by demonstrating that such a configuration would achieve 5-meter, 3-dimensional navigation accuracy. Much credit for the painstaking analysis of these results should go to Bill Fees of Aerospace who wrote the final detailed test report. These test results answered most of the remaining issues regarding the CDMA signal.
The tests also confirmed the power of the modulated signal by showing that all satellite signals could, indeed, be received simultaneously on the same frequency. These tests also corroborated the expectation that ranging to four satellites eliminated the need for a highly precise user atomic clock, while still supporting full, three-dimensional navigation. This became an extremely important feature of GPS. If each user had required an atomic-clock class frequency-standard, no inexpensive user equipment could have been produced within the technology horizon visible at that time. This is still true today.
All this evidence supported CDMA as the passive ranging signal of choice and was available to the Air Force’s 621B team when the system configuration was selected at the September 1973 Pentagon meeting that will be discussed later.
621B Demo, Operational Differences. From the time of the 1966 Woodford/Nakamura study on, the Air Force and Aerospace advocated the use of atomic clocks in the operational satellites with the modulation also originating in the satellites. There were two significant risks to placing atomic clocks in the satellites: First, the technology readiness risk: no hardened atomic clocks had yet been designed and flown; and second, the political/budgeting risk associated with gaining approval for a development/demonstration program for the full capability. The Air Force developed a plan to reduce both risks.
In late 1968, the Air Force’s NavSat program in the Plans Office (XR) at the Space and Missile Systems Organization (SAMSO) was redesignated as 621B. All of the various proposals that went forward from SAMSO to Headquarters came henceforth from the 621B office in XR. This included a proposal in early 1972 to deploy a four-satellite demonstration system. This proposal addressed both risks. It would reduce the technology readiness risk in the clocks by launching simple L-band transponders. At the same time, it would save substantial money, thereby reducing the political/budgeting risk.
QZSS (Credit: Bradford W. Parkinson and Stephen T. Powers)
In many circles, this proposal was erroneously thought of as 621B because it came from that office, but in fact, the operational concept for 621B never contemplated or advocated using transponders in the final operational system. Transponders had been rejected for the operational system because they could be easily jammed from the ground. Such a jamming signal would overpower the transponder and steal all of the transmitted energy away from the transponded navigational signal. This enemy jamming would shut down the entire system, clearly an unacceptable risk.
Proposed Initial Constellation. To demonstrate four-satellite, passive ranging capability, 621B had studied a number of orbital configurations, including geo-synchronous and lower inclined orbits. The program proposed to place a constellation of three or four synchronous satellites in orbits over the United States. This array would allow extended periods of four-satellite testing without committing to a full global employment. If this demonstration were successful, the next step would have been to add three more longitudinal sectors, each with its own array. Again, the principal redeeming feature of this approach was that there was some hope of it being funded. The Air Force in the Pentagon placed enormous pressure on the 621B program to come up with the absolutely cheapest way to demonstrate the four-satellite approach.
This proposed constellation design was a reasonable compromise, given the boundary conditions of a four-satellite demonstration and absolutely minimal cost. It is interesting that the Japanese, with a requirement to supplement GPS with satellite signals to improve coverage in urban areas (where there are high shading angles), have designed a very similar constellation. The Japanese configuration is intended to improve coverage restricted to their longitudinal sector of the globe. The new system is called Quasi-Zenith Satellite System (QZSS), and the Japanese appear to be well on the way to fielding it.
Timation and NRL
In 1964, the U.S. Navy initiated a second satellite program, named Timation, under the direction of Roger L. Easton, Sr., a long-time member of the NRL staff. The NRL’s Timation project was aimed at exploring techniques for passive ranging to satellites, as well as time transfer between various timing centers around the world. This project ran parallel to, and was in competition with, the Air Force Program. It subsequently developed a number of experimental satellites, the first of which was called Timation 1. This small satellite, weighing 85 pounds and producing 6 watts of power, was launched on May 27, 1967.
Timation 1, developed by NRL, was a miniaturized, innovative design. The quartz clock was less stable than expected, apparently due to temperature and cosmic-ray effects. (Credit: Bradford W. Parkinson and Stephen T. Powers)
The key feature of Timation 1 was that it included a very stable quartz clock. The fundamental ranging technique was to synchronize a clock at the user’s location with the clock on the satellite and use a passive-ranging signal structure called side-tone ranging. By 1968, NRL demonstrated single-satellite position fixes, accurate to about 0.3 nautical miles, that required about 15 minutes of data collection (Global Positioning System, Volume 1, chapter “Navigation Technology Program,” R.L. Easton, p.16). NRL engineers encountered two significant problems during their testing: sol
ar radiation caused shifts in the clock’s frequency, and ionospheric group delay created ranging errors.
The NRL launched a second satellite, Timation 2, into a 500-mile orbit on September 30, 1969. To calibrate ionospheric group delay, the satellite broadcast on two frequencies very similar to the technique pioneered by the Transit program. Its quartz oscillator was expected to be somewhat more stable, about one part in 1011. Again, a large frequency shift was observed in the clocks that was finally traced to a solar proton storm. NRL was able to demonstrate ranging accuracies of approximately 200 feet to a fixed location.
Timation NTS-1. The last satellite in the original Timation series was launched in July 1974. By that time the Timation program had been placed under the GPS Joint Program Office in Los Angeles, reporting through the Navy Deputy, Cdr. Bill Huston, to the Program Director Col. Bradford Parkinson. The JPO had renamed the satellite as Navigation Technology Satellite (NTS-1). The gross weight had been increased to 650 pounds with a power requirement of 125 watts. This satellite, developed by Pete Wilhelm of NRL, was placed at an orbital altitude of 7,500 nautical miles.
Timation NTS-1 carried two slightly modified commercial rubidium clocks. Unfortunately, attitude-stabilization problems induced temperature variations that masked any quantitative performance evalulation. The atomic clocks were not useful as prototypes for GPS. (Credit: Bradford W. Parkinson and Stephen T. Powers)
The NTS satellites were strictly technology-testing satellites. For many reasons, they had no role in the development of the operational satellites by the JPO and Rockwell. The latter were operational satellites and were called NDS, for Navigation Development Satellites. They were the only ones used in the operational testing during phase I of GPS.
NTS-1 included two small, lightweight rubidium oscillators as clocks. A German commercial company called Efratom had independently developed these models. Amazing at the time, they only consumed about 13 watts of power and weighed some four pounds each. Further Efratom involvement will be pointed out later. While NRL made some electronic modifications, the modified clocks were not in any sense able to withstand the radiation of the GPS orbits. The NTS-1 clocks were certainly not prototypes for the Rockwell clocks that were developed directly for the JPO and flown on the first block of GPS satellites.
NRL tests showed that the modified rubidium clocks had an unacceptable level of sensitivity to temperature variations. Al Bartholemew of the NRL later wrote that “the lack of attitude stabilization system on NTS-1 resulted in large temperature variations which ultimately masked any quantitative evaluation of rubidium standard performance.” (Global Positioning System, volume 1, chapter “Satellite Frequency Standards,” C.A. Bartholomew, p. 25.) This apparently occurred because the satellite used a two-axis gravity gradient stabilization system that does not function well at these altitudes. The Navigation Development Satellites (NDS) satellites, later developed by the JPO, avoided this by developing a new, full three-axis, attitude-control system. NTS-1 carried other space technology demonstrations including highly efficient solar cells.
Later, NRL developed a second (and last) satellite (NTS-II) for the GPS Program Office, after the Pentagon had approved the project in December 1973. The vehicle included two modified cesium beam oscillators developed by Frequency and Time Systems Inc. (FTS) of Danvers Massachusetts. The key atomic clock developer was the engineer and creative entrepreneur Robert Kern. This clock showed great initial promise but it was not yet a space prototype in terms of radiation hardening and parts life. In addition, the JPO provided a Rockwell-developed navigation payload for NTS-II that the JPO had developed for the operational GPS satellites. This would allow the NRL satellite to broadcast the GPS CDMA signal.
Credit: Bradford W. Parkinson and Stephen T. Powers
NTS-II was launched on June 23, 1977, from Vandenberg Air Force Base. Originally it was hoped that NTS-II would be a part of the initial GPS test constellation. It could then have supplemented the satellites being developed by Rockwell, providing another passive ranging signal for the user equipment tests at Yuma Proving Ground. Unfortunately, the NRL ranging transmitter in NTS-II failed prior to the launch of the first JPO NDS satellites, rendering the NRL satellite unusable for the Yuma Proving Ground testing. “Of the two experimental cesium standards carried on NTS-II,” Ron Beard of NRL wrote, “one experienced a power supply failure after a period of satisfactory operation.” It is known that the other cesium clock continued to operate for over a year, but quantitative drift rates on orbit were never available. As a result of these failures, the cesium clock tests were inconclusive. (Proceedings of the IEEE 43rd Annual Symposium on Frequency Control, 1989, R.L. Beard, p. 276.) Only tests with the first four JPO/Rockwell satellites were available to support the full-scale development approval on June 5, 1979.
For the next step, NRL defined a radiation-hardening program and contracted with FTS to develop a hardened cesium clock. This new clock was flown on the fourth operational GPS satellite (NDS 4, launched December 10, 1978). Unfortunately, the clock suffered a premature failure of the power supply after only 12 hours of operation. FTS soon found the root cause and fixed the design. Beginning with NDS 5, the on-board cesium clocks performed well and were equal or better in stability to the Rockwell rubidium oscillators.
Competition, Lonely Halls
By 1972, a few Pentagon authorities had recognized that a new satellite-based navigation system would be a valuable asset with multiple military applications. Literally hundreds of positioning and navigation systems in use by the DoD were expensive to maintain and upgrade. Obviously, a single replacement system offered significant cost savings. Unfortunately, the two competing concepts from 621B and NRL apparently confused the decision-makers. Discussions grew very acrimonious at times. As a result of this inter-service competition and a reluctance to commit the necessary monies, the Pentagon put off making any decision.
In November of 1972, Col. Bradford Parkinson was the director of engineering for the Advanced Ballistic ReEntry Systems Program (ABRES) at SAMSO. Brig. Gen. Bill Dunn, who led the advance planning group (XR), identified Parkinson as a potential candidate to head the floundering 621B program. At Dunn’s behest, Lt. Gen. Kenneth Schultz, commander of SAMSO, asked Parkinson if he would like to be assigned to the 621B program. Parkinson had a very relevant background in navigation, guidance, and control that included a Ph.D. from Stanford in astronautical engineering. He had been chair of the Astronautics Department at the U.S. Air Force Academy, spent three years as a guidance analyst at the Central Inertial Guidance Test Facility, and was operationally oriented with 26 combat missions in AC-130 gunships.
The background was a match, but Parkinson expressed an unwillingness to volunteer for the assignment if he were not assured that he would be the program director. Schultz said he could not yet make that promise. However, immediately after Parkinson left his office, the general reassigned him to the 621B program and effectively made him the director.
Beginning in December, immediately after he assumed control of 621B, Parkinson instituted a series of 7 a.m. educational meetings. At these gatherings, the program staff reexamined every aspect of the proposed 621B program, including alternatives. This educational process was a key to having everyone in the Program Office completely understand the technical issues they faced.
During this period Gen. Schultz supported the program in every way that he could. In particular, Parkinson was allowed to recruit Air Force officers whose background and experience were aligned with the needs of the fledgling program. All had advanced engineering degrees from the very best universities in the country including MIT, Michigan, and Stanford. In addition, virtually every officer had experience in developing real hardware or in testing inertial guidance systems. The first officer Parkinson brought aboard was Air Force Major Gaylord Green, who had worked for him on ABRES. Green’s creativity, focused on satellites and orbits, had an extremely important impact on the success of GPS.
The result of Parkinson’s hunting license was a cadre of about 25 of the best and brightest people that the Air Force had to offer.
In addition there was a small, carefully-selected group of Aerospace technical support personnel (led by Walt Melton from 1970 to 1972). This fine group of Aerospace engineers and scientists was experienced in an all technical aspects of space navigation programs and particularly skilled at issues relating to signal modulation, satellite position prediction, and building long-life satellites. Many of their names will be highlighted in Part Two of this story. The Aerospace contingent continued to enjoy the strong support of the president of the Aerospace Corporation, Ivan Getting.
Replacing Melton early in Phase One was Ed Lassiter, who had extensive space-flight experience and was a mainstay of the early GPS development.
Credit: Bradford W. Parkinson and Stephen T. Powers
During early spring of 1973, the director of Defense Research and Engineering (DDR&E), Dr. Malcolm Currie, formerly of Hughes Aircraft, who had just been appointed to the number three position in the DoD, found himself flying between Washington, D.C. and Los Angeles on most weekends. His secondary purpose was to oversee the relocation of his family, but he needed an official reason to travel to Los Angeles. So, each Friday afternoon he would visit SAMSO in Los Angeles for a presentation. After a few weeks, his host Gen. Schultz ran out of subjects to present, and instead invited Currie to spend an afternoon with his new program director, Col. Parkinson.
Schultz’s invitation led to an astonishing meeting, because a newly-promoted colonel does not usually have the opportunity to confer with the number three person in the DoD over an uninterrupted three- or four-hour period. This informal meeting was held in private, in a very small cubicle within the JPO offices. With a Ph.D. in physics, Currie was a very quick study, so the interaction was lively and deep, delving into every aspect of the 621B proposal. After that meeting, Currie became a good friend to and a sponsor of the new satellite-based navigation program. He later played a critical role in ensuring DoD support, particularly in light of the Air Force’s attempts to cancel the infant program.
DSARC 1. On August 17, 1973, Parkinson was invited to the Defense Systems Acquisition Review Council meeting to make a presentation on 621B. The meeting’s purpose was to determine whether to proceed with the concept demonstration program. It was held at the Pentagon, and attended by senior officers of all services, with Mal Currie presiding. At the meeting’s conclusion, the Council voted against approving the 621B program. Currie immediately invited Parkinson into his private office to tell him he wanted a new system proposal developed that would incorporate the best features of all the technical alternatives. He emphasized the need for a joint program involving all services.
Lonely Halls Meeting. Parkinson immediately called a meeting in the Pentagon over Labor Day weekend, September 1973. Over that weekend, the world’s largest office building appeared to be a series of poorly-lit, uninhabited tunnels because everyone was away on vacation. The light at end of those tunnels, both figuratively and literally, came from a small conference room on the top floor, seating about a dozen attendees, all Air Force officers except for three Aerospace Corporation engineers. The purpose of the meeting was to define modifications to the 621B proposal that would meet Currie’s directive. Parkinson wanted the isolation to ensure unfettered creativity in defining the new proposal.
Leading to this, the Analytical Sciences Corporation (TASC) under the guidance of Gaylord Green had completed a new systems study, a review and update of the earlier systems study directed by Jim Woodford and Hideyoshi Nakamura for project 621B in 1964–66.
After much deliberation, over that weekend the JPO defined the GPS with ten facets:
The fundamental 621B concept of simultaneous passive ranging to four satellites would be the underlying principle of the new system proposal, ensuring that user equipment would not require a synchronized atomic clock.
The signal structure would be the 621B CDMA modulation. It would include both a clear, acquisition modulation (C/A) and a precision military modulation (P/Y). The C/A modulation was to be freely available to civil users throughout the world.
There would be two GPS broadcast frequencies in the L band, using the same dual-frequency technique that Transit had employed to correct for ionospheric group delay, as well as providing redundancy.
Based on the progress that NRL had made in satellite clocks, the program committed to space-hardened atomic clocks on the first operational/demonstration GPS satellites (called Navigation Development Satellites, or NDS). At the Lonely Halls meeting, Parkinson concluded that the NRL technology was relatively low-risk, obviating the need to use the ground-relay, experimental demonstration scheme that 621B had previously proposed. It later turned out that the clock development was not as mature as it appeared, but the JPO backup clock development by Rockwell was available in time for the first launch.
The orbits for the satellites were to be inclined at 62º and not geosynchronous. Green proposed 11-hour, 58-minute (sidereal synchronous) orbits that gave about two hours of testing over the same United States test area each day. NRL had advocated similar 8- or 12-hour inclined orbits. Because of the need for an extensive testing program on an instrumented range, exact 8- or 12-hour orbits would have been unsatisfactory, because they would continuously shift relative to the Earth. While these orbits resembled those advocated by NRL, Green’s modification was critical to the success of the testing program.
Orbit prediction would be handled with modifications to the Transit-developed orbit-prediction programs called Celeste.
The initial test constellation would include four operational satellites, competitively procured, one of which would be a refurbished qualification model. They would be launched on refurbished Atlas-F rockets, which minimized cost, but also limited the number of solar panels that could be carried because of weight.
A family of user equipment prototypes would be procured competitively. This equipment would span all normal military uses, and also include a low-cost set that would prototype civilian use. Where affordable, competitive contracts would be let. Particular attention would be devoted to user equipment integration with inertial navigation units and demonstration of anti-jam capabilities.
The master control station and its backup would be on U.S. soil, but monitor stations would be placed around the world. >
The testing would be principally performed at the Army’s Yuma test range with accuracy measured from a tri-lateration laser configuration. Using three laser ranging devices at the same time would ensure that all test vehicles could be measured to about a meter of positioning error. It was expected (and later proven) that this technique could even calibrate Air Force or Navy fighter aircraft flying close to Mach 1. Testing would make use of the inverted range concept, with satellites replacing each range transmitter as each newly launched GPS satellite became operational on orbit.
Dual Use. One aspect should be strongly pointed out. Contrary to some versions of GPS history, from the very beginning, GPS was configured to be a dual-use system. Civilian users were to be given free access to the signal specification and were expected to use the so-called clear acquisition signal for navigation and other purposes. In fact, Parkinson highlighted civilian use when he testified before Congress on the proposed new system.
GPS Approval. That Labor Day weekend of September 1973 had been a very busy three days. With help from the Air Staff Program Element Monitor (PEM) Lt. Col. Paul Martin, the Lonely Halls gathering developed a seven-page Decision Coordinating Paper (DCP) and a presentation of the new concept. Over the next two-and-a-half months there was a flurry of activity as Parkinson made presentations and defended the concept before all those who could block the proposal in the Pentagon. This effort was culminated with the approval to proceed on December 14, 1973. There were no significant modifications to the proposal that had been developed during the Lonely Halls meeting in the Pentagon.
During the whole Phase I development, Parkinson resolved to avoid any conflict with the other original competitors to build a satellite-based navigation system. He deliberately ignored dubious claims of invention and statements regarding the origins of GPS technology. Until quite recently, he has overlooked these false claims by those who did not directly participate in determining the GPS architecture and did not participate in the specific GPS design and deployment. He felt the real purpose was to build the system, not to fight over credit.
Recently an article appeared that implied that the GPS design was essentially the same as Timation. (“In what ways did GPS improve on Timation?” Easton: “I can’t think of any ways in which GPS improved on Timation. Essentially, they are the same system.” Interview in High Frontier magazine.)
Aware that this incorrect statement denigrated the people who had first analyzed, advocated, and demonstrated the fundamental concept, as well as built the system, Parkinson resolved to correct the record, and highlight the names of those who deserve credit. This is a major purpose of this article. This article has been reviewed and approved for veracity by virtually all the key figures (still alive) who actually designed, built, and tested GPS.
End of Part One. Watch for Part Two in our June issue.
