A version of the NeQuick G algorithm using a new coding approach is now available for download on the GSC website. This version is the result of intensive recoding by engineers at the EU’s Joint Research Centre.
GNSS signals traveling through the ionosphere can be significantly delayed by the electrical charges in this atmospheric layer before reaching the users’ terminal. To compensate for this delay in the signal, Galileo receivers integrate a dynamic model of the ionosphere composition known as the NeQuick G model.
Receiver manufacturers will now be able to benefit from a version of the NeQuick G correction algorithm that implements a new coding approach.
Rigorous testing
The JRC concluded its work recently after successful rigorous testing in the framework of the gLAB tool (GNSS software suite from the Universitat Politecnica de Catalunya). This version of the code has been designed to be highly modular, rendering it more legible for a potential programmer with no specific knowledge about signal propagation in the ionosphere. A library has been also developed to enable its quick integration into existing applications.
This software will be released as free and open source software under the terms of the European Union Public Licence (EUPL), version 1.2.
The open-source code is now ready to be implemented on single-frequency platforms and can be used on a global scale without limitation under the EUPL. This freedom should contribute to a wider adoption of the NeQuick G model at user level.
Combining data from GNSS and IMUs ensures accuracy during GNSS outages.
Leti, a research institute of France’s CEA Tech, and Orolia have announced a new sensor-data-fusion engine that ensures resilient positioning and navigation even in cases of GNSS jamming or spoofing.
Orolia is a leader in accuracy and performance for terrestrial, aeronautic and naval transportation positioning, navigation and timing applications.
Called FlexFusion, the algorithm technology processes data from GNSS, inertial management units (IMU) and odometers to provide precise positioning in all conditions.
Orolia will present its latest technological developments at ION GNSS+, booth 311, taking place in Miami, Florida, Sept. 17-19.
FlexFusion’s design relies on a modelization of GNSS and IMU (triple-axis accelerometer, triple-axis gyrometer and triple-axis magnetometer) output for synthetic trajectory generation.
The fusion approach exploits Bayesian estimators, such as Kalman filters. The first algorithm was setup on modeling signals, and its optimization relies on an extensive real-life sample database acquired through field test. This process used CEA-Leti’s HYLOC reference platform, which provides a reference positioning of a few centimeters.
More than 100 trajectory samples were collected in urban, suburban, forest and mountain environments with different GNSS outage conditions.
The new positioning technology supports edge artificial intelligence (AI) because the data-fusion algorithm is performed locally to ensure that positioning and navigation information is available locally