Some of the JPO Heroes at a Dining In. From left, Major Mel Birnbaum (made many important contributions. He was famous for marathon code reviews that could last 18 hours straight. He hated to miss schedules!); Col. Don Henderson (later Maj. Gen.), second Air Force Deputy; Major Ralph Tourino (later Maj. Gen.), Program Control; Lt. Col. Ken Juvette, director of procurement; and Lt. Cdr. Joe Strada, a key leader in the extensive test program. (Credit: Bradford W. Parkinson and Stephen T. Powers)
Our Story Continues
Part 2 of “The Origins of GPS” appears in the June 2010 issue of GPS World. GPS Phase I program approval meant that the real work could begin. By January 1974, the GPS program at the JPO was well underway. Of course there were many challenges, but Five Challenges, principally engineering, stand out as particularly daunting. Part Two also describes GPS’ most fundamental innovation, more on system origins, innovations of the Joint Program Office (see photo of key figures), and thoughts on the future of GPS and GNSS.
True to its word origins, accuracy demands careful and thoughtful work. This article provides a close look at the differences between the precision and accuracy of GPS-determined positions, and should alleviate the confusion between the terms — making abuse of the truth perhaps less likely in the business of GPS positioning.
INNOVATION INSIGHTS by Richard Langley
JACQUES-BÉNIGNE BOSSUET, the 17th century French bishop and pulpit orator, once said “Every error is truth abused.” He was referring to man’s foibles, of course, but this statement is much more general and equally well applies to measurements of all kinds. As I am fond of telling the students in my introduction to adjustment calculus course, there is no such thing as a perfect measurement. All measurements contain errors. To extract the most useful amount of information from the measurements, the errors must be properly analyzed.
Errors can be broadly grouped into two major categories: biases, which are systematic and which can be modeled in an equation describing the measurements, thereby removing or significantly reducing their effect; and noise or random error, each value of which cannot be modeled but whose statistical properties can be used to optimize the analysis results.
Take GPS carrier-phase measurements, for example. It is a standard approach to collect measurements at a reference station and a target station and to form the double differences of the measurements between pairs of satellites and the pair of receivers. By so doing, the biases in the modeled measurements that are common to both receivers, such as residual satellite clock error, are canceled or significantly reduced. However, the random error in the measurements due to receiver thermal noise and the quasi-random effect of multipath cannot be differenced away. If we estimate the coordinates of the target receiver at each epoch of the measurements, how far will they be from the true coordinates?
That depends on how well the biases were removed and the effects of random error. By comparing the results from many epochs of data, we might see that the coordinate values agree amongst themselves quite closely; they have high precision. But, due to some remaining bias, they are offset from the true value; their accuracy is low. Two different but complementary measures for assessing the quality of the results.
In this month’s column, we will examine the differences between the precision and accuracy of GPS-determined positions and, armed with a better understanding of these often confused terms, perhaps be less likely to abuse the truth in the business of GPS positioning.
“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.
For many, Global Positioning System (GPS) measurement errors are a mystery. The standard literature rarely does justice to the complexity of the subject. A basic premise of this article is that despite this, most practical techniques to evaluate differential GPS measurement errors can be learned without great difficulty, and without the use of advanced mathematics. Modern statistics, a basic signal-processing framework, and the careful use of language allow these disruptive errors to be easily measured, categorized, and discussed.
The tools that we use today were developed over the last 350 years as mathematicians struggled to combine measurements and to quantify error, and to generally understand the natural patterns. A distinguished group of scientists carried out this work, including Adrien-Marie Legendre, Abraham de Moivre, and Carl Friedrich Gauss. These luminaries developed potent techniques to answer numerous and difficult questions about measurements.
We use two special terms to describe systems and methods that measure or estimate error. These terms are precision and accuracy. They are terms used to describe the relationship between measurements, and to underlying truth. Unfortunately, these two terms are often used loosely (or worse used interchangeably), in spite of their specific definitions. Adding to the confusion, accuracy is only properly understood when divided into its two natural components: internal accuracy and external accuracy.
GPS measurements are like many other signals in that with enough samples the probability distribution for each of the three components is typically bell-shaped, allowing us to use a particularly powerful error model. This bell-shaped distribution is often called a Gaussian distribution (after Carl Friedrich Gauss, the great German mathematician) or a normal distribution. Once enough GPS signal is accumulated, a normal distribution forms. Then, potent tools like Gauss’s normal curve error model and the associated square-root law can be brought to bear to estimate the measurement error.
An interesting aspect of GPS, however, is that over short periods of time, data are not normally distributed. This is of great importance because many applications are based upon small datasets. This results in a fundamental division in terms of how measurement error is evaluated. For short periods of time, the gain from averaging is difficult to quantify, and it may or may not improve accuracy. For longer periods of time the gain from averaging is significant, a normal distribution forms, and the square-root law is used to estimate the gain. The absence of a Gaussian distribution in these datasets (1 hour or less) is one source of the confusion surrounding measurement error. Another source of confusion is the richly nuanced concept of accuracy. By closely looking at each of these, a clear picture emerges about how to effectively analyze and describe differential GPS measurement error.
The GPS Signal
It is helpful to consider consecutive differential GPS measurements as a signal, and thus from the vantage of signal processing. Here, we use the term measurement to refer to position solutions rather than the raw carrier-phase and pseudorange measurements a receiver makes. Sequential position measurements from a GPS system are discrete signals, the result of quantization, transformation, and other processing of the code and carrier data into more meaningful digital output. In comparison, a continuous signal is usually analog based and assumes a continuous range of values, like a DC voltage. A signal is a way of describing how one value is related to another.
Figure 1 shows a time series consisting of a discrete signal from a typical GPS dataset (height component). These data are based on processing carrier-phase data from a pair of GPS receivers, in double-difference mode, holding the position of one fixed while estimating that of the other. The vertical axis is often called the dependent variable and can be assigned many labels. Here it is labeled GPS height. The horizontal axis is typically called the independent variable, or the domain. This axis could be labeled either time or sample number, depending on how we want this variable to be represented. Here it is labeled sample number. The data in Figure 1 are in the time domain because each GPS measurement was sampled at equal intervals of time (1 second). We’ll refer to a particular data value (height) as xi.
Figure 1. A 10-minute sample of GPS height data.
Ten minutes of GPS data are displayed in Figure 1. These data are the first 600 measurements from a larger 96-hour dataset that forms the basis of this paper. The mean (or average) is the first number to calculate in any error-assessment work. The mean is indicated by . There is nothing fancy in computing the mean; simply add all of the measurements together and divide by the total sample number, or N. Equation 1 is its mathematical form:
[1]
The mean for these data is 474.2927 meters, and gives us the average value or “center” of the signal. By itself, the mean provides no information on the overall measurement error, so we start our investigation by calculating how far each GPS height determination is located away from the mean, or how the measurements spread or disperse away from the center. In mathematical form, the expression denotes how far the ith sample differs from the mean.
As an example, the first sample deviates by 0.0038 meters (note that we always take the absolute value). The average deviation (or average error) is found by simply summing the deviations of all of the samples and dividing by N. The average deviation quantifies the spreading of the data away from the mean, and is a way of calculating precision. When the average deviation is small, we say the data are precise. For these data, the average deviation is 0.0044 meters.
For most GPS error studies, however, the average deviation is not used. Instead, we use the standard deviation where the averaging is done with power rather than amplitude. Each deviation from the mean, , is squared, , before taking the average. Then the square root is taken to adjust for the initial squaring. Equation 2 is the mathematical form of the standard deviation (SD):
[2]
The standard deviation for the data in Figure 1 is 0.0052 meters.
But note that these data have a changing mean (as indicated by the slowly varying trend). The statistical or random noise remains fairly constant, while the mean varies with time. Signals that change in this manner are called nonstationary. In this 10-minute dataset, the changing mean interferes with the calculation of the standard deviation. The standard deviation of this dataset is inflated to 0.0052 meters by the shifting mean, whereas if we broke the signal into one-minute pieces to compensate, it would be only 0.0026 meters.
To highlight this, Figure 2 is presented as an artificially created (or synthetic) dataset with a stationary mean equal to the first data point in Figure 1, and with the standard deviation set to 0.0026 meters. This figure, with its stable mean and consistent random noise, displays a Gaussian distribution (as we will soon see graphically), and illustrates what our dataset is not.
Figure 2. A 10-minute sample of synthetic data.
Contrasting these two datasets helps us to understand a critical aspect of differential GPS data. Analyzing a one-minute segment of GPS data from Figure 1 would provide a correct estimate of the standard deviation of the higher frequency random component, but would likely provide an incorrect estimate of the mean. This is because of its wandering nature; a priori we do not know which of the 10 one-minute segments is closer to the truth. It is tempting then to think that by calculating the statistics on the full 10 minutes we will conclusively have a better estimate of the mean, but this is not true.
The mean might be moving toward or away from truth over the time period. It is not yet centered over any one value because its distribution is not Gaussian. What’s more, when we calculate the statistics on the full 10 minutes of data, we will distort the standard deviation of the higher frequency random component upwards (from 0.0026 meters to 0.0052 meters).
This situation results in a great deal of confusion with respect to the study of GPS measurement error. When we look at Figures 1 and 2 side by side we see the complication. Figure 2 is a straightforward signal with stationary mean and Gaussian noise. Averaging a consecutive series of data points will improve the accuracy. Figure 1 is composed of a higher frequency random component (shown by the circle), plus a lower frequency non-random component. It is the superimposition of these two that causes the trouble. We cannot reliably calculate the increase in accuracy as we accumulate more data until the non-random component converges to a random process. This results in a very interesting situation; in numerous cases gathering more data can actually move the location parameter (the mean, ) away from truth rather than toward it.
To fully understand the implications of this, consider its effect on estimating accuracy. If the mean is stationary, statistical methods developed by Gauss and others could be used to estimate the measurement error of an average for any set of N samples. For example, the so-called standard error of the average (SE) can be computed by taking the square root of the sample number, multiplying it by the standard deviation, and then dividing by the sample number (a method to provide an estimate of the error for any average that is randomly distributed). Equation 3 is its mathematical form:
[3]
which simplifies to S/√N . This model can only be used if the data have a Gaussian distribution. Clearly this model cannot be used for the data in Figure 1, but can be used for the data in Figure 2. The implications are significant. The data from Figure 1 are not Gaussian because of the nonstationary mean, so we do not know if the gain from 10 minutes of averaging is better or worse than the first measurement. By contrast, the data in Figure 2 are Gaussian, so we know that the average of the series is more accurate than any individual measurement by a factor equal to the square root of the measurements.
By shifting these data into another domain we can see this more clearly. Figure 3 shows the 10 minutes of GPS data from Figure 1 plotted as a histogram or distribution of the number of data values falling within particular ranges of values. We call each range a bin. The histogram shows the frequencies with which given ranges of values occur. Hence it is also known as a frequency distribution. The frequency distribution can be converted to a probability distribution by dividing the bin totals by the total number of data values to give the relative frequency. If the number of observations is increased indefinitely and simultaneously the bin size is made smaller and smaller, the histogram will tend to a smooth continuous curve called a probability distribution or, more technically, a probability density function. A normal probability distribution curve is overlain in Figure 3 for perspective. This curve simultaneously demonstrates what a normal distribution looks like, and serves to graphically display the underlying truth (by showing the correct frequency distribution, mean, and standard deviation). It was generated by calculating the statistics of the 96-hour dataset, then using a random-number generator with adjustable mean and standard deviation (this is an example of internal accuracy, and will be discussed at length in an upcoming section). We can see that our Figure 1 dataset is not Gaussian because it does not have a credible bell shape. By contrast, when we convert the synthetic data from Figure 2 into a frequency distribution, we see the effect of the stationary mean — the data are distributed in a normal fashion because the mean is not wandering.
Figure 3. Frequency distribution of a 10-minute sample of GPS height data.
Recall that all that is needed to use the Gauss model of measurement error is the presence of a random process. Mathematically, the measurement accuracy for the average of the data in Figures 1 and 3 is the overall standard deviation, or 0.0052 meters, because there is no gain per the square-root law. In comparison, the measurement accuracy for the average in Figure 4 is SE = (√ 600•0.0026) / 600 = 0.0001 meters. The standard deviation from the mean is still 0.0026 meters, but the accuracy of the averaged 600 samples is 0.0001 meters. Recall that precision is the spreading away from the mean, whereas accuracy is closeness to truth. When a process is normally distributed, the more data we collect the closer we come to underlying truth. The difference between the two is remarkable. Measurement error can be quickly beaten down when the frequency distribution is normal. This has significant implications for people who collect more than an hour of data, and raises the following question: At what point can we use the standard error model?
Figure 4. Frequency distribution of a 10-minute sample of synthetic data.
Frequency Distribution
In an ideal world, GPS data would display a Gaussian distribution over both short and long time intervals. This is not the case because of the combination of frequencies that we saw earlier (random + non-random). As an aside, this combination is a good example of why power is used rather than amplitude to calculate the deviation from the mean. When two signals combine, the resultant noise is equal to the combined power, and not amplitude.
Interesting things happen as we accumulate more data and continue our analysis of the 96-hour dataset. Earlier we discussed calculating the SD and the mean, and we looked at short intervals of GPS data in the time domain and the frequency-distribution domain. Moving forward, we will continue to look at the data in the frequency-distribution domain because it is far easier to recognize a Gaussian distribution there. The goal is to discover the approximate point at which GPS data behave in a Gaussian fashion as revealed by the appearance of a true bell curve distribution.
Figure 5 shows one minute of GPS data along with the “truth” curve for perspective. This normal curve, as discussed above, was generated using a random number generator with programmable SD and mean variables. The left axis shows the probability distribution for the GPS data, and the right axis shows the probability distribution function for the normal curve. This figure reinforces what we already know: one minute of GPS data are typically not Gaussian (Figure 3 shows the same thing for 10 minutes of data).
Figure 5. Frequency distribution of a 1-minute sample of GPS height data.
Figure 6 shows 1 hour of GPS data. The data in Figure 6 show the beginnings of a clear normal distribution. Note that the mean of the GPS data is still shifted from the mean of the overall dataset. The appearance of a normal distribution at around 1 hour of data indicates that we can begin use of the standard error model, or the Gaussian error model. Recall that this states that the average of the collection of measurements is more accurate that any individual measurement by a factor equal to the square root of the number of measurements, provided the data follow the Gauss model and are normally distributed. For one hour of data, the gain is square root of 1 times the SD divided by N. In effect, no gain. But from this point forward each hour of data provides √N gain. Figure 7 shows 12 hours of data with a gain of √12. By calculating the standard error for the average of 12 hours of data, SE = (√12•0.0069)/12, or 0.0020 meters, we see a clear gain in accuracy. Notice also that at 12 hours the normal curve and the GPS data are close to being one and the same.
Figure 6. Frequency distribution of a 1-hour sample of GPS height data.Figure 7. Frequency distribution of a 12-hour sample of GPS height data.
Several things are worth pointing out here. The non-stationary mean converts to a Gaussian process after approximately 1 hour. There is nothing magical about this; conversion at some point is a necessary condition for the system to successfully operate. If it did not, the continually wandering mean would render it of little use as a commercial positioning system. Because it is non-stationary over the shorter occupations considered normal for many applications, it is confusing. Collecting more data in some instances can contribute to less accuracy. This situation also creates a gulf between those who collect an hour or two, and those who collect continuously. It is worth emphasizing that the distribution of data under our “truth” curve fills out nicely after 12 hours. This coincides with one pass of the GPS constellation, suggesting (as we already know) that a significant fraction of the wandering mean is affected by the geometrical error between the observer and the space vehicles overhead.
By looking at the 12 one-hour Gaussian distributions that comprise a 12-hour dataset, we see clearly what Francis Galton discovered in the 1800s. A normal mixture of normal distributions is itself normal, as Figure 8 shows. This sounds simple, but in fact it has significant implications. The unity between consecutive 1-hour segments of our dataset is the normal outline, reinforcing the increasing accuracy of the location parameter, , as more and more normal curves are summed together.
Figure 8. (a) Frequency distribution of 12 1-hour samples of GPS height data; (b) the 12 1-hour samples combined.
Internal vs. External Accuracy
Figure 9 shows the relationship between precision and accuracy. The dashed vertical line indicates the mean of the dataset (the inflection point at which the histogram balances). The red arrows bracket the spread of the dataset at 1 standard deviation from the mean (precision), while the black arrows bracket the offset of the mean from truth (accuracy). Notice that the mean ( ) is a location parameter, while the standard deviation (<e
m>s) is a spread parameter. What we do with the mean is accuracy related; what we do with the standard deviation is precision related.
Figure 9. Relationship between precision and accuracy.
Accuracy is the difference between the true value and our best estimate of it. While the definition may be clear, the practice is not. Earlier we discussed two techniques used to calculate precision — the average deviation, and the standard deviation. We also discussed the square-root law that estimates the measurement error of a series of random measurements. As we saw, it was not possible to calculate this until roughly 1 hour of data had been collected. Furthermore, the data were said to be accurate when a good correlation appeared between the overlain curve and the GPS data at 12 hours.
But here is the interesting thing; the truth curve was derived internally. As previously discussed, data were accumulated for 96 hours, and then statistics were calculated on the overall dataset. Then a random number generator with programmable mean and standard deviation was used to generate a perfectly random distribution curve with the same location parameter and spread. This was declared as truth, and then smaller subsets of the same dataset were essentially compared with a perfect version of itself! This is an example of what is called internal accuracy.
By contrast, external accuracy is when a standard, another instrument, or some other reference system is brought to bear to gauge accuracy. A simple example is when a physical standard is used to confirm a length measurement. For instance, a laser measurement of 1 meter might be checked or calibrated against a 1-meter platinum iridium bar that is accepted as a standard. The important point here is that truth does not just appear — it has to be established through an internal or external process.
Accuracy can be evaluated in two ways: by using information internal to the data, and by using information external to the data. The historical development of measurement error is mostly about internal accuracy. Suppose that a set of astronomical measurements is subjected to mathematical analysis, without explicit reference to underlying truth. This is internal accuracy, and was famously expressed by Isaac Newton in Book Three of his Principia: “For all of this it is plain that these observations agree with theory, so far as they agree with one another.”
Internal accuracy constrains and simplifies the problem. It eliminates the need to bring other instruments or systems to bear. It makes the problem manageable by allowing us to use what we already have. Most importantly, it eliminates the need to consider point of view. Because we are not venturing outside of the dataset, it becomes the reference frame. By contrast, when you ponder bringing an external source of accuracy to bear it gets complicated, especially with GPS.
For example, is it sufficient to use one GPS receiver to check the accuracy of another, or should an entirely different instrument be used? Is it suitable to use the Earth-centered, Earth-fixed GPS frame to check itself, or should another frame be used? If we use another frame, should it extend beyond the Earth, or is it sufficient to consider accuracy from an Earth perspective? When we say a GPS measurement is accurate, what we are really saying is that it is accurate with respect to our reference frame. But what if you were an observer located on the Sun? An Earth-centric frame no longer makes sense when the point that you wish to measure is located on a planet that is rotating in an orbit around you. For an observer on the Sun, a Sun-centered, Sun-fixed reference frame would probably make more sense, and would result in easier to understand measurements. But we are not on the Sun, so a reference frame that rotates with the Earth — making fixed points appear static — makes the most sense. The difference between the two is that of perspective, and it can color our perception of accuracy.
Internal accuracy assessments sidestep these complications, but make it difficult to detect systematic errors or biases. Keep in mind that any given GPS measurement can be represented by the following equation: measurement = exact value + bias + random error. The random-error component presents roughly the same problem for both internal and external assessments. The bias however, requires external truth for detection. There is no easy way to detect a constant shift from truth in a dataset by studying only the shifted dataset.
In practice, people generally look for internal consistency, as Newton did. We look for consistency within a continuous dataset, or we collect multiple datasets at different times and then look for consistency between datasets. It is not uncommon to use the method taken in this article: let data accumulate until one is confident that the mean has revealed truth, and then use this for all further analysis. For this approach, accuracy implies how the measurements mathematically “agree with one another.”
All of this shows that accuracy is a very malleable term. Internal accuracy assumes that the process is centered over truth. It is implicitly understood that more measurements will increase the accuracy once the distribution is normal. The standard error is calculated by taking the square root of the sample number, multiplying it by the standard deviation, and then dividing by the sample number. With more samples, the standard error of the average decreases, and we say that the accuracy is increasing. Internal accuracy is a function of the standard deviation and the frequency distribution.
External accuracy derives truth from a source outside the dataset. Accuracy is the offset between this truth and the measurement, and not a function of the standard deviation of the dataset. The concept is simple, but in practice establishing an external standard for GPS can be quite challenging. For counterpoint, consider the convenient relationship between a carpenter and a tape measure. He is in the privileged position of carrying a replica of the truth standard. GPS users have no such tool. It is impossible to bring a surrogate of the GPS system to bear to check a measurement. Fortunately, new global navigation satellite systems are coming on line to help, but a formal analysis of how to externally check GPS accuracy leads one into a morass of difficult questions.
Accuracy is not a fundamental characteristic of a dataset like precision. This is why accuracy lacks a formal mathematical symbol. One needs to look no further than internal accuracy for the proof. For a dataset that is shifted away from truth, or biased, no amount of averaging will improve its accuracy. Because it is possible to be unaware of a bias using internal accuracy assessments, it follows that accuracy cannot be inherent to a dataset.
Looking at the interplay between mathematical notation and language provides more insight. For example, we describe the mathematical symbol with the word mean. We don’t stop there, however; we also sometimes call it the average. Likewise, the mathematical symbol s is described by the words standard deviation, but we also know s as precision, sigma, repeatability, and sometimes spread. English has a wealth of synonyms, giving it an ability to describe that is unparalleled. In fact, it is one of only a few languages that require a thesaurus. This is why it is important to make a clear distinction between the relatively clear world of mathematical notation and the more free-form world of words. Language gives us flexibility and power, but can also confound with its ability to provide subtle differences in meaning.
When we look at the etymology of the word accuracy, we can see that it is aptly named. It comes from the Latin word accuro, which means to take care of, to prepare with care, to trouble about, and to do painstakingly. Accuro is itself derived from the root cura, which means roughly the same thing and is familiar to us today in the form of the word curator. It is fitting language for a process that requires so much care.
When we discuss measurement error we seldom use mathematical symbols; we use language that is every bit as important as the symbols. The word error itself derives from the Latin erro, which means to wander, or to stray, and suitably describes the random tendency of measurements.
Whether we describe it with mathematics or language, error describes a fundamental pattern we see in nature; independent measurements tend to randomly wander around a mean. When the frequency distribution is normal, accuracy from the underlying truth occurs in multiples of √N. Error is the umbrella covering the other terms because it is the natural starting point for any discussion. Because of this, precision and accuracy are naturally subsumed under error, with accuracy further split into internal and external accuracy. By contemplating all of this, we expose the healthy tension between words and mathematical notation. Neither is perfect. Mathematics establishes natural patterns and provides excellent approximation tools, but is not readily available to everyone. Language opens the door to perspective and point of view, and invites questions in a way that mathematical notation does not.
Final Notes
Making sense of GPS error requires that we take a close look at the intricacies of the GPS signal, with particular attention to the ramp up to a normal distribution. It also requires a good hard look at the language of error. Shifting the GPS data back and forth between the frequency-distribution and time domains nicely illustrates the complications imposed by a non-stationary mean. Datasets that are an hour or less in duration do not always increase in accuracy when the measurements are averaged. Averaging may provide a gain, but it is not a certainty. When the non-stationary mean converges to a Gaussian process after an hour or so, we begin to see what De Moivre discovered almost 275 hundred years ago: accuracy increases as the square root of the sample size.
The GPS system is so good that the division of accuracy into its proper internal and external accuracy components is shimmering beneath the surface for most users. It is rare that a set of GPS measurements has a persistent bias, so internal accuracy assessments are usually appropriate. This should not stop us from being careful with how we discuss accuracy, however. Some attempt should be made to distinguish between the two types, and neither should be used interchangeably with precision. What’s more, while accuracy is not something intrinsic to a dataset like precision, it is still much more than just a descriptive word. Accuracy is the hinge between the formal world of mathematics and point of view. Its derivation from N and s in internal assessments stands in stark contrast to the more perspective-driven derivation often found in external assessments. When carrying out internal assessments, we must be aware that we are assuming that the measurements are centered over truth. When carrying out external assessments, we must be mindful of what outside mechanism we are using to provide truth. True to its word origins, accuracy demands careful and thoughtful work.
David Rutledge is the director for infrastructure monitoring at Leica Geosystems in the Americas. He has been involved in the GPS industry since 1995, and has overseen numerous high-accuracy GPS projects around the world.
FURTHER READING
• Highly Readable Texts on Basic Statistics and Probability The Drunkard’s Walk: How Randomness Rules Our Lives by L. Mlodinow, Pantheon Books, New York, 2008.
Noise by B. Kosko,Viking Penguin, New York, 2006.
• Basic Texts on Statistics and Probability Theory A Practical Guide to Data Analysis for Physical Science Students by Louis Lyons, Cambridge University Press, Cambridge, U.K., 1991.
Principles of Statistics by M.G. Bulmer, Dover Publications, Inc., New York, 1979.
• Relevant GPS World Articles
“Stochastic Models for GPS Positioning: An Empirical Approach” by R.F. Leandro and M.C. Santos in GPS World, Vol. 18, No. 2, February 2007, pp. 50–56.
“GNSS Accuracy: Lies, Damn Lies, and Statistics” by F. van Diggelen in GPS World, Vol. 18, No. 1, January 2007, pp. 26–32.
“Dam Stability: Assessing the Performance of a GPS Monitoring System” by D.R. Rutledge, S.Z. Meyerholtz, N.E. Brown, and C.S. Baldwin in GPS World, Vol. 17, No. 10, October 2006, pp. 26–33.
“Standard Positioning Service: Handheld GPS Receiver Accuracy” by C. Tiberius in GPS World, Vol. 14, No. 2, February 2003, pp. 44–51.
“The Stochastics of GPS Observables” by C. Tiberius, N. Jonkman, and F. Kenselaar in GPS World, Vol. 10, No. 2, February 1999, pp. 49–54.
“The GPS Observables” by R.B. Langley in GPS World, Vol. 4, No 4, April 1993, pp. 52–59.
“The Mathematics of GPS” by R.B. Langley in GPS World, Vol. 2, No. 7, July/August 1991, pp. 45–50.
Aeroflex has introduced the GPSG-1000, a portable GPS and Galileo positional simulator. The GPSG-1000 is lightweight and configurable. It fills a gap in the market by providing a low-cost 12-channel test set that creates three-dimensional simulations, Aeroflex said.
With the advent of GPS signal modernization, many GPS simulators on the market today are now obsolete, according to the company, which is based in Witchita, Kansas. The GPSG-1000 supports civil and military avionics field and bench maintenance technicians, production test technicians, and system integrators with a modern simulator for L1, C/A code and L1C, L2C, L5 GPS modernization signals, as well as new Galileo E1, E5, E6 services. It can be configured with single channel, 6-channel, or 12-channel simulation. Typical tests include acquisition sensitivity, tracking sensitivity, time-to-first-fix for cold/warm/hot starts, time-to-second-fix, positional accuracy, RAIM failure tolerance, and subsystem stimulation for 3D flight execution.
The Aeroflex GPSG-1000 uses modular technology for RF and baseband signal generation to produce highly accurate and repeatable test results. Unlike bench top simulators, Aeroflex’s approach also allows the test system to be upgraded at low cost.
Features include:
Simulation of GPS L1C, L2C, L5 signals, supporting the modernization of signals used by the latest designs of GPS receivers.
Simulation of Galileo E1, E5, E6 signals to support unencrypted services.
SBAS, WAAS/EGNOS L1, L5, for automatic SBAS simulation.
Built-in GPS C/A code receiver for automatic GPS almanac download.
Waypoint navigation, a 3D-navigation scheme that allows airport-to-airport flight plan simulation.
Programmable satellite parameters allow specific tests to be conducted to determine receiver behaviour under degraded or invalid signal conditions.
Dynamic satellite signal simulation for real-world constellation signal conditions.
The GPSG-1000 Portable Positional Simulator is available in single channel, 6-channel, and 12-channel configurations. The GPSG-1000 is available in 16 weeks upon receipt of order.
A Sideways Look at How the Global Positioning System Works
In his 200th Innovation column, Contributing Editor Richard Langley takes a look at GPS by the numbers, getting a sense of how GPS works by examining the key numbers that govern its remarkable capabilities, from zero to pi and beyond.
INNOVATION INSIGHTS by Richard Langley
WELCOME TO INNOVATION COLUMN NUMBER 200. I have managed this column continuously since the first issue of GPS World magazine, which appeared back in 1990. From the outset, we established that the column should deal with issues that have broad application and interest and are presented in terms that are accessible to as wide a range of readers as possible. Since 1990, we have covered a wide range of topics, some of them at the leading edge of GPS development and some of them reviewing the basics of GPS operation in tutorial fashion. The column has appeared 199 times and now we come to number 200.
So clearly 200 is an important number for me and, I hope, for you. But the number 200 is interesting for other reasons, too. It is the smallest base 10 unprimeable number — you can’t turn it into a prime number by changing just one of its digits to any other digit. It’s how many dollars you get when you pass Go in Monopoly. And in 2012, it will be how many years have elapsed since The War of 1812 — the last time Canada and the United States had a serious quarrel (other than in hockey). But more to the point of this column, it is the designation of the basic reference document that describes how GPS works: IS-GPS-200. Formerly known as an Interface Control Document or ICD, it has gone through several revisions since its first public release in July 1991. It is full of numbers. Numbers that tell us how the GPS signals are generated and how a receiver is to interpret the signals to provide a position fix.
If you are a regular reader of the Innovation column, then likely you have an inquisitive bent. You like to know how things work — GPS in particular. And you don’t have to be convinced about the importance of numbers and their role in understanding the world around us. As Sir William Thomson, a.k.a. Lord Kelvin, said in one of his lectures,
“I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.”
So in this column, the 200th, we’re going to look at GPS by the numbers, getting a sense of how GPS works by examining some of the key numbers that govern its remarkable capabilities, from the smallest to the largest. I’ll draw heavily on material from the past 199 columns.
Let’s get started.
“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.
Numbers. We use them for counting and measuring, for labeling and ordering, and for codes and calculations. The number of numbers is infinite. However, there are some special numbers that characterize how GPS works. Some of these are peculiar to GPS; others are more common, finding utility in other global navigation satellite systems or even in our everyday lives. In this article, we’ll take a look at some of these special numbers and their importance to GPS.
We’ll begin with the smallest non-negative number and work our way up to one of the largest GPS-relevant numbers, concluding with an imaginary but very important number.
0
Zero. The smallest cardinal number and the smallest non-negative integer. While zero is a pure real number (a number on an infinitely long number line), it is also a purely imaginary number (see the last entry in this article) because it lies on both the real and imaginary axes on the complex plane. It is used to indicate a null amount. The English mathematician, Alfred North Whitehead, wrote in his 1911 book An Introduction to Mathematics, “The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilized of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought.” Perhaps it was not needed for daily operations in 1911 but it is indispensible in our modern world. For zero is also one of the two binary digits (the other is one, of course) used in the binary or base-2 number system that is fundamental to how computers, digital electronics, and communications systems operate. For example, we represent the GPS pseudorandom noise (PRN) ranging codes and the navigation message as sequences of zeros and ones and the zeros are just as important as the ones.
The C/A- and P(Y)-codes (see entries 1023 and 235,469,592,765,000), along with the navigation message, are modulated onto the signal carriers using binary phase-shift keying or BPSK. BPSK is a digital modulation scheme that conveys a signal by changing, or modulating, the phase of the carrier wave between two values separated by 180°. The spectrum of a BPSK-modulated signal is a sinc function, with most of the power concentrated around the carrier frequency. An alternative modulation technique is binary offset carrier (BOC) modulation. BOC modulation uses a square-wave subcarrier to offset the spectral power from the carrier frequency and thus allows a BOC-modulated signal to share the same bandwidth as a BPSK signal. The new GPS M-code on L1 and L2 uses a BOC(10.23,5.115) — abbreviated as BOC(10,5) — modulation, which specifies a subcarrier frequency of 1021.023 MHz and a spreading-code chipping rate of 5.115 megachips per second. The spreading code is a pseudorandom bit stream from a signal protection algorithm, having no apparent structure or period. The future L1C signal, the new civil signal to be implemented on L1 by Japan’s Quasi-Zenith Satellite System and the GPS III satellites, will also use BOC modulation. And Europe’s Galileo system, now in development, will also use this modulation technique, which has already been tested in space by the forerunner GIOVE test satellites.
0.00000000000001
(Or 1 x 10-14 in scientific notation). The approximate frequency stability of the rubidium atomic frequency standards in the GPS Block IIR satellites. These devices are used to control the frequency and timing of all aspects of the navigation signals, including the generation of the carrier frequencies and the pseudorandom noise modulation codes. Given their role in controlling the timing of the signals, they are also referred to as clocks.
Each Block IIR satellite contains three rubidium clocks, only one of which is active at any time. The others are spares and the GPS Control Segment carries out a “clock swap” when the performance of an active clock begins to deteriorate, cycling through the remaining units. Many of the Block IIR satellites are still on their first clock.
The Block IIF satellites will also contain three clocks, however, only two will be rubidium clocks. The third clock will be a cesium clock. This mixture of clock types is patterned after the arrangement used on the Bloc
k II and IIA satellites, which used two rubidium clocks and two cesiums.
0.77922077922…
The rational number 60/77. A rational number is any number that can be expressed as a fraction or quotient a/b of two integers, with the denominator b not equal to zero. The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same sequence of digits over and over again. The digits 077922 of this particular rational number repeat ad infinitum. And why should we be interested in this particular number? It is the ratio of the L2 and L1 carrier frequencies. This number and its inverse ( — the dot above the 3 indicates it repeats indefinitely) are used in various combinations of GPS measurements. For example, if we let η = 60/77, then the ionosphere-free pseudorange combination is
where P1 is a pseudorange measurement on L1 and P2 is the corresponding pseudorange measurement on L2.
1
The loneliest number according to the American rock band Three Dog Night and the Google calculator (try typing “loneliest number” into the Google search engine). It was also the space vehicle number (SVN) of the first Block I GPS satellite, which was launched on February 22, 1978. The satellite did not stay lonely for long. By the end of the year, three more Block I satellites were launched. In total, 10 Block I satellites were successfully orbited between 1978 and 1985 to demonstrate the feasibility of GPS. SVN1 continued in operation until July 17, 1985.
The first satellite of the Block II operational constellation was launched in February 1989. The four-year hiatus in launches was due, in part, to the Space Shuttle Challenger disaster as it had been planned to launch the operational satellites using the Shuttle. Following the accident, it was decided to continue with expendable rockets for GPS launches but to switch to the newly designed Delta II rocket.
The pace of Block II launches was rapid, with five launches of the original Block II design in 1989 and four in 1990. A modified version of the Block II satellite — the IIA — was developed, and between 1990 and 1997 19 Block IIAs were launched. The Block II and IIA satellites established the operational GPS constellation. Full operational capability was declared on April 27, 1995.
A new variant of the Block II satellite was developed for replenishing the constellation as the earlier satellites were retired. Following an initial launch failure, 12 of the Block IIR satellites were launched between 1997 and 2004.
Under the GPS modernization program, the remaining eight Block IIR satellites were modernized with a new navigation payload that included the L2C and M-code signals as well as a new antenna panel (also included on the last four of the classic Block IIRs). The IIR-M satellites were launched between 2005 and 2009, bringing the total number of GPS satellites ever placed in orbit to 58.
One is also the PRN number of SVN49, the Block IIR-M satellite that was modified to transmit the first L5 GPS signals (see 1176.45).
2.4
The approximate delay, in meters, experienced by a GPS signal propagating vertically (from the zenith) through the neutral atmosphere to a receiver at mean sea level. Although the electrically neutral, or unionized, atmosphere extends from ground level up to 50 kilometers and more, the bulk of it is in the lowest most part we call the troposphere. Consequently, the neutral atmosphere delay is often termed the tropospheric delay. The delay varies with actual atmospheric conditions and the elevation angle at which a GPS signal arrives at the receiver’s antenna. If unaccounted for, tropospheric delay would result in position errors of several meters in the horizontal plane and two to three times these values in the vertical. Predictive or “blind” tropospheric models based on climatology attempt to significantly reduce the effect of the troposphere on GPS position fixes.
One such model is UNB3m, developed at the University of New Brunswick. Using a look-up table of surface meteorological parameter values from standard atmospheric models, it can compute the tropospheric delay for a given day of year, latitude, and station height. For example, the UNB3m zenith delay for a sea-level site at a latitude of 60° on day-of-year 201 is 2.435 meters. UNB3m is able to predict zenith delays with an average root-mean-square error of 4.9 centimeters. Better and more consistent performance has been obtained with a wide-area model developed specifically for North America, UNBw.na.
A version of an earlier UNB model became the basis of the RTCA Minimum Operational Performance Standards (MOPS) troposphere model that is included in the firmware of most GPS receivers.
3.1415926…. π
Every nerd’s favorite number. It is the ratio of a circle’s circumference to its diameter in conventional or Euclidean space. We use it, for example, to convert angles measured in radians to degrees (π radians 4 180 degrees). π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. But we sometimes use an easily remembered fraction, such as 22/7, to get an approximate value. In this case, 3.14. But, if we compute more digits with this fraction, we get 3.1428571…, clearly an incorrect result. A better way to remember π to eight digits is to count the number of letters in each word of the mnemonic “May I have a large container of coffee?”
In computations related to GPS, how many digits of π should be used? It depends. If you are developing your own algorithms and software for modeling GPS observations or determining precise orbits for the satellites, you’ll likely need π to 16 digits for double-precision floating-point calculations. But it would be a mistake to use π to this precision in computing the position of a satellite from the broadcast ephemeris. The GPS interface specification document, IS-GPS-200, specifies a 14-digit value for π (3.1415926535898) in the satellite coordinate computation. Use fewer or more digits, and the resulting satellite coordinates will not be as accurate.
4
This is the minimum number of satellites that a receiver needs to track and generate a pseudorange measurement to produce a three-dimensional “instantaneous” position fix. The receiver solves a system of four nonlinear equations to obtain the three receiver coordinates and the offset of the receiver’s clock from GPS (System) Time. It is possible to use fewer than four satellites for positioning or navigation, but then additional information must come from elsewhere. For example, if we are navigating and we know our height accurately or can safely assume a value, say, so many meters above the sea surface, then only three pseudoranges would be needed to determine the horizontal coordinates. If the number of satellites drops to two, then another assumption must be made to continue navigation (for example, holding the receiver clock offset constant or assuming a constant driving direction). If the clock offset is held constant, then position accuracy deteriorates quickly since the actual receiver clock offset will diverge from the assumed value. On the other hand, if the direction of travel is held constant, the GPS receiver can at least compute the position along the assumed trajectory. In reality, the vehicle will likely not travel along a perfectly straight path and navigation fails after the first turn.
For single-satellite navigation, three assumptions must be made concerning height, trajectory, and clock offset, but the navigation results are, at best, educated guesses.
If a receiver can acquire and track more than four satellites, it typically uses an optimizing Kalman filter procedure to obtain its position.
10.23
The frequency of a GPS satellite atomic frequency standard in megahertz and the fundamental frequency for signal generation in the satellite. The carrier frequencies and the code chipping rates are harmonically related to this frequency. The P-code chipping rate is identical to the fundamental frequency, while the C/A-code rate is 1/10 of it.
12.5
The length of the full navigation message in minutes. To convert the measured signal delays or pseudoranges between the receiver and the satellites, the receiver must know where the satellites are. To do this in real time requires that the satellites broadcast this information. Accordingly, there is a message superimposed on both the L1 and L2 carriers along with the PRN codes. Each satellite broadcasts its own message, which consists of orbital information (the ephemeris) to be used in the position computation, the offset of its clock from GPS Time, and information on the health of the satellite and the expected accuracy of the range measurements.
The message also contains almanac data for all of the satellites in the GPS constellation, as well as their health status and other information. The almanac data, a crude description of the satellite orbits, is used by the receiver to determine the location of each satellite. The receiver uses this information to quickly acquire the signals from satellites that are above the horizon but are not yet being tracked. So, once one satellite is tracked and its message decoded, acquisition of the signal from other satellites is quite rapid. A receiver will store a copy of the almanac to speed up initial acquisition of satellites when it is switched on.
The GPS navigation message is sent at a relatively slow rate of 50 bits per second, taking 12.5 minutes for all of the information to be transmitted. To minimize the time it takes for a receiver to obtain an initial position, the ephemeris and satellite clock offset data is repeated every 30 seconds.
24
The number of satellites in the current GPS baseline constellation. The GPS constellation went through a number of design alternatives even after the first satellites were launched with different numbers of orbit planes, satellites per plane, and orbit inclinations. The current design has four satellites, irregularly spaced, in six orbit planes. The orbit planes, labeled A through F, are spaced at 60° intervals around the equator with a nominal inclination to the equator of 55°. However, we have typically had a surfeit of satellites with more than 24 in operation since the mid-1990s. In fact, during 2008, as many as 31 satellites were transmitting healthy signals at the same time. However, although a modern GPS receiver should be able to handle a 32-satellite active constellation, there are limits imposed by the GPS Control Segment and some legacy military equipment that currently imposes a 30-satellite active constellation limit.
Although the number of active satellites is well in excess of 24, the constellation has been operated as a 24-satellite constellation without optimizing the orbit locations of the “bonus” satellites. In fact, several pairs of satellites are bunched together minimizing geometrical performance. This is in the process of being changed. The GPS Wing recently announced the transition to a 24+3 or “Expandable 24” baseline constellation. Taking about 24 months to complete, six on-orbit satellites are being rephased within their respective orbit planes to improve the overall geometry of the active constellation so that the number of GPS satellites in view from anywhere on Earth will increase, enhancing the possibility of getting a position fix in partially obscured environments, and potentially improving the accuracy of fixes.
Of course, 24 is also the number of hours in the day during which GPS is available at any point on the Earth’s surface with good sky visibility. It is also the title of a popular American TV series, whose protagonist, Jack Bauer, frequently makes use of imaginary GPS tracking capabilities.
40.3
The scaling factor, which together with the signal frequency and the total electron content, is used to compute the delay experienced by a GPS signal as it propagates through the ionized part of the Earth’s atmosphere. The total electron content is the integrated electron density along the signal’s path. Basically, it is the total number of electrons in a tube with a cross-sectional area of one square meter centered on the signal path. To a very good approximation, the delay, in meters, is computed as
where TEC is the total electron content in so-called TEC units or TECUs (1016 electrons per square meter) and f is the signal carrier frequency in MHz. The scaling factor is a function of the electron’s charge and mass and a constant of electromagnetism theory called the permittivity of free space also known as the electric constant. The scaling factor is actually 40.308193 but this much precision is not generally needed in GPS calculations.hile the code signals are delayed, making pseudoranges longer than they would be in the absence of the ionosphere, the phases of the signal carriers are advanced, make carrier-phase measurements shorter — but by exactly the same magnitude as the code delays.
TEC is highly variable both temporally and spatially. The dominant variability is diurnal following the variation in incident solar radiation. Maximum ionization occurs at approximately 1400 local time. On the ionosphere’s nighttime side, in the absence of solar radiation, free electrons and ions tend to recombine, thereby reducing the TEC. The protonosphere, or uppermost region of the ionosphere, may contribute up to 50 percent of the electron content during the nighttime hours. Typical nighttime values of vertical TEC for mid-latitude sites are of the order of 10 TECU or less with corresponding daytime values of the order of 100 TECU. However, such typical daytime values can be exceeded by a factor of two or more, especially in near-equatorial regions. TEC also varies seasonally with higher values during equinoxes.
1023
This is the number of chips in the C/A-code. The C/A-, or coarse/acquisition-, code is one of the two legacy PRN ranging codes that have been transmitted by all GPS satellites. These PRN codes consist of sequences of binary values (zeros and ones) that, at first sight, appear to have been randomly chosen. But a truly random sequence can only arise from unpredictable causes over which, of course, we would have no control, and which we could not duplicate. However, using a mathematical algorithm or special hardware devices called tapped feedback registers, we can generate sequences that do not repeat until after some chosen interval of time. Such sequences are termed pseudorandom. The apparent randomness of these sequences makes them indistinguishable from certain kinds of noise such as the hiss heard when a conventional AM radio is tuned between stations.
The C/A-code is a sequence of 1,023 binary digits, or chips, which is repeated every millisecond. This means that the chips are generated at a rate of 1,023 million per second and that one chip has a duration of about 1 microsecond.
The C/A-code is generated by two 10-cell feedback registers referred to as G1 and G2. A delayed version of the G2 sequence is obtained by binary adding the contents of a pair of tapped G2 cells and binary adding that result to the output of G1. That becomes the C/A-code. The various alternative pairs of G2 taps (delays) are used to generate the complete set of 36 unique PRN C/A-codes. There are actually 37 PRN C/A-codes, but two of them (34 and 37) are identical. The first 32 codes are assigned to satellites. Codes 33 through 37 are reserved for other uses such as for ground transmitters. This family of codes is a subset known as Gold codes, which have the property that any two have a very low cross correlation (are nearly orthogonal). The term for the codes comes from the inventor, Robert Gold, not from their lustrous properties.
The C/A-code is modulated only onto the L1 carrier, unlike the P(Y)-code (see 235,469,592,765,000) which appears on both L1 and L2. However, beginning with the first Block IIR-M or modernized Block IIR satellite, a new civil code, L2C or L2 Civil, has been transmitted on the L2 frequency. The future Block IIF satellites will also transmit L2C.
1023 is also the maximum value of the GPS week. This is the number of full weeks that have elapsed since the GPS Time zero point of midnight UTC beginning January 6, 1980 — but with a special counting procedure. GPS weeks are numbered consecutively with week zero starting on January 6 and ending on January 12, 1980. The GPS week, together with the Z-count (see 403199), specifies an epoch or event related to GPS signals or measurements. The current GPS week is included in subframe one of the navigation message, which — along with other subframes containing satellite clock, ephemeris data, and other user-required information — is transmitted every 30 seconds. Only 10 bits are used to represent the GPS week, and so the largest possible week number is 1023 (210–1). In other words, the GPS week number is modulo 1024 (see the “Modular Arithmetic” sidebar). At the end of week number 1023, the week number rolls over to zero. This first occurred on August 21/22, 1999, and caused difficulties for some GPS receivers as their manufacturers had failed to account for the “end-of-week rollover” in receiver firmware. The next occurrence will be in April 2019. By that time, the new Civil Navigation (CNAV) message will be in use, in which the GPS week number is represented as a 13-bit value, meaning it rolls over after 8192 weeks, or about every 157 years.
Although officially the GPS week number is still modulo 1024, some agencies, such as the International GNSS Service, prefer to use a running count of the GPS week, ignoring the rollover. The number of the week beginning April 4, 2010, is then alternatively given as 1578 or 554. Or, mathematically speaking (see sidebar), 1578 ≡ 554 (mod 1024).
1176.45
The L5 carrier frequency in megahertz. The L5 carrier frequency is obtained by electronically multiplying the satellite 10.23 MHz standard frequency by 115. It is the lowest and the newest of the GPS frequencies and is used for the new civil-only GPS signal.
The addition of the L5, or Link 5, civil signal to the suite of signals transmitted by the satellites is a key feature of GPS modernization. The introduction of such a signal on a different carrier frequency than that used by the legacy L1 GPS signal was proposed in the 1995 reports by the U.S. National Research Council and the National Academy of Public Administration on the future of GPS. The reports argued that an unencrypted signal on a second frequency would offer civil users the benefit of ionospheric delay correction, wide-lane carrier-phase ambiguity resolution, improved interference rejection, and faster accuracy recovery in multipath environments. The frequency is in a protected aeronautical radionavigtion services band and, unlike L2, means that L5 can be used for safety-of-life services. The L5 signal will be standard on all Block IIF and future satellites. An L5 demonstration payload was included on Block IIR-M satellite SVN49 to secure the L5 frequency under the rules of the International Telecommunication Union.
1227.60
The L2 carrier frequency in megahertz. The L2, or Link 2, carrier is modulated with the P(Y)-code. Additionally, starting with the Block IIR-M satellites, a new civil ranging code, L2C, is being transmitted on L2 along with the new military M-code. These new signals are also part of the GPS modernization effort. The L2 carrier frequency is obtained by electronically multiplying the satellite 10.23 MHz standard frequency by 120.
1381.05
The L3 carrier frequency in megahertz. This frequency is used in conjunction with the GPS satellites’ secondary purpose, which is to detect nuclear detonations. The L3 carrier frequency is obtained by electronically multiplying the satellite 10.23 MHz standard frequency by 135.
1575.42
The L1 carrier frequency in megahertz. The L1, or Link 1, carrier is modulated with the C/A-code and the P(Y)-code. Starting with the Block IIR-M satellites, the new military M-code is also transmitted on L1. The L1 carrier frequency is obtained by electronically multiplying the satellite 10.23 MHz standard frequency by 154. If you’ve been counting, you’ll have noticed that we didn’t list an L4 frequency. L4 has never been implemented but it has been studied. For example, a frequency of 1841.40 MHz (10.23×180) was once considered for ionospheric correction.
403199
The maximum value of the GPS time of week count. The GPS satellites count and communicate GPS Time in a unique manner that is ultimately related to how they generate the PRN ranging codes. As described below, the P-code is generated by combining two shorter PRN codes, X1 and X2, which are clocked in phase at a chipping rate equal to the satellite’s 10.23-MHz oscillator frequency. X1 has a repetition interval, or period, of 1.5 seconds — a fundamental GPS timing unit. The start of each 1.5-second interval identifies an epoch. The number of X1 epochs since the beginning of the week is called the time of week (TOW) count, which runs from zero to 403,199 at the end of week. The TOW count returns to zero coincident with the resetting of the PRN codes.
The TOW count can be represented as a 19-bit binary number, a truncated version (the 17 most significant bits) of which is part of the handover word (HOW) that a satellite transmits every six seconds. The HOW appears as the second word in each data subframe of the navigation message. These 17 bits correspond to the TOW count at the X1 epoch that occurs at the start of the immediately following subframe, and so effectively preannounces the arrival of a time marker, just like telephone “speaking clocks” and shortwave radio time and frequency stations.
The TOW count by itself cannot be used to unambiguously establish the date of an event. It can only time an event at modulo 604,800 seconds [(403199+1)x1.5] because it is reset every week. This time ambiguity is reduced by noting the number of full weeks that have elapsed since January 6, 1980 modulo 1024 — the GPS week number (see 1023). The TOW count and the GPS week number combine to form the 29-bit Z count. The 19 least-significant bits are the TOW count and the 10 most-significant bits are the GPS week number.
299,792,458
The speed of light in meters per second. This is the speed with which all electromagnetic radiation propagates in a vacuum. Until 1983, the speed of light was measured experimentally using adopted standards for the length of the second and the length of the meter. However, compared to the second, the definition of the meter had a large uncertainty. So in 1983, the 17th General Assembly of Weights and Measures defined the meter as the distance travelled by light in a vacuum during 1/299,792,458 of a second, fixing the speed of light at 299,792,458 meters per second — exactly. This constant is used by a GPS receiver, for example, to convert the measured signal propagation time in seconds to a pseudorange in meters.
235,469,592,765,000
(Or 2.35469592765000 x 1014 in scientific notation). This is the number of chips in the P-code if it were allowed to continue without being reset. The P-, or precision code, is one of the two legacy PRN ranging codes that have been transmitted by all GPS satellites. The other is the C/A-code, already discussed.
The P-code is actually the product of two PRN codes, each of which is generated with a pair of feedback registers. The X1 code has a length of 15,345,000 chips while the X2 code has a length of 15,345,037 or 37 chips longer. So the complete P-code has a length equal to the product of the lengths of the X1 and X2 codes, or 235,469,592,765,000. The codes are clocked at a rate of 10.23 MHz so that each chip has a length of about 0.097752 microseconds. This means the pattern of chips in the full P-code would not repeat for almost 266 days. Each satellite is assigned a unique one-week segment of the P-code, which is reset at Saturday/Sunday midnight each week. The individual P-codes have low cross-correlations with each other. In other words, no significant segments of the P-code of one satellite matches that of another.
Before transmission, a P-code chip sequence is encrypted to form a new sequence called the Y-code. The combined sequence is usually referred to as P(Y). Although civil GPS receivers cannot use conventional correlation procedures to acquire and track the P(Y) code, they can use knowledge of the underlying P-code sequence and C/A-code tracking on L1 to produce pseudorange and carrier-phase measurements on both the L1 and L2 frequencies.
√-1
The square root of -1. This is the unit of imaginary numbers. The concept of imaginary numbers, actually known to the ancient Greeks, was introduced in the effort to solve algebraic equations. Not all equations can be solved using real numbers. In particular, x2=-1 has no real-valued solution. But we can say some solution exists and represent it by the symbol i. (Mathematicians and physicists use this symbol whereas electrical engineers prefer j, since i usually describes a varying electrical current.) Then i has the property — by definition — that its square is -1. Of course, that equation would also permit the solution -i. An imaginary number — sometimes called pure imaginary — is any number of the form bi, where b is a non-zero, real number. A real number, a, and an imaginary number, bi, can be combined into a complex number, a+bi, or a+ib, the more usual notation. Using complex numbers and a set of rules governing their manipulations, any algebraic equation can be solved.
It is useful to consider the real and imaginary parts of a complex number to be orthogonal so that we can represent a complex number geometrically on a plane — the complex plane — where the real component is plotted on the x-axis and the imaginary component on the y-axis. We can then represent a 2-dimensional vector as a complex number, with one component considered real and the other imaginary. The magnitude or modulus of the vector, r, is the positive square root of the sum of the squares of the real and imaginary components with the vector making an angle, Φ , with respect to the positive real axis.
It can be easily shown that
This is Euler’s famous formula, which provides an enlightening connection between plane geometry and algebra.
And, we may also write any complex number in the form
or even more compactly as
If the vector rotates counterclockwise with angular speed ω, its projection onto the real axis generates a sine wave. The modulus of this vector is the amplitude of the oscillations, while its argument is the total phase,
where t is time. The phase constant θ represents the angle that the vector forms with the real axis at t=0. This representation of a sine wave as a phase vector, or phasor, finds great utility in signal theory including descriptions of the propagation of radio waves such as those emitted by GPS satellites.
Modular Arithmetic
GPS Time, like all time systems, is based on modular arithmetic. This arithmetic is a little different from conventional arithmetic in that numbers, typically restricted to integers, have a finite maximum value. Adding one to that number doesn’t get you a larger number — it gets you a smaller one, a much smaller one: zero.
Modular arithmetic is known to us all as clock arithmetic. Take the 24-hour time system as an example. If it’s currently 1800, then 8 hours later we say it’s 0200, not 2600. Similarly, if it’s currently 0400, then 6 hours earlier it was not -0200 but 2200. The idea here is that if two numbers differ by 24 or a multiple of 24, then they are “equal.” We could simply write 26 = 2 but this could be confusing. So we write 26 ≡ 2 (mod 24), and -2 ≡ 22 (mod 24), or in words, 26 is congruent (or somehow “equal”) to 2 (modulo 24) and -2 is congruent to 22 (modulo 24). In arithmetic modulo 24, any number larger than 24 is congruent to some number less than 24 because we can always subtract a multiple of 24 from the larger number to get the smaller one. Similarly, any negative number is congruent to some positive number less than 24, and 24 is congruent to 0. This means that in arithmetic modulo 24, we need deal only with integers from 0 to 23.
We can choose any positive integer for the modulus and carry out arithmetic operations accordingly. Using a modulus of 4, for example, we would have 2+2=0 in our loose notation — a disturbing result if interpreted as conventional arithmetic. But when written 2+2 ≡ 0 (mod 4), the meaning is clear.
As another example of modular arithmetic, consider this question: If today is Monday, what day of the week is it 185 days from now? The modulus here of course is 7, the number of days in the week. So, mathematically stated: 1+185 ≡ ? (mod 7). The answer: 4 or Thursday. The answer is obtained by dividing the sum on the left side of the congruency by 7, using “long division,” and noting the remainder. Or, alternatively, the sum is divided by 7, and the decimal part of the result is then multiplied by 7.
An interesting quirk of modular arithmetic is that a number and the sum of its digits are congruent, modulo 9. This property is the basis for a formerly well-known procedure (before the days of calculators and computers) for checking the correctness of hand multiplication — the rule for casting out nines, which states that the product of two numbers and the product of the sums of their digits must have the same remainder on division by 9.
Many computer languages have a built-in modular arithmetic function or operator. Typically called MOD, it returns the remainder from an integer division operation. In BASIC, for example, if we enter 5 MOD 2, we get 1 because 5 divided by 2 is 2 with a remainder of 1. The same computation is coded 5 2 MOD in Forth, 5 % 2 in Python, and MOD (5,2) in FORTRAN.
The following line of FORTRAN code by Henry Fliegel of The Aerospace Corporation inherently uses modular arithmetic by way of integer division to determine the Julian day (JD) number from the year, month, and day of an AD Gregorian calendar date, incorporating all leap year rules:
And just how can the GPS end-of-week rollover be described using modular arithmetic? Very simply: 1023+1 ≡ 0 (mod 1024).
FURTHER READING
• GPS Interface Control Documents
Navstar GPS Space Segment / Navigation User Interfaces, Interface Specification, IS-GPS-200 Revision D (IRN-200D-001), prepared by ARINC Engineering Services LLC, El Segundo, California, March 2006.
Navstar GPS Space Segment / User Segment L5 Interfaces, Interface Specification, IS-GPS-705 Revision IRN-705-003, prepared by ARINC Engineering Services LLC, El Segundo, California, 22 September 2005.
Navstar GPS Space Segment / User Segment L1C Interfaces, Interface Specification, IS-GPS-800,
prepared by Science Applications International Corporation, El Segundo, California, 4 September 2008.
• Imaginary Numbers
An Imaginary Tale: The Story of √-1 by Paul J. Nahin, Princeton University Press, Princeton, New Jersey, paperback edition, 2007.
By Axel van den Berg, Tom Willems, Graham Pye, and Wim de Wilde, Septentrio Satellite Navigation, Richard Morgan-Owen, Juan de Mateo, Simone Scarafia, and Martin Hollreiser, European Space Agency
A fully stand-alone, multi-frequency, multi-constellation receiver unit, the TUR-N can autonomously generate measurements, determine its position, and compute the Galileo safety-of-life integrity.
Development of a reference Galileo Test User Receiver (TUR) for the verification of the Galileo in-orbit validation (IOV) constellation, and as a demonstrator for multi-constellation applications, has culminated in the availability of the first units for experimentation and testing. The TUR-N covers a wide range of receiver configurations to demonstrate the future Galileo-only and GPS/Galileo combined services:
Galileo single- and dual-frequency Open Services (OS)
Galileo single- and dual-frequency safety-of-life services (SoL), including the full Galileo navigation warning algorithms
Galileo Commercial Service (CS), including tracking and decoding of the encrypted E6BC signal
GPS/SBAS/Galileo single- and dual- frequency multi-constellation positioning
Galileo single- and dual-frequency differential positioning.
Galileo triple-frequency RTK.
In parallel, a similar test user receiver is specifically developed to cover the Public Regulated service (TUR-P). Without the PRS components and firmware installed, the TUR-N is completely unclassified.
Main Receiver Unit
The TUR-N receiver is a fully stand-alone, multi-frequency, multi-constellation receiver unit. It can autonomously generate measurements, determine its position, and compute Galileo safety-of-life integrity, which is output in real time and/or stored internally in a compact proprietary binary data format.
The receiver configuration is fully flexible via a command line interface or using the dedicated graphical user interface (GUI) for monitoring and control. With the MCA GUI it is also possible to monitor the receiver operation (see Figure 1), to present various real-time visualizations of tracking, PVT and integrity performances, and off-line analysis and reprocessing functionalities. Figure 2 gives an example of the correlation peak plot for an E5 AltBOC signal.
FIGURE 1. TUR-N control screen.FIGURE 2. E5 AltBOC correlation peak.
A predefined set of configurations that map onto the different configurations as prescribed by the Test User Segment Requirements (TUSREQ) document is provided by the receiver.
The unit can be included within a local network to provide remote access for control, monitoring, and/or logging, and supports up to eight parallel TCP/IP connections; or, a direct connection can be made via one of the serial ports.
Receiver Architecture
The main receiver unit consists of three separate boards housed in a standard compact PCI 19-inch rack. See Figure 3 for a high-level architectural overview.
FIGURE 3. Receiver architecture.
A dedicated analog front-end board has been developed to meet the stringent interference requirements. This board contains five RF chains for the L1, E6, E5a/L5, E5b, and E5 signals. Via a switch the E5 signal is either passed through separate filter paths for E5a and E5b or via one wide-band filter for the full E5 signal. The front-end board supports two internal frequency references (OCXO or TCXO) for digital signal processing (DSP).
The DSP board hosts three tracker boards derived from a commercial dual-frequency product family. These boards contain two tracking cores, each with a dedicated fast-acquisition unit (FAU), 13 generic dual-code channels, and a 13-channel hardware Viterbi decoder. One tracking core interacts with an AES unit to decrypt the E6 Commercial Service carrier; it has a throughput of 149 Mbps.
Each FAU combines a matched filter with a fast Fourier transform (FFT) and can verify up to 8 million code-frequency hypotheses per second. Each of the six tracker cores can be connected with one of the three or four incoming IF streams. To simplify operational use of the receiver, two channel-mapping files have been defined to configure the receiver either for a 5-frequency 13-channel Galileo receiver, or for a dual-frequency 26-channel Galileo/GPS/SBAS receiver. Figure 4 shows all five Galileo signal types being tracked for nine visible satellites at the same time.
FIGURE 4. C/N0 plot with nine satellites and all five Galileo signal types: L1BC (green), E6BC (blue), E5a (red), E5b (yellow), and E5 Altboc (purple).
The receiver is controlled using a COTS CPU board that also hosts the main positioning and integrity algorithms. The processing power and available memory of this CPU board is significantly higher than what is normally available in commercial receivers. Consequently there is no problem in supporting the large Nequick model used for single-frequency ionosphere correction, and achieving the 10-Hz update rate and low latency requirements when running the computationally intensive Galileo integrity algorithms. For commercial receivers that are normally optimized for size and power consumption, these might prove more challenging.
The TUR project included development of three types of Galileo antennas:
a triple-band (L1, E6, E5) high-end antenna for fixed base station applications including a choke ring;
a triple-band (L1, E6, E5) reference antenna for rover applications;
a dual-band (L1, E5b) aeronautic antenna for SOL applications
Figure 5 shows an overview of the main interfaces and functional blocks of the receiver, together with its antenna and a host computer to run the MCA software either remotely or locally connected.
FIGURE 5. TUR-N with antenna and host computer.
Receiver Verification
Currently, the TUR-N is undergoing an extensive testing program. In order to fully qualify the receiver to act as a reference for the validation of the Galileo system, some challenges have to be overcome. The first challenge that is encountered is that the performance verification baseline is mainly defined in terms of global system performance. The translation of these global requirements derived from the Galileo system requirements (such as global availability, accuracy, integrity and continuity, time-to-first/precise-fix) into testable parameters for a receiver (for example, signal acquisition time, C/N0 versus elevation, and so on) is not trivial. System performances must be fulfilled in the worst user location (WUL), defined in terms of dynamics, interference, and multipath environment geometry, and SV-user geometry over the Galileo global service area.
A second challenge is the fact that in the absence of an operational Galileo constellation, all validation tests need to be done in a completely simulated environment. First, it is difficult to assess exactly the level of reality that is necessary for the various models of the navigation data quality, the satellite behaviour, the atmospheric propagation effects, and the local environmental effects. But the main challenge is that not only the receiver that is being verified, also the simulator and its configuration are an integral part of the verification. It is thus an early experience of two independent implementations of the Galileo signal-in-space ICD being tested together. At the beginning of the campaign, there was no previously demonstrated or accepted test reference.
Only the combined efforts of the various receiver developments benchmarked against the same simulators together with pre-launch compatibility tests with the actual satellite payload and finally IOV and FOC field test campaigns will ultimately validate the complete system, including the Galileo ground and space segments together with a limited set of predefined user segment configurations. (Previously some confidence was gained with GIOVE-A/B experimental satellites and a breadboard adapted version of TUR-N). The TUR-N was the first IOV-compatible receiver to be tested successfully for RF compatibility with the Galileo engineering model satellite payload.
Key Performances
Receiver requirements, including performance, are defined in the TUSREQ document.
Antenna and Interference. A key TUSREQ requirement focuses on receiver robustness against interference. It has proven quite a challenge to meet the prescribed interference mask for all user configurations and antenna types while keeping many other design parameters such as gain, noise figure, and physical size in balance. For properly testing against the out-of-band interference requirements, it also proved necessary to carefully filter out increased noise levels created by the interference signal generator.
Table 2 gives an overview of the measured values for the most relevant Antenna Front End (AFE) parameters for the three antenna types. Note: Asymmetry in the AFE is defined as the variation of the gain around the centre frequency in the passband. This specification is necessary to preserve the correlation peak shape, mainly of the PRS signals.
The gain for all antenna front ends and frequencies is around 32 dB. Figures 6 and 7 give an example of the measured E5 RHCP radiating element gain and axial ratio against theta (the angle of incidence with respect to zenith) for the high-end antenna-radiating element. Thus, elevation from horizontal is 90-theta.
UERE Performance. As part of the test campaign, TUR performance has been measured for user equivalent range error (UERE) components due to thermal noise and multipath.
TUSREQ specifies the error budget as a function of elevation, defined in tables at the following elevations: 5, 10, 15, 20, 30, 40, 50, 60, 90 degrees. The elevation dependence of tracking noise is immediately linked to the antenna gain pattern; the antenna-radiating element gain profiles were measured on the actual hardware and loaded to the Radio Frequency Constellation Simulator (RFCS), one file per frequency and per antenna scenario. The RFCS signal was passed through the real antenna RF front end to the TUR. As a result, through the configuration of RFCS, real environmental conditions (in terms of C/N0) were emulated in factory.
The thermal noise component of the UERE budget was measured without multipath being applied, and interference was allowed for by reducing the C/N0 by 3 dB from nominal. Separately, the multipath noise contribution was determined based on TUSREQ environments, using RFCS to simulate the multipath (the multipath model configuration was adapted to RFCS simulator multipath modeling capabilities in compliance with TUSREQ). To account for the fact that multipath is mostly experienced on the lower elevation satellites, results are provided with scaling factors applied for elevation (“weighted”), and without scaling factors (“unweighted”). In addition, following TUSREQ requirements, a carrier smoothing filter was applied with 10 seconds convergence time.
Figure 8 shows the C/N0 profile from the reference antenna with nominal power reduced by 3 dB. Figure 9 shows single-carrier thermal noise performance without multipath, whereas Figure 10 shows thermal noise with multipath. Each of these figures includes performance for five different carriers: L1BC, E6BC, E5a, E5b, and E5 AltBOC, and the whole set is repeated for dual-frequency combinations (Figure 11 and Figure 12).
FIGURE 8. Reference antenna, power nominal-3 dB, C/N0 profile.FIGURE 9. Reference antenna, power nominal-3 dB, thermal noise only, single frequency.FIGURE 10. Reference antenna, power nominal-3 dB, thermal noise with multipath, single frequency.FIGURE 11. Reference antenna, power nominal-3 dB, thermal noise only, dual frequency.FIGURE 12. Reference antenna, power nominal-3 dB, thermal noise with multipath, dual frequency.
The plots show that the thermal noise component requirements are easily met, whereas there is some limited non-compliance on noise+multipath (with weighted multipath) at low elevations. The tracking noise UERE requirements on E6BC are lower than for E5a, due to assumption of larger bandwidth at E6BC (40MHz versus 20MHz). Figures 9 and 10 refer to UERE tables 2 and 9 of TUSREQ. The relevant UERE requirement for this article is TUSREQ table 2 (satellite-only configuration). TUSREQ table 9 is for a differential configuration that is not relevant here.
UERRE Performance. The complete single-frequency range-rate error budget as specified in TUSREQ was measured with the RFCS, using a model of the reference antenna. The result in Figure 13 shows compliance.
FIGURE 13. UERRE measurements.FIGURE 14. L1 GPS CA versus E5 AltBOC position accuracy (early test result).
Position Accuracy. One of the objectives of the TUR-N is to demonstrate position accuracy. In Figure 14 an example horizontal scatter plot of a few minutes of data shows a clear distinction between the performances of two different single-frequency PVT solutions: GPS L1CA in purple and E5AltBOC in blue. The red marker is the true position, and the grid lines are separated at 0.5 meters. The picture clearly shows how the new E5AltBOC signal produces a much smoother position solution than the well-known GPS L1CA code. However, these early results are from constellation simulator tests without the full TUSREQ worst-case conditions applied.
FIGURE 14. L1 GPS CA versus E5 AltBOC position accuracy (early test result).
The defined TUSREQ user environments, the basis for all relevant simulations and tests, are detailed in Table 3. In particular, the rural pedestrian multipath environment appears to be very stringent and a performance driver.
This was already identified at an early stage during simulations of the total expected UERE and position accuracy performance compliance with regard to TUSREQ, summarized in Table 4, and is now confirmed with the initial verification tests in Figure 10. UERE (simulated) total includes all other expected errors (ionosphere, troposphere, ODTS/BGD error, and so on) in addition to the thermal noise and multipath, whereas the previous UERE plots were only for selected UERE components. The PVT performance in the table is based on service volume (SV) simulations.
The non-compliances on position accuracy that were predicted by simulations are mainly in the rural pedestrian environment. According to the early simulations:
E5a and E5b were expected to have 43-meter vertical accuracy (instead of 35-meter required).
L1/E5a and L1/E5b dual-frequency configurations were expected to have 5-meter horizontal, 12-meter vertical accuracy (4 and 8 required).
These predictions appear pessimistic related to the first position accuracy results shown in Table 5. On single frequency, the error is dominated by ionospheric delay uncertainty. These results are based on measurements using the RFCS and modeling the user environment; however, the simulation of a real receiver cannot be directly compared to service-volume simulation results, as a good balance between realism and worst-case conditions needs to be found. Further optimization is needed on the RFCS scenarios and on position accuracy pass/fail criteria to account for DOP variations and the inability to simulate worst environmental conditions continuously.
Further confirmations on Galileo UERE and position accuracy performances are expected after the site verifications (with RFCS) are completed, and following IOV and FOC field-test campaigns.
Acquisition. Figure 15 gives an example of different signal-acquisition times that can be achieved with the TUR-N after the receiver boot process has been completed. Normally, E5 frequencies lock within 3 seconds, and four satellites are locked within 10 seconds for all frequencies. This is based on an unaided (or free) search using a FAU in single-frequency configurations, in initial development test without full TUSREQ constraints.
FIGURE 15. Unaided acquisition performance.
When a signal is only temporarily lost due to masking, and the acquisition process is still aided (as opposed to free search), the re-acquisition time is about 1 second, depending on the signal strength and dynamics of the receiver. When the PVT solution is lost, the aiding process will time out and return to free search to be robust also for sudden user dynamics.
More complete and detailed time-to-first-fix (TTFF) and time-to-precise-fix (TTPF), following TUSREQ definitions, have also been measured.
In cold start the receiver has no prior knowledge of its position or the navigation data, whereas in warm start it already has a valid ephemeris in memory (more details on start conditions are available in TUSREQ). Table 6 shows that the acquisition performances measured are all compliant to TUSREQ except for warm start in E5a single frequency and in the integrity configurations. However, when the navigation/integrity message recovery time is taken off the measurement (as now agreed for updated TUSREQ due to message limitations), these performances also become compliant.
Specific examples of statistics gathered are shown in figures 16–21, these examples being for dual-frequency (E5b+L1) with integrity configuration. The outliers, being infrequent results with high acquisition times, are still compliant with the maximum TTFF/TTPF requirements, but are anyway under further investigation.
FIGURE 16. TTFF cold-start performance, dual frequency with integrity E5b+L1.FIGURE 17. TTFF cold-start distribution, dual frequency with integrity E5b+L1.FIGURE 18. TTPF cold-start performance, dual frequency with integrity E5b+L1.FIGURE 19. TTPF cold-start distribution, dual frequency with integrity E5b+L1.FIGURE 20. TTFF warm-start performance, dual frequency with integrity E5b+L1.FIGURE 21. TTFF warm-start distribution, dual frequency with integrity E5b+L1,
Integrity Algorithms. The Galileo SoL service is based on a fairly complex processing algorithm that determines not only the probability of hazardous misleading information (PHMI) based on the current set of satellites used in the PVT computation (HPCA), but also takes into consideration the PHMI that is achieved when one of the satellites used in the current epoch of the PVT computation is unexpectedly lost within the following 15 seconds. PHMI is computed according to alarm limits that are configurable for different application/service levels. These integrity algorithms have been closely integrated into the PVT processing routines, due to commonality between most processing steps.
Current test results of the navigation warning algorithm (NWA) indicate that less than 10 milliseconds of processing time is required for a full cycle of the integrity algorithms (HPCA+CSPA) on the TUR-N internal CPU board. Latency of the availability of the integrity alert information in the output of the receiver after it was transmitted by the satellite has been determined to be below 400 milliseconds. At a worst-case data output rate of 10 Hz this can only be measured in multiples of 100 millisecond periods. The total includes 100 milliseconds of travel time of the signal in space and an estimated 250 milliseconds of internal latency for data-handling steps as demodulation, authentication, and internal communication to make the data available to the integrity processing.
Conclusions
The TUR-N is a fully flexible receiver that can verify many aspects of the Galileo system, or as a demonstrator for Galileo/GPS/SBAS combined operation. It has a similar user interface to commercial receivers and the flexibility to accommodate Galileo system requirements evolutions as foreseen in the FOC phase without major design changes.
The receiver performance is in general compliant with the requirements. For the important safety-of-life configuration, major performance requirements are satisfied in terms of acquisition time and position accuracy.
The receiver prototype is currently operational and undergoing its final verification and qualification, following early confirmations of compatibility with the RFCS and with the Galileo satellite payload.
“This is an event where one gets one’s goals for the next year.” Paul Verhoef, program director for satellite navigation programs of the European Commission, may have exaggerated for effect, and for the benefit of his audience and hosts at the Munich Satellite Navigation Summit in March. But not by much.
The conference, now in its eighth year, has assumed increasing importance on the international circuit of GNSS policymakers and communicators. Although with a decidedly European bent, it draws representatives from most if not all systems to mingle and present. A 16-member delegation from China’s Compass system furnished one of the liveliest topics of conversation — and speculation.
“When we started in 2003, there were many technical conferences on the one side, and we saw a niche for the institutional and political side of satellite navigation,” said Berned Eissfeller of the Institute of Geodesy and Navigation, German Federal Armed Forces University, conference director and host. You can watch video clips of Eissfeller and other speakers.
GNSS came in for a check-up, a sort of self-examination this time. The 2009 conference was titled “The GNSS Race,” but this year it was “GNSS — Quo Vadis?” The Latin phrase means “Where are you going?” Following program updates, sessions focused on safety-of-life, compatibility, legal/intellectual property, and privacy issues.
Galileo. Paul Verhoef continued his remarks that open this story. “I have been given [my goal]: Galileo must succeed.
“You know the world today is not what it was a year ago. It means obviously the financial crisis has had an impact on our economies, on public finance, and therefore I would not be surprised it may leave its mark on satellite navigation. The reason is simple: the systems that are either operating or being deployed are being publicly financed. Galileo is the only system that is financed from a purely civilian budget. All the systems need more than ever to demonstrate their public utility.
“I put it to you that this is an opportunity. As we’ve already heard, there is much to be gained in this market. After the PC, mobile communications, and Internet, satellite navigation is the next breakthrough technology. There are enormous revenues foreseen and already present in this market. There are many jobs possible for those who want to get it, and we think from the European side we have an enormous chance of capitalizing on this among other things by investing in this technology. Therefore, Galileo- and EGNOS-based innovation is certainly politically of interest.
“Obviously, it is not a path of roses. There will no doubt be many more critical questions during these days. However, from our side, we have set our goals. I think they are modest, but they are firm. We want to be the second system of choice. At least in the first instance, we will see where we will go after that. Obviously, this is going to cost a bit of time. I shall invite you, if you get impatient, if the public gets impatient, to look at the history of the other systems. Developing and deploying these other systems is costing time.
“We think that Galileo will meet its deadlines. I think one of the important messages this year, and you have seen it, we are putting things in place. There are contracts in place, there are satellites on order, there are launches on order, there are installations being built — Oberpfaffenhoffen, Fucino, there are others around the world — EGNOS is operational, we’re going to declare the safety-of-life of EGNOS later this year. So we are really moving forward at good speed at the moment.
“We need to win the hearts of the users, the application providers, and the service providers. At the downstream market is the real challenge for these systems. We need to help do that. We are addressing this among other things by providing a more and more reliable schedule for availability of Galileo and EGNOS services.”
Galileo ICD Soon. “We are about to publish in the next couple of weeks the so-called signal-in-space Open Service interface control document, which I know a number of you have waited for a long time.
“We need also to move forward at a political level. In this case, no GNSS system can be credible if it is not backed by a long-term political commitment particularly by its owner. So after the decision of the Parliament and the Council to deploy the system, these two institutions are now clearly called upon to provide us such political long-term commitment that is credible in the eyes of the users.”
GPS. Anthony Russo, director of the U.S. National Space-Based PNT Coordination Office, said “Keeping cards close to the chest in a competitive situation can well become a liability, creating a future need for a re-work or undoing if you paint yourself into a technological corner.” This appeared to refer to China and its Compass system; information has been singularly difficult to obtain on almost every aspect of this budding constellation.
Regarding the April 2009 U.S. General Accountability Office report that forecast gaps in constellation availability, Russo stated, “The GAO will revise its report somewhat. They were using a model that was a little too cautious, one used by the [GPS] Wing. But satellites on orbit have been performing past estimated life. Further, we can turn off secondary payloads to conserve energy onboard satellites [and thus extend life] if needed.”
The next morning, Lt. Col. Liz Roper, Air Force Space Command, gave a status and modernization briefing; the most eagerly awaited development is the launch of the first Block II-F satellite, scheduled for some time in May. She alluded to “a few setbacks” from the August 2009 launch of SVN49 with its well-documented signal problems, but emphasized the episode’s “positive aspects: the relationships we’ve been able to build in seeking solutions to that situation.”
GLONASS. Grigoriy Stupak, deputy general director and general designer on GLONASS systems, briefed the audience in fluent Russian. For a recent launch update, see story below.
Compass. Two of the Chinese delegates spoke in the opening session. Jiao Wenhai from China Satellite Navigation Office did elaborate the basic principles of the Beidou (Compass) system:
openness (“China will widely and thoroughly communicate with other countries on satellite navigation issues.”)
independence
compatibility (“China will pursue solutions to realize compatibility and interoperability with other satellite navigation systems.”)
the frequencies Compass will use: 1561.098, 1207.14, and 1268.52 Mhz in Phase II until 2012; and 1575.42, 1191.795, and 1268.52 in Phase III by 2020.
the general development plan: five geosynchronous, five inclined geosynchronous, and four mid-Earth orbit satellites providing a Chinese regional service using mainly Compass Phase II signals; then development of a global service broadcasting mainly Compass Phase III signals from five GEO, three IGSO, and 27 MEO satellites.
The Chinese speakers displayed a certain disingenuousness in giving verbally and in their slides the location of the January launch, Beidou G1 geostationary satellite, as 160 degrees East, somewhere over the open Pacific. When GPS World pointed out that NORAD satellite tracking shows G1 has been repositioned to a slot at 144.5 degrees East longitude, they huddled for several minutes before stating that yes, it had moved to that position and was undergoing in-orbit testing. That spot was previously occupied by Beidou 1D, apparently decommisioned about a year ago due to power problems. 1D currently orbits in graveyard above geostationary altitude.
A personage civilly associated with the U.S. Air Force confirmed the actual G1 location to the magazine, and could only speculate that it was more advantageous to Chinese ground control for monitoring and testing. As to why spokespersons misstated the location, that remains inscrutable.
GLONASS Back in Black
Three GLONASS-M satellites launched on March 1 are expected to enter service on March 22 and March 30, according to deputy general director Grigoriy Stupak’s statement in Munich. This would bring the constellation, according to his calculations, to 23 operational satellites, though two of those are held in reserve.
With 21 satellites broadcasting signals, the system claim 98.5 percent global availability. Block 42 (three more satellites) has an August 2010 launch date, and Block 43 one for November 2010. By December, Stupak predicted 24 active satellites on orbit, for 99.5 percent global availability.
The GLONASS-M satellites have a stated seven-year lifetime. CDMA signals will begin with next-generation GLONASS-K satellites, while FDMA signals continue in parallel. The Russians plan to “reach 5-meter accuracy by 2017, almost equal to accuracy of other GNSS,” and are “paying more attention to differential corrections for integrity monitoring.”
ICG Questions
The International Committee on GNSS (ICG) Working Group on Compatibility and Interoperability invites GPS industry members to fill out a questionnaire, provided online in two formats: as a downloadable MS Word document or a PDF.
The Industry and User Community Questionnaire is designed to obtain worldwide input from industry, academic institutions, and other representatives of the GNSS user community with technical expertise regarding GNSS signals and other system characteristics that aid or hinder the combined use of the signals in applications, equipment, or services. For instance, respondents are asked to grade certain signal characteristics as to their importance in overall interoperability considerations for a particular type of application.
Respondents are asked to e-mail completed questionnaires to the ICG by May 28.
A Prototype System for Navigation in GPS-Challenged Environments
By Chris Rizos, Dorota A. Grejner-Brzezinska, Charles K. Toth, Andrew G. Dempster, Yong Li, Nonie Politi, Joel Barnes, Hongxing Sun, and Leilei Li
A team of Australian and U.S. researchers have integrated a ground-based system with GPS and INS to create a hybrid system that provides precise and accurate position information continuously in a variety of environments where GPS alone comes up short.
INNOVATION INSIGHTS by Richard Langley
GPS HAS ITS LIMITATIONS. Although it is a 24/7 global system, it doesn’t work everywhere. The microwave radio signals transmitted by the satellites are rather weak, and although they can provide excellent positioning performance when a receiver’s antenna has a direct line-of-sight view of a sufficient number of satellites well spread out in the sky, positioning accuracy degrades or becomes impossible when the signals are effectively blocked by obstacles such as trees, rock faces, and buildings outdoors and by roofs, ceilings, and walls indoors.
In many obstructed environments, the signals aren’t completely blocked but rather their power is severely attenuated so that they are no longer strong enough to be acquired and tracked by a conventional GPS receiver. Remarkable progress has been made in the development of super-sensitive receivers that, in conjunction with an appropriate antenna and assistance information provided over a mobile phone network, can provide position fixes in such environments. However, the precisions and accuracies of these pseudorange-based positions are often very poor — perhaps as low as 100 meters or more.
So, is it possible to obtain precise and accurate positions in obstructed environments? Well, we could add measurements from GLONASS (or other satellites) to GPS measurements, but GLONASS suffers the same problem as GPS, and while the additional satellites could be an advantage in some partially obscured areas there are many places where we won’t be any better off. We could use an inertial navigation system (INS), but such devices have their own weaknesses such as the requirement of initial calibration and the accumulation of position error with time. Are there any other technologies available?
We know GPS works very well when there is a direct line-of-sight view between the satellite transmitters and the receivers and carrier-phase measurements can provide decimeter- and even centimeter-accuracies. So why not develop a ground-based system that works in a similar way to GPS, which would allow you to place the transmitters wherever you like? Well, such a system has indeed been developed and in this month’s column, a team of Australian and U.S. researchers describes how they integrated the ground-based system together with GPS and INS to create a hybrid system that provides precise and accurate position information continuously in a variety of environments where GPS alone comes up short.
“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.
The determination of the position and orientation (or “pointing direction”) of a device (or platform to which it is attached), to high accuracy, in all outdoor environments, using reliable and cost-effective technologies is something of a “holy grail” quest for navigation researchers and engineers.
However, ongoing research has identified two classes of applications that place stringent demands on the positioning/orientation device: (a) man-portable mapping and imaging systems that operate in a range of difficult urban and rural environments, often used for the detection of underground utility assets (such as pipelines, cables, conduits), unexploded ordnances and buried objects, and (b) the guidance/control of construction or mining equipment in environments where good “sky view” is not guaranteed.
The solution to this positioning/orientation problem is increasingly seen as being based on an integration of several technologies: satellite (GNSS including GPS) and terrestrial ranging systems, inertial navigation systems (INSs), laser guidance/scanning systems, and even electro-optical devices such as surveyors’ total stations or laser scanners. Each has its shortcomings, but within an integrated system, advantage can be taken of the complementary characteristics of several of these sensor technologies.
Centimeter-level accuracy positioning systems for outdoor use typically have at their core the GPS technology. GPS is, in fact, the most effective general-purpose navigation tool ever developed because of its ability to address a wide variety of applications: air, sea, land, and space navigation; precise timing; geodesy; surveying and mapping; machine guidance/control; military and emergency services operations; hiking and other leisure activities; personal location; and location-based services. The varied applications use different and appropriate receiver instrumentation, operational procedures, and data processing techniques. But all require signal availability from a minimum of four GPS satellites for three-dimensional fixes.
However, one of the usual limiting factors in using GPS is the need for direct line-of-sight between the satellites and the ground receiver. In particular, the robustness of positioning is compromised when GPS receivers are near or under trees, in urban/suburban areas, or in deep open-pit mines and construction sites, where there is partial sky view obstruction by buildings or walls. The traditional means of overcoming the gaps in navigation coverage due to satellite signal blockages is to use an INS. An INS (with its inertial measurement unit or IMU) is also the most convenient means of determining the orientation of the device or platform. The integration of GPS and INS can, in principle, overcome the defects of standalone INS (sensor errors that grow unbounded with time) and GPS (signal availability requirement). But navigation accuracy degrades rapidly if there are no GPS measurements to calibrate the INS sensor errors.
A new terrestrial RF-based distance measurement technology offers promise of continuous signal coverage, even in difficult urban/rural environments. This technology is known as “Locata.”
The Locata approach is to deploy a network of ground-based transceivers that cover an area with strong time-synchronized ranging signals. When a Locata receiver uses four or more ranging signals it can compute a high-accuracy position entirely independent of GPS or INS. However, a standalone Locata receiver has its own shortcomings: (a) in some situations it may be difficult to achieve good vertical dilution of precision due to logistical constraints of placing transmitters (to give a variation in elevation angle between the terrestrial transmitters and the receiver whose positions are to be determined), and (b) as with GPS, multiple receivers/antennas are required to derive orientation information.
What is therefore required is several carefully selected navigation sensor technologies, integrated within a single hardware package, the measurements from which are simultaneously processed to provide continuous, reliable, and accurate navigation solutions (that is, both position and orientation information).
In cooperation with Locata Corporation, the SNAP Laboratory within the School of Surveying and Spatial Information Systems at the University of New South Wales (UNSW) and the SPIN Laboratory at The Ohio State University have assembled a working prototype of a hybrid system based on GPS, inertial navigation, and Locata receiver technology to provide seamless and reliable navigation aimed at supporting vehicle guidance and control, open-pit mining, mobile and GIS mapping, and industrial applications.
Locata Technology
The SNAP Lab has been conducting pseudolite research for many years, and has experimented with pseudolites in nonsynchronous and synchronized modes for a variety of applications, using both the GPS L1 frequency as well as the 2.4 GHz ISM band frequencies. Locata Corporation has developed state-of-the-art RF terrestrial positioning technology (“Locata”), which consists of a network (“LocataNet”) of time-synchronized pseudolite-like transceivers (“LocataLites”). UNSW has assisted in the development of the technology through experimental testing and benchmarking. In a relatively open outdoor environment, the LocataNet can provide real-time stand-alone kinematic positioning (without a base station) at centimeter-level accuracy. Even in an indoor environment where LocataLite signals arrive at a Locata receiver via non-line-of-sight paths (penetrating the walls of buildings), the static positioning quality can be at the sub-centimeter level, and also at the sub-meter level for kinematic positioning.
Locata has several advanced features that have been developed over a period of about 10 years through several technology generations, including a time-synchronized positioning network, network propagation to many LocataLites, improved signal penetration, change of transmitting frequency and signal structure, and spatial and frequency diversity.
In TABLE 1, the key characteristics of the two generations of Locata technology are listed. Using 2.4 GHz not only means the frequency is license-free, but also permits transceiver output power of up to 1 watt, which means greater operating distances (up to 10 kilometers). Using dual-frequency signals changes the initial phase-bias resolution from known-point initialization to on-the-fly (OTF), where the initial phase bias is resolved while the receiver is moving. The higher chipping rate (10 MHz) results in less pseudorange multipath error, because the delay in a reflected signal will rarely be more than two chips. The 10-Hz measurement rate allows relatively high velocities of the receiver.
Table 1. Specification summary of Locata’s first- and second- generation systems.
In terrestrial-based RF-based positioning, multipath error is more severe than with GPS, because the terrestrially transmitted signal arrives at the receiver at a very low (typically less than 10 degrees) or even a negative elevation angle, which can result in severe multipath signal fading. In the second-generation Locata system, spatial and frequency diversity techniques are employed. Spatial and frequency diversity are two of the three types of diversity principles (the other being polarization) that are common practices in terrestrial RF communications to mitigate against signal fading. The LocataLite transceiver uses two spatially separated (usually in the vertical) antennas, which transmit two signals at different frequencies. This gives a cluster of four diverse signals transmitted from one LocataLite. With this diversity technology, Locata kinematic positioning in moderately obstructed environments can provide centimeter-level quality with 100-percent coverage, as well as consistent geometry and high reliability. The Locata’s multipath mitigation technology is very important and relevant to this project, because the operational environments are often vegetated or wooded.
Triple Integration
As discussed in the preceding sections, there are both advantages and disadvantages to every navigation sensor. GPS and Locata have high positioning accuracy in open or moderately obstructed environments, but they are sensitive to signal blockage such as the case in dense forests, urban canyons, deep mine pits, and indoors. In contrast, INS is totally autonomous — that is, independent of external signal sources — and has high output rate for position, velocity, and attitude, but its unaided navigation error grows rapidly with time.
The most common data-processing tool to integrate GPS and INS is the Kalman filter, which forms the basis for multi-sensor integration in this research. The basic Kalman filter applies to linear system models. Therefore, several variations were developed to cope with the non-linear navigation model, such as the extended Kalman filter and the unscented Kalman filter.
The following discussion of the integration of the GPS/INS/Locata sensors is focused on two aspects: 1) the system state selection, and 2) the measurement model or integration model that decides which information to pass to the filter.
The error state vector consists of a nine-dimensional navigation error state sub-vector (three for the position, three for the velocity, and three for the orientation), an accelerometer error state sub-vector, a gyroscope error state sub-vector, and a three-dimensional gravity disturbance state sub-vector. Of course, other sensor error models can be considered for the gyroscope and accelerometer sensors, such as a combination of random constants, first-order Gauss-Markov variables, scale factors, and so on. In this case, the state space could have a dimension of more than 30. The objective is to adjust the sensor error model later based on experimental results (if needed). However, because of the limitations of observability, it is not yet known whether an augmented error state vector would give better results.
When integrating INS hardware with other sensors, the sensors cannot share the same physical location, which would be ideal from a theoretical point of view. Knowing the spatial relationship among the sensors is important to ensure the highest possible navigation performance. The displacement vectors or mounting biases are offsets, also referred to as lever arms, from the center of the IMU to the centers of the other sensors. These lever-arm parameters may be included in the Kalman filter and thus can be estimated. However, if the lever arms are precisely measured during the assembly of the system, they do not need to be included in the filter as estimable parameters.
For multiple sensor integration in a Kalman filter, there are essentially two types of general models: loosely coupled and tightly coupled. The loosely-coupled model uses a decentralized filter that has several sub-filters to process the sub-systems independently. In other words, the Kalman filter solutions from the sub-systems are combined in an overall Kalman filter that provides the integrated navigation solution. In contrast, the tightly-coupled model uses a single main filter to process the output of all sensors. In GPS/INS integration, tightly-coupled systems have obvious advantages in environments where GPS signals are frequently lost, because they can rely on the other sensor(s) when GPS positioning becomes impossible.
In the tightly-coupled model, the raw observations of all sensors will be input to the main filter. For GPS and Locata, the primary observations will be the carrier phase measurements, as code (pseudorange) observations cannot provide the required accuracy. High-accuracy GPS positioning needs to address the issue of carrier-phase ambiguity. The ambiguity can be treated as an unknown in the Kalman filter, but it may take several minutes to resolve the ambiguity using GPS alone. Using certain ambiguity resolution techniques, however, the ambiguity can be resolved outside the main filter in the GPS/INS high-precision (carrier-phase) integration filter. Note that if the ambiguity were to be resolved within the filter, this would increase the number of states of the filter. For the GPS component, ionospheric delay should be included for applications that cover a large area. Ionospheric delay can be resolved using network-based differential techniques,
but it will affect the ambiguity resolution for single baseline differential positioning if it is not included in the local solution. The filter is designed either to use, or not to use, ionospheric delay, which can ensure flexibility to accommodate network-based and single-baseline differential positioning.
As mentioned above, the measurement model in the tightly-coupled model is based on the raw observations. For GPS and Locata, the observations will be the carrier-phase observations. The approximate values for the linearization of the GPS and Locata measurement equations are provided by the INS navigation solution.
The GPS carrier-phase ambiguity is solved independently outside the Kalman filter with OTF techniques. The GPS differential positioning coefficient matrix remains the same regardless of whether or not a network-based differential technique is used. For velocity determination, the double-differenced Doppler observation is used to eliminate the clock error rate as an unknown (because it is difficult to model this in the filter). The initial carrier-phase bias of the Locata is also not included in the filter, because it can be resolved instantaneously with dual-frequency data in the Locata second-generation system.
The implementation of the filter will be flexible, so adjustments can be made to account for actual environmental conditions. The filter is designed with an open interface and is modular in structure, so that components can be added (or removed) from the model. In open-sky areas, GPS is sufficient for system positioning, so only its observations need to be processed. In moderately obstructed environments, GPS and Locata observations will be processed. In this case the number of GPS observation equations is limited and sometimes will be less than four. FIGURE 1 illustrates the flowchart of the triple-integration of GPS, INS, and Locata.
Figure 1. Workflow of the integrated GPS/ INS/Locata system.
Field Tests
For experimental purposes, we used a dual INS, based on a navigation grade unit and a tactical grade unit. In addition, a Locata receiver and a dual-frequency GPS receiver were placed on a vehicle at Locata’s Numeralla Test Facility (NTF) near Canberra, Australia. This test site features both open-sky and obscured environments, allowing for testing the system’s performance under truly challenging scenarios. The test was repeated by mounting the devices on an autonomous electrical car, driven on the UNSW campus. In both cases, the separation between the rover and the terrestrial transmitters was between a few tens of meters to several kilometers. The GPS and Locata data were processed separately (for testing the internal consistency) as well in a hybrid solution, resulting in few-centimeter-level accuracy per coordinate, depending primarily on GPS availability and the geometry between the rover and Locata devices, as well as the level of multipath fading.
Test 1: NTF. The first integration test was conducted at the NTF on March 17, 2008. The NTF covers an area of approximately three hundred acres (2.5 kilometers × 0.6 kilometers) and is ideally suited to real-world system testing over a wide area. At the NTF, a number of LocataNet configurations are possible through the installation of permanent antenna towers. The network configuration used for this experiment is illustrated in FIGURE 2.
Figure 2. NTF: LocataLite network.
Before the test, a special mounting platform was designed and built. The platform, shown in FIGURE 3, consists of a two-level metal frame. The bottom level can accommodate two inertial measurement units, while the top level can hold up to four antennas. The platform can be easily attached to either the roof of the NTF test vehicle or to the body of UNSW’s small electric car (described later).
Figure 3. Devices setup for the NTF test.
The devices used in the test include two dual-frequency GPS receivers (one used as the rover receiver and the other as the base station), one navigation grade INS, and one Locata rover unit. The GPS antenna and the Locata antenna were mounted with the INS together on the top of a truck. The GPS data rates were set to 1 Hz. The average length of the GPS differential baselines was about 1.2 kilometers. The GPS observation conditions were good during the testing period. The Locata data rate was set to 10 Hz, while INS data rate was 256 Hz, and both were synchronized with the GPS time using SNAP-Lab-developed time synchronization devices based on field-programmable gate array (FPGA) technology.
The GPS/INS data were first processed in tightly-coupled mode. The trajectory is depicted in FIGURE 4. The standard deviation of position, velocity, and attitude are shown in FIGURES 5-7 respectively.
Figure 4. The trajectory of the vehicle in the NTF testFigure 5. The standard deviation of position in the test.Figure 6. The standard deviation of velocity in the test.Figure 7. The standard deviation of attitude in the test.
In Figures 5-7, it can be seen that the standard deviations of position and velocity are less than 0.02 meters and 0.01 meters per second respectively. The standard deviations of pitch and roll angles are less than 0.001 degrees as well as that of yaw, which is less than 0.01 degrees after the vehicle starts to move, at about the 1500th second.
The Locata data was post-processed using Locata’s Integrated Navigation Engine (LINE). It provides an unsmoothed single point position using carrier-phase measurements. The initial ambiguity bias was resolved using the data from the GPS carrier-phase position. Following this initialization, the Locata solution was computed independently of GPS. A 15-meter tower LocataLite location in the vicinity of the start and end of the test (indicated by the “figure eight” pattern in FIGURE 8) allowed sufficient geometry for 3D positioning using Locata. For the rest of the data where there was insufficient vertical geometry, GPS height aiding was used. Figures 8 and 9 show the independent Locata and GPS solutions (without lever arm correction) for the section of the trajectory in the vicinity and the end of the test, respectively. The Locata solution compared to the GPS solution to within a few centimeters for the entire trajectory.
Figure 8. Section of trajectory showing independent Locata solution (black) vs. GPS (blue) with no lever-arm correction.Figure 9. End of trajectory showing independent Locata solution (black) vs. GPS (blue) with no lever-arm correction.
To test the GPS/INS/Locata integration, some GPS observation epochs were deleted to simulate two GPS blockages from seconds of week 94100 to 94250 and from 94500 to 94600. The INS standalone navigation errors with this deleted GPS data were about 8 meters and 2.6 meters, respectively.
In the final GPS/INS/Locata integration test, Locata compensated for the missing GPS data. The integration result was almost identical to the GPS/INS integration result obtained with the original GPS observed data clearly showing that the Locata system could seamlessly replace GPS in this scenario.
Test 2: Electric Car. Early in 2007, UNSW researchers established a permanent LocataNet on the university campus to provide a research and test facility at UNSW devoted to the Locata technology. The LocataNet setup at UNSW is illustrated in FIGURE 10. It consists of four dual-frequency LocataLites situated on tops of four buildings surrounding a lawn test area. The master LocataLite is on the Civil Engineering building and the other three LocataLites are synchronized to it.
Figure 10. LocataLites on the UNSW campus.
Currently, to be able to obtain a carrier-phase position solution with Locata, the initial ambiguities need to be resolved by initializing the rover receiver on a known position. For this purpose, a point in the middle of the test area was surveyed, and the coordinates were used to initialize the Locata receiver.
SNAP Lab has developed a small electric car that can be driven using an attached handheld controller (see FIGURE 11). The controller enables the car to move in both forward and reverse and to steer the front wheels.
Figure 11. The electronic car used in the test.
For these tests, the same mounting platform as the one used in the previous experiment allowed all the sensors and ancillary equipment to be attached to the car. For this experiment, we used the following equipment: a Locata receiver, two GPS receivers, a tactical grade INS, a 360-degree prism (tracked by a robotic total station), and two time-sync FPGA data-logging devices.
The starting position was the known point in the middle of the Locata network. The car was then driven in a circular path three times before finishing back at the starting position.
During the test the raw data stream from the Locata receiver, the GPS receivers, and the INS were recorded using the time-sync data-logging devices. In addition, a robotic total station (RTS), which was set up at the edge of the test area, automatically tracked the prism position (the data was recorded internally).
The Locata data was post-processed using LINE to give a single point unsmoothed carrier-phase solution. The initial ambiguity bias was resolved using the data from the GPS carrier-phase position. Following this initialization, the Locata solution was computed independently of GPS. Where there was insufficient vertical geometry (at the very west end of the trajectory shown in FIGURE 12), GPS height aiding was used. The Locata-only solution and the RTS result are shown in Figure 12. The two solutions compare to within a few centimeters of each other.
Figure 12. The trajectory from the Locata-only and robotic total station solutions.
We then carried out the integrated GPS/INS processing. To test the GPS/INS/Locata integration, two GPS outages were simulated by simply removing the data from the GPS file, between seconds of week 103703 and 103713 and 103834 and 103844, respectively.
We then carried out the integrated GPS/INS processing. To test the GPS/INS/Locata integration, two GPS outages were simulated by simply removing the data from the GPS file, between seconds of week 103703 and 103713 and 103834 and 103844, respectively.
In comparison to the original GPS/INS integration, the standalone INS solution has errors of about 35 meters and 12 meters during the first and second outages, respectively.
The Locata/INS integration significantly reduced the navigation error during the GPS outages, as summarized in TABLE 2.
Table 2. The difference between the Locata/INS solution and the original GPS/ INS solution
From Table 2 it can be seen that 3D position differences between the Locata/INS and the original GPS/INS integration result have been reduced to 1.143 meters and 0.053 meters during the two GPS outages, respectively. However, the improvement in the accuracy of the attitude angles is not obvious because a 10-second GPS outage is not long enough to cause a significant INS drift.
Concluding Remarks
The test experiments described here are a demonstration of the proof-of-concept of a triple-integration GPS/INS/Locata system. The navigation results indicate that this sensor combination may support navigation in GPS-denied environments, as long as some partial view of the LocataLites within the network is available. Further development of this triple integration system is being undertaken.
Acknowledgments
The research is funded by the Australian Research Council. This article is based on the paper “A Hybrid System for Navigation in GPS-challenged Environments: A Case Study,” presented at ION GNSS 2008, the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, September 16-19, 2008.
Manufacturers
The Numerella test equipment included Locata devices, a Honeywell H-764G navigation-grade INS, a Boeing (now Systron Donner) C-MIGITS II tactical grade INS, and a Leica System 1200 dual-frequency GPS receiver. The UNSW campus test equipment included Locata devices, an Omnistar GPS receiver, a Leica MC500 GPS receiver, a Boeing C-MIGITS II INS, a Leica GRZ4 360-degree prism, and a Leica robotic total station TCRP 1203+.
CHRIS RIZOS is a graduate of the University of New South Wales (UNSW), Sydney, Australia, where he obtained a Ph.D. in satellite geodesy. He is head of the School of Surveying and Spatial Information Systems at UNSW.
DOROTA BRZEZINSKA is a professor and leader of the Satellite Positioning and Inertial Navigation (SPIN) Laboratory at The Ohio State University (OSU) in Columbus, Ohio. She received her M.S. and Ph.D. in geodetic science from OSU.
CHARLES TOTH is a senior research scientist at OSU’s Center for Mapping. He received a Ph.D. in electrical engineering and geo-information sciences from the Technical University of Budapest, Hungary.
ANDREW G. DEMPSTER is the director of research in the School of Surveying and Spatial Information Systems at UNSW.
YONG LI is a senior research fellow at the SNAP Lab. He obtained a Ph.D. in aerospace engineering.
NONIE POLITI is a graduate of the School of Electrical Engineering and Telecommunications at UNSW. He obtained a Bachelor’s degree in Telecommunication Engineering and an M.Eng.Sc. in electronics.
JOEL BARNES is director of navigation R&D for Locata Corporation and is also a senior visiting research fellow at the SNAP Lab.
HONGXING SUN is a post-doctoral researcher in the SPIN Lab. He received a bachelor’s degree in geodesy and M.S. and Ph.D. degrees in photogrammetry from Wuhan University, China.
LEILEI LI is a Ph.D. candidate at Chongqing University, China. He is also a visiting Ph.D. student in the SPIN Lab. He received an M.S. degree in instrument science and technology from Chongqing University.
FURTHER READING
• Locata
“Locata: A New Technology for High Precision Positioning” by N. Politi, Y. Li, F. Khan, M. Choudhury, J. Bertsch, J.W. Cheong, A. Dempster, and C. Rizos in Proceedings of ENC-GNSS 2009, the European Navigation Conference, Naples, Italy, May 3-6, 2009.
“Deploying a Locata Network to Enable Precise Positioning in Urban Canyons” by J.-P. Montillet, G.W. Roberts, C. Hancock, X. Meng, O. Ogundipe, and J. Barnes in Journal of Geodesy, Vol. 83, 2009, pp. 91–103 (doi: 10.1007/s00190-008-0236-7).
“High Accuracy Positioning Using Locata’s Next Generation Technology” by J. Barnes, C. Rizos, M. Kanli, A. Pahwa, D. Small, G. Voigt, N. Gambale, and J. Lamance 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. 2049–2056.
“A Positioning Technology for Classically Difficult GNSS Environments from Locata” by J. Barnes, C. Rizos, M. Kanli, and A. Pahwa in Proceedings of IEEE/ION PLANS 2006, the Position, Location, and Navigation Symposium, San Diego, California, April 25–27, 2006, pp. 715–721.
• Integrated Positioning
“Seamless Navigation Through GPS Outages – A Low-cost GPS/INS Solution” by Y. Li, P. Mumford, and C. Rizos in Inside GNSS, Vol. 3, No. 5, July/August 2008, pp. 39–45.
“Ubiquitous Positioning: Anyone, Anything: Anytime, Anywhere” by X. Meng, A. Dodson, T. Moore, and G. Roberts in GPS World, Vol. 18, No. 6, June 2007, pp. 60–65.
“Photogrammetry for Mobile Mapping: Bridging Degraded GPS/INS Performance in Urban Centers” by T. Hassan, C. Ellum, S. Nassar, W. Cheng, and N. El-Sheimy in GPS World, Vol. 18, No. 3, March 2007, pp. 44–48.
“Development of a GPS/INS Integrated System on the Field Programmable Gate Array Platform” by Y. Li, P. Mumford, J. Wang, and C. Rizos in Proceedings of ION GNSS 2006, the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 26–30, 2006, pp. 2222–2231.
“An Integrated Positioning System: GPS + INS + Pseudolites” by Y. Yi, D. Grejner-Brzezinska, C. Toth, J. Wang, and C. Rizos in GPS World, Vol. 14, No. 7, July 2003, pp. 42–49.
• Kalman Filtering for Integrated Systems
“Tightly-coupled GPS/INS Integration Using Unscented Kalman Filter and Particle Filter” by Y. Yi and D.A. Grejner-Brzezinska in Proceedings of ION GNSS 2006, the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 26–30, 2006, pp. 2182–2191.
“Low-cost Tightly Coupled GPS/INS Integration Based on a Nonlinear Kalman Filtering Design” by Y. Li, J. Wang, C. Rizos, P. Mumford, and W. Ding in Proceedings of NTM 2006, the National Technical Meeting of The Institute of Navigation, Monterey, California, January 18–20, 2006, pp. 958–966.
• Data Time Synchronization
“A Time-synchronisation Device for Tightly Coupled GPS/INS Integration” by P. Mumford, Y. Li, J. Wang, C. Rizos, and W. Ding in Proceedings of IGNSS Symposium 2006, International Global Navigation Satellite Systems Society, Gold Coast, Australia, July 17–21, 2006.
Workshop participants from Cote d’Ivoire and Kenya assemble a Mindstorm robot to trial autonomous navigation.
By Patricia Doherty
Last year I helped coordinate a three-week workshop for 50 scientists from 15 African countries, introducing the basics of GPS for applications with socioeconomic benefits and scientific exploration. Held in Trieste, Italy, the workshop was quite successful, producing new initiatives on the African continent. We repeat the workshop next month, April 6–24, again in Trieste.
Since the 2009 training, regional GNSS workshops have taken place in Nigeria, Egypt, Kenya, and Ethiopia. We have initiated scientific collaborations with universities in Nigeria, Kenya, Zambia, Egypt, and Uganda, deploying GPS receivers at each institution, with the understanding that the data will ultimately be shared within Africa and the world.
This effort is a way to share with Africa and Africans the wealth that GNSS has brought to the developed world.
Africa’s 2006 Science and Technology Plan of Action states Africa’s commitment to develop and use science and technology for socio-economic transformation and full integration into the world economy. The leading problems that continue to cripple much of Africa include hunger, extreme poverty, erosion of natural resources, and natural disasters. GNSS can help address these problems and ultimately meet the plan’s goals. Specifically, GNSS applications can increase food security, manage natural resources, provide efficient emergency location services, improve surveying and mapping, and provide greater precision and safety in land, water, and air navigation systems. GNSS also has applications in scientific study including space weather, geophysics, geography, geology, ecology, and biology.
Workshop participants included professors and graduate students from Cote d’Ivoire, Egypt, Ethiopia, Ghana, Kenya, Morocco, Nigeria, Uganda, and Zambia. The more than 25 lecturers came from the United States, Europe, and Africa.
The workshop integrated formal lectures with hands-on practice in GNSS architecture, signal structure, hardware design, state-of-the-art applications, and scientific exploration. An on-site computer laboratory enabled participants to perform positioning calculations; use mapping and surveying software; plan a precision farming procedure; and analyze atmospheric and ionospheric data — all from GPS measurements. In addition, participants built Lego Mindstorm robots to demonstrate autonomous navigation.
One of the benefits of this program was that scientists and engineers from the United States had opportunities to discuss common interests with African scientists and engineers. Many research programs utilize GPS ground- and space-based measurements. Unfortunately, studies over the African region have not been possible due to the lack of dependable long-term measurements. This workshop opened the door to establishing a base of measurements for joint studies with our African colleagues.
Many lecturers remarked that this was the most enriching teaching experience of their careers. The African participants said that they learned a great deal and were very appreciative of the opportunity to participate in this program.
Workshop sponsors include Boston College’s Institute for Scientific Research (where I work), the Abdus Salam International Center for Theoretical Physics in Trieste (where my colleague and workshop co-director Sandro Radicella is head of the Radiopropagation Laboratory), Institute of Navigation, Federal Aviation Administration, Air Force Research Laboratory, National Aeronautics and Space Administration, United Nations Office for Outer Space Affairs, National Science Foundation, Trimble, and NovAtel.
To learn more about the workshop, participate, or contribute, please contact Patricia.Doherty @ bc.edu
By Tony Haddrell, Marino Phocas, and Nico Ricquier
We examine the antenna designs that provide GPS functionality to mobile phones and why most phones still do not provide GPS operation indoors. We also see what it will take to make them better.
INNOVATION INSIGHTS by Richard Langley
WHAT ARE THREE THINGS THAT MATTER MOST for a good GPS signal? Antenna, antenna, antenna. The familiar real-estate adage can be rephrased for this purpose, although the original — location, location, location — is valid here, too.
GPS satellite signals are notoriously weak compared to familiar terrestrial signals such as those of broadcast stations or mobile-phone towers. However, if an appropriate antenna has a clear line-of-sight to the satellite, excellent receiver performance is the norm. But what constitutes an appropriate antenna? The GPS signals are right-hand circularly polarized (RHCP) to provide fade-free reception as the satellite’s orientation changes during a pass. A receiving antenna with matching polarization will transfer the most signal power to the receiver. Microstrip patch antennas and quadrifilar helices, two RHCP antennas commonly used for GPS reception, have omnidirectional (in azimuth) gain patterns with typical unamplified boresight gains of a few dB greater than that of an ideal isotropic RHCP antenna.
But what happens when signals are obstructed by trees or buildings or, worse yet, when we move indoors? Received signal strength plummets. A conventional receiver, even with a good antenna, will then have difficulty acquiring and tracking the signals, resulting in missed or even no position fixes. However, thanks in large part to massive parallel correlation, receivers have been developed with 1,000 times more sensitivity than conventional receivers, permitting operation in restricted environments, albeit usually with reduced positioning accuracy. But such operation requires a standard antenna.
So, do the GPS receivers in our mobile phones now work everywhere? Sadly, no. Consumers demand that their phones not only provide voice communications and GPS but also Bluetooth connectivity to headsets, Wi-Fi, and even an FM transmitter, all in a small form factor at reasonable cost. This requires miniaturizing the GPS antenna and possibly integrating it with the other radio services on the platform. Such compromises can, if the designer is not careful, significantly reduce receiver effectiveness with dramatically reduced antenna gain and distorted antenna patterns. This month we look at some antenna designs providing GPS functionality to mobile phones and examine why most phones still do not provide GPS operation indoors or in other challenging environments. We also find out what it will take to make them better.
“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.
GPS is becoming a must-have feature in mobile phones, with major manufacturers launching new designs regularly, and second-tier manufacturers rapidly catching up. A quick test of any early GPS-equipped phone shows that although the incumbent GPS chip (or chipset) has high sensitivity, the integrated end result cannot perform in low signal conditions. Several challenges facing the phone designer are responsible for this, with the main two being the antenna performance and interference in the GPS band generated within the phone platform itself.
Here we explore the antenna’s role in determining overall performance of the GPS function in a mobile phone, and the potential for avoiding some platform jamming signals by choice of antenna technology.We present some results from an ongoing company study, as part of our remit to assist customers at the system integration level in support of GPS chip sales.
Many handset makers are not GPS or even RF experts, and rely on catalog components to provide their GPS and antenna hardware. Often unsuitable antennas are chosen, or the antennas are integrated in such a way that the original operation mode does not work. Study of a number of candidate phones has shown that, due to the small ground plane available, the antenna component may be merely a band-tuning device, with the ground plane contributing the signal collection function.
At the beginning of 2008, our team launched a project to understand and prioritize the problems for handset makers in the antenna area, and to provide better solutions than those currently in use.
The handset designer faces several problems when incorporating a GPS antenna. First, it has to be very low cost (a few cents, probably). Secondly, it has to be broadly omnidirectional, since there is no knowledge of “up” on a mobile phone, although some manufacturers rely on the fact that location will only be needed when the phone is in the user’s hand or an in-car holder. From the GPS receiver point of view, we would like the antenna to be as far from the communications (transmitting) antenna as possible, and also removed from other transmitting services such as Bluetooth, Wi-Fi, and FM. Users must not be able to detune the antenna out of band by placing their hands on the phone, or by raising the phone to their ears. In a perfect world, they would not obscure an antenna either.
Of course, we would also like to remove some of that platform interference at the antenna stage, and techniques such as differential RF inputs (with a differential antenna) have been proposed in the search for better noise-cancellation performance.
All of this leaves the handset designer with an impossible task, since he has run out of space to fit a decent GPS antenna with all the isolation requirements, and we typically measure GPS antennas that average 26 to 215 dB of gain with respect to a reference dipole, which measures around 21 dB compared to an isotropic antenna when integrated in the handset. Given that a 2 dB loss equates to double the time to fix (in low signal environments) or, alternately, double the amount of baseband signal-search hardware in the GPS chip, it follows that we must exert some effort to help handset integrators implement better antennas. In this respect, some larger manufacturers have in-house projects running, but smaller ones do not have antenna design teams and rely on their suppliers to provide solutions.
So, we start with cataloging the requirements, and given that most current implementations are only in the “mediocre to terrible” class, we look at ways of improving things accordingly. Of course, there are good GPS antenna solutions out there, but handset designers have mostly shunned them on the grounds of cost or even size. Restrictions on these parameters severely hamper the antenna designer, as reducing a GPS L1 antenna below its “natural” size — about 4 centimeters for a monopole on commonly used FR4-type printed circuit board (PCB) material — inevitably means either using some higher dielectric material, which adds cost, or folding the structure up, which decreases performance.
Single-ended antennas, such as monopoles and microstrip patches, rely on a ground plane, which in a handset is undersized anyway, and is usually difficult to identify and model. True differential designs (such as a dipole) overcome this problem, but are automatically larger. As handsets get smaller and encompass more “connectivity”
(that is, more radio links, including GPS) and competition for antenna space increases, combined antennas become attractive, as they would at least help with the size issue. However, the isolation problems are increased, and since our various radios all (currently) need individual RF inputs, some new layer of complexity and filtering is needed between antenna and chip.
Theory, Performance. We undertook some practical experiments to get a feel for the gap between an antenna’s theoretical performance and its installed performance when integrated with the other phone functions. At present, the idea of modeling all the radiation interactions and mechanical arrangements within such a platform is beyond the scope of the available tools, and so practical measurements are really our only choice in the quest for better antennas.
Finally, we provide some insight into the future, given the rapid advancements driven by mobile-phone technology and the advent of the low-cost handset for new emerging markets. New challenges loom ahead for GNSS antennas, not the least being more bandwidth and multiple frequencies, and we look briefly at what must be done to keep up with handset manufacturers’ requirements in this regard.
Size of the Problem
Location-based services in mobile phones is now an expected function by the more discerning user. With more than 500 million users of such services expected by 2011, pressure on manufacturers to provide ever better user experiences and competition between phone manufacturers will bring pressure on the GPS industry for improved performance. GNSS is now the location technology of choice for mobile phones and will remain so provided that the industry can maintain leadership in cost, size, and performance. FIGURE 1 shows the expected penetration of GNSS (mostly just GPS) in the next few years.
Figure 1. GNSS penetration, mobile phones (Image: Tony Haddrell, Marino Phocas, and Nico Ricquier)
With this many users, the market will soon decide whether the performance is up to expectation or not; this in itself will determine GPS penetration going forward.
Vanishing Space. The first challenge facing the RF antenna designer working on a mobile phone is the size of the whole platform. As the size of the average phone continues to fall, manufacturers are understandably reluctant to increase size again to add new features, such as GPS. Consider the wavelengths of a phone’s various RF services. If the corresponding antennas were implemented as dipoles, the antennas would be bigger than the phone. Clearly the competition for antenna space is high. The designer will want to separate the antennas as much as possible to reduce coupling between them, both in the sense of coupling interference from one service to another (known as isolation) and in the sense of spoiling the pattern (or field) of one antenna with another (interaction).
The chip business addresses the space issue through the advent of combination or combo chips, containing such peripheral services as FM (both receive and transmit), Bluetooth, GPS, and Wi-Fi. While helping with space constraints, this development brings new challenges as these radios have to cohabit the same silicon and still perform individually, whatever the other radios are doing (transmitting music to the car radio using FM while navigating with GPS, for example). It follows that combo antennas similarly save space, but since this might involve simultaneous transmit and GPS receive functions, it is very difficult to achieve the necessary isolation, especially if the user’s body can change the coupling between functions.
FIGURE 2 shows a modern phone with some antennas identified. Not shown is the FM transmit antenna on the rear (the receive function uses the headset cable). One commercially available combo antenna and two custom-made antennas are designed to fit the mechanical layout of the phone. The GPS antenna has been placed at the top of the phone, relegating the communications antenna (really another combo since it handles four frequency bands) to the bottom of the phone, where it is subject to detuning by the user’s hand. The GPS antenna is of the PIFA (planar inverted F antenna) type, working against the ground plane of the main PCB, and is printed on a plastic molding that also implements a loudspeaker and its electrical connections.
Figure 2. Antennas in a mobile phone: 1. GSM/WCDMA antenna, 2.Wi-Fi/Bluetooth combined ceramic chip antenna, 3. GPS antenna (Image: Tony Haddrell, Marino Phocas, and Nico Ricquier)
Size. Until now, we have not looked at the size of GPS antennas. We know that a dipole (on FR4 PCB material) is about 8 centimeters in length, just a little shorter than the average phone platform. Changing to a monopole halves the natural length, but requires an “infinite” ground plane to work against. Ignoring this requirement, some manufacturers simply print a monopole on the main PCB, and put up with the coupling, losses, and pattern deficiencies that arise. Some while ago, we measured the gain of such an arrangement at about 212 dB relative to the reference dipole. So designers have turned to size-reduced antennas, either by using higher dielectric materials to form them, or by using complex shape and feed derivatives (such as the PIFA in Figure 2.)
Another combo idea is to use the communications antenna. In the case shown in FIGURE 3, this is a whip-type antenna on a clamshell-type phone. Although the antenna is free for GPS and uses no additional space, the components to tune the whip for GPS and prevent the transmit bands reaching the GPS low noise amplifier (LNA) add both cost and size. So this is not really too attractive, especially when measurements show a 216 dB performance relative to our dipole, along with a poor coverage pattern. In this model, removing the whip and leaving the ferrule to which it connects provided a 6 dB improvement in performance (for GPS only; obviously it spoils the communications function).
Figure 3. Whip antenna combination (Image: Tony Haddrell, Marino Phocas, and Nico Ricquier)
A more conventional approach is to fit an off-the-shelf GPS antenna. The problem here is that any component-type antenna will have been tested with some standardized ground plane, and most are reliant on the ground plane for both tuning, and pattern and gain. A truly balanced design avoids this problem; FIGURE 4 shows an example. Although these antennas have found favor in personal navigation devices for their superior performance, they are not usually considered for mobile phones because of cost and size considerations. This antenna did, however, give us a reference device against which we could make comparative measurements when undertaking the practical test campaign.
Figure 4. Sarantel miniature volute antenna (Image: Tony Haddrell, Marino Phocas, and Nico Ricquier)
A more usual selection is the patch type, long standard in the GPS industry. One such installation is shown in FIGURES 5 and 6, which offer two views of the same stripped-down phone. The main drawback of this arrangement is the lack of a ground plane visible to the patch antenna, giving both tuning and gain/pattern problems. We measured the gain of this antenna at about 28 dB compared to a dipole antenna connected to the same point in the circuit, which is actually at the better end of the performance range that we see. The designers gave the antenna a position at the top of the phone, as in the Figure 2 phone, but it is still squeezed for space onto the edge of the PCB in favor of the phone’s speakers and the camera components. In this phone, the communications antenna is again at the bottom of the PCB.
Figure 5. Phone with GPS patch antenna at edge of PCB (Image: Tony Haddrell, Marino Phocas, and Nico Ricquier)Figure 6. Edge view of GPS antenna, top of phone removed. This phone includes an external GPS antenna input connector seen here mounted below the patch antenna. (Image: Tony Haddrell, Marino Phocas, and Nico Ricquier)
Interference and Isolation. The related characteristics of interference and isolation are difficult to specify and model, leading to practical measurements as the only way of accurately characterizing them. Of course, since the mechanical arrangement (including plastics, screen, battery, and PCB components) plays such a large part in determining the levels of interference and isolation, these tests can only be carried out once the phone is at the prototype stage, when major surgery to improve any particular aspect is not really an option. This also creates a problem when considering new approaches, as the result may not resemble the stand-alone tests, unless the antenna element chosen really has no significant interaction with the rest of the phone.
Most interference we see in mobile phones gets into the GPS receiver at the antenna. Typically this is followed by an RF filter of some sort, which although it spoils the noise figure, does eliminate the out-of-band transmissions from the other radios on the platform. Usually we see a plethora of self-generated in-band signals that have entered the GPS receiver via the antenna. Although we can’t filter them out, we can reduce the coupling between antenna and source as much as possible. One effect seen in current offerings is that the GPS antenna may actually be much better at coupling to interferers than it is at extracting GPS signals from free space, thus making the problem worse.
To get a view of the coupling between antennas, we tested a few available phone types to see what was the actual coupling in the antenna band of interest (see TABLE 1). Of course, one advantage of a poor antenna is that its coupling is likely to be less to adjacent antennas. Coupling is also seriously affected by the user holding the phone or the surface on which it is placed. Phones in a pocket seem to be more affected in this way. The table shows measurements with the phone assembled as completely as possible (we have to get connectivity at the antennas) but not being affected by a user or the phone’s environment.
Table: Tony Haddrell, Marino Phocas, and Nico Ricquier
Requirements
To develop requirements for a better antenna implementation, we need to consider the factors discussed above, and to develop numerical specifications against each. Given the variables involving user interaction, mechanical changes from model to model, use cases and the ever-increasing pressure on cost and size, this is far from straightforward. Our team has spent considerable time defining requirements, and a short synopsis is reported here.
In addition to the coexistence requirements (see the next section), the antenna should fulfill the following criteria:
Minimum cost. The antenna should be of low implementation cost, preferably printed and not requiring complex connectivity to the main PCB, or to require any setup and/or tuning in production;
Low loss. The GPS industry is used to antennas delivering around 0–3 dB (isotropic) in an upper hemispheric direction. We believe this will not be attainable in a mobile phone, but we set the gain target at an aggressive -4 dB (isotropic);
Detuning. The antenna must continue to perform to specification with any reasonable detuning environment (such as user handling, pocket, and metal surfaces);
Mechanical arrangement. The antenna should be of minimum dimensions that can fit the phone mechanics. For example, long and thin may be acceptable along one side of the phone. Also placement near the GPS chip avoids lossy RF tracking;
Gain pattern. Essentially omnidirectional, accepting that other parts of the phone may cause localized dips in the pattern.
Coexistence and Cohabitation. Initially we aim to define the parameters affecting interaction with other services on the phone platform. By coexistence, we mean the ability to share a platform with the other radios and antennas and only be marginally affected by them, whatever they are doing (such as transmitting full power, low power, or idling, and with any frequency choice). This produces a straightforward immunity table (see TABLE 2) once we have determined the basic isolation between all of the elements. For the purposes of Table 2, we have chosen 15 dB as the minimum isolation value between any two antennas. Obviously there are similar tables for the other functions (GSM, 3G, Wi-Fi, Bluetooth, FM) as well.
Table: Tony Haddrell, Marino Phocas, and Nico Ricquier
A glance at Table 2 will tell the reader that the modern mobile phone implements a vast number of transmit and receive frequencies, modulation types, and standards. Of particular concern to the GPS designer is the advent of wideband CDMA signals, which can cause intermodulation products to appear in band at the intermediate frequency of the GPS receiver. Special receiver techniques are required in this case, but the antenna is unable to help except by being of naturally narrow bandwidth.
Cohabitation is a newer concept that describes the isolation between functions of the same device. In this respect, we are investigating GPS antennas combined with Wi-Fi and Bluetooth services. This is a fairly natural development, since these functions are all add-ons to a conventional phone platform, and there is a space-saving advantage in the combination. Since Wi-Fi and Bluetooth share the same band at 2.4 GHz, they have arrangements internally that allow them to coexist or choose which service is to be used if a clash is inevitable.
As a precursor to forming some specifications, our team measured a commercially available combined antenna, and TABLE 3 shows the isolation results.
Table: Tony Haddrell, Marino Phocas, and Nico Ricquier
The table highlights the need to measure antennas on a representative PCB, since other coupling factors reduce the specified isolation by >6 dB compared to the manufacturer’s reference setup, where the part is the only component on the demonstration board.
Real-Life Testing
A number of tests were carried out on available solutions to gain some information and experience about current offerings and platforms.
At one of our facilities, we have a GTEM (gigahertz transverse electromagnetic) cell, which was constructed in house and has been verified to be working properly (see FIGURE 7). A GTEM cell is an expanded transmission line within which a uniform electromagnetic field can be generated for determining antenna properties such as gain and bandwidth. The internal space at the septum (40 centimeters) is big enough to handle antenna sizes used by GPS. It has a small side door and some feedthroughs (coaxial) to the bottom plate. The RF foam absorbers used inside the GTEM work well at 1.5 GHz (the cell can work from 100 MHz to above 10 GHz).
Figure 7. The GTEM cell and related test equipment (Photo: Tony Haddrell, Marino Phocas, and Nico Ricquier)
Differential vs. Single-Ended Antennas. The first test conducted concerned comparison of balanced and unbalanced antennas, the theory being that a balanced antenna would help with interference because it would be presented to the GPS receiver as a common mode signal (that is, balanced on the positive and negative inputs). The NXP GNS7560 single-chip GPS solution is configurable for single or differential input to the LNA, and was used to conduct the tests.
The trial began with calibration of the test setup using the balanced antenna shown in Figure 4, against which we measured a printed dipole antenna and a monopole equivalent, arranged to incorporate a balun to make it of the same size as the dipole (see FIGURE 8). Once this calibration had been made, we sought to generate an interfering signal on the GPS receiver test board so that comparisons of interference rejection could be made. This was done in two different ways, in case the method of exciting the GPS board was subject to resonances or peculiar standing-wave modes. First, we injected an RF interferer into the power supply via the USB cable that was both powering the GPS board and the communications link to it. The jamming created in this manner was increased until a predetermined drop in GPS sensitivity was reached. A number of frequencies were tried and the results compared. In the second setup, we directly applied an RF signal across the ground plane of the GPS board, using a coaxial feed to excite the ground plane, and repeated the stages described above.
Figure 8. Antennas used in the balanced vs. unbalanced antenna testing (Photo: Tony Haddrell, Marino Phocas, and Nico Ricquier)
Results for both tests were within 2 dB of each other, and showed that the differential approach could reduce local jammer pickup by only 4–6 dB. This is probably due to the differential structure being of similar size to the test platform (chosen to be similar to a phone platform), and therefore not achieving true differential coupling to the on-board radiated jammer. With this marginal advantage, we concluded that the benefit was barely justified by the extra complexity and size involved in differential antennas. Note that this conclusion may be different for smaller (for example, high dielectric) differential antennas, although these are currently not available. We are resolved to revisit this possibility at a later date.
Testing Some Commercial Parts. Having elected to continue in unbalanced-only mode, we tested some commercially available antenna components, which are all aimed at mobile phones and span a range of technologies. Each antenna was tested on its recommended reference design without other mobile phone components or features. However, we did use phone-sized boards, representative plastics, and a real user’s hand in these tests. TABLE 4 shows the comparative results.
Table: Tony Haddrell, Marino Phocas, and Nico Ricquier
For return loss measurements we used a vector network analyzer and a ferrite absorber clamp to suppress cable common-mode effects. For measuring the antenna-received voltage, we used an open-air setup with a horn antenna placed 1 meter away from the DUT (device under test) antenna. The horn is fed with a 100 dBuV 1575 MHz CW signal and the received signal at the DUT is inspected with a spectrum analyzer. The horn is mounted so that we have vertical polarization. Initially, we were only concerned with looking for the maximum attainable voltage and we have positioned the DUT also to vertical polarization. Wooden tables were used to avoid reflections. The last two columns in Table 4 are with plastic in close proximity to the antenna element and the last column is with the plastic grabbed by the hand (as one would grab a phone).
The first thing to note is that of the antennas reported above (which were the best of a bigger number of test pieces) the performance is roughly the same for all of them when configured in their reference mechanical arrangement and not interacting with the phone environment. From the table, we can see that for the particular antenna tested in two positions, its location on the ground plane defines its performance (the ceramic-loaded antenna lost 3 dB in voltage terms when moved to the shorter side of the board). This may be a problem in that the best position performance-wise is not the best for the case where the user interacts with the complete assembly. Also, we see that the user and the plastics have a big effect. In short, the component-type antennas currently available don’t show exciting performance in a real environment, but most are competent GPS antennas when integrated according to their makers’ instructions. However, this is often not possible due to mechanical and other constraints. One drawback of the monopole type of device is its need for a ground-plane-free area underneath the component, and this often conflicts with the requirements of the other antennas, which are looking to maximize the ground plane in the phone.
Novel Approaches, Validation
We started this program to identify the requirements of a good GPS antenna, test some theories and current components, and then develop a new approach. From the foregoing, it is clear that a design that is part of the phone mechanics itself will be better integrated and more predictable in the final implementation. Our design team has begun to model and test some more PCB-centric solutions that attempt to mimic at least the current performance of commercial components, and to minimize the amount of ground-plane loss. We do all our testing on representative (in size and conductivity) phone PCBs. A new approach to thinking about potential arrangements is to use the previously mentioned concept that the whole board is the radiator and the antenna is actually a tuning and feed device. One promising possibility is a slot antenna (or slot feed) formed by removing a small notch of ground plane along the top edge of the phone PCB. Some phones have demonstrated success in forming Bluetooth antennas in this manner, although the lower frequency of GPS does not help.
On a separate path, another idea is to print a PIFA (or similar structure) on the plastics themselves and have it work against the phone ground plane in total. In this case, it is relatively easy to get good performance, but connection of the feed to the main board (where the GPS chipset will be located) is a non-trivial mechanical problem.
Testing of some candidate solutions is under way, and we expect reference designs for customer use to be the deliverable from this work. In addition, it is clear that there is not a one-solution-fits-all conclusion, and that more work will be necessary as phone and GPS designs are further developed.
Acknowledgments
The authors thank the antenna engineering team at NXP’s Mobile and Personal Innovation Center, especially Tony Kerselaers, Felix Elsen, and Norbert Philips who conducted the trials reported here. This article is based on the paper “A New Approach to Cellphone GPS Antennas” presented at ION GNSS 2008.
TONY HADDRELL is a fellow staff architect.
ST-Ericsson in Daventry, England, and a director of iNS Ltd., Weedon, England.
MARINO PHOCAS is an RF systems engineer with ST-Ericsson.
NICO RICQUIER heads the Connectivity Group at NXP Semiconductors in Leuven, Belgium.
Some Mobile Phone Terms
Bluetooth (BT). A communications protocol operating in the 2.4 GHz Industrial, Scientific and Medical (ISM) frequency band, enabling electronic devices to connect and communicate in short-range ad hoc networks.
CDMA. Code division multiple access is a channel access method used by some mobile-phone carriers that allows multiple users to share the same radio frequencies using spread spectrum signals.
DCS1800. Digital Cellular Service version of GSM operating in the 1700 and 1800 MHz bands.
EDGE. Enhanced Data Rates for GSM Evolution, a third-generation (3G) version of GSM.
EGSM900. The Extended GSM 900 MHz band.
FDD. Frequency-division duplexing, a communications protocol that uses different carrier frequencies for transmitt
ing and receiving.
FM. The broadcast frequency modulation band.
GMSK. Gaussian minimum shift keying, a continuous-phase frequency-shift keying modulation scheme used for GSM communications.
GSM. Global System for Mobile communications, the most popular mobile phone standard.
GSM850. A GSM version operating in the 800 MHz band.
PCS1900. Personal Communications Service version of GSM operating in the 1800 and 1900 MHz bands.
QPSK. Quadrature phase-shift keying. A modulation technique used in CDMA systems.
Triplexer. A filtering device to provide isolation between communications and GPS circuits when sharing an antenna.
W-CDMA. Wideband CDMA, an enhanced, 3G version of CDMA.
Wi-Fi 802.11b/g. Wi-Fi describes a standard class of wireless local area network (WLAN) protocols based on the IEEE 802.11 standards operating primarily in the 2.4 GHz band.
FURTHER READING
• Mobile Phone Development
“The Smartphone Revolution” by F. van Diggelen in GPS World, Vol. 20, No. 12, December 2009, pp. 36–40.
• Signal Compatibility Issues
“Jammers – the Enemy Inside!” by M. Phocas, J. Bickerstaff, and T. Haddrell in Proceedings of ION GNSS 2004, the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation, Long Beach, California, September 21–24, 2004, pp. 156–165.
• High Sensitivity GPS Receiver
“A Single Die GPS, with Indoor Sensitivity – the NXP GNS7560” by T. Haddrell, J.P. Bickerstaff, and M. Conta 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, 2009, pp. 1201–1209.
• Mobile Phone GPS Antennas
“A Compact Broadband Planar Antenna for GPS, DCS-1800, IMT-2000, and WLAN Applications” by R. Li, B. Pan, J. Laskar, M.M. Tentzeris in IEEE Antennas and Wireless Propagation Letters, Vol. 6, 2007, pp. 25–27 (doi:10.1109/LAWP.2006.890754).
“Getting into Pockets and Purses: Antenna Counters Sensitivity Loss in Consumer Devices” by B. Hurte and O. Leisten in GPS World, Vol. 16, No. 11, November 2005, pp. 34–38.
“Miniature Built-in Multiband Antennas for Mobile Handsets” by Y.X. Guo, M.Y.W. Chia, and Z.N. Chen in IEEE Transactions on Antennas and Propagation, Vol. 52, No. 8, August 2004, pp. 1936–1944 (doi: 10.1109/TAP.2004.832375).
“Mobile Handset System Performance Comparison of a Linearly Polarized GPS Internal Antenna with a Circularly Polarized Antenna” by V. Pathak, S. Thornwall, M. Krier, S. Rowson, G. Poilasne, L. Desclos in Proceedings of IEEE Antennas and Propagation Society International Symposium 2003, Columbus, Ohio, June 22-27, 2003, Vol. 3, pp. 666–669 (doi:10.1109/APS.2003.1219935).
Planar Antennas for Wireless Communications by K.L. Wong, published by John Wiley & Sons, New York, 2003.
• Basics of GPS Antennas
“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. 50–54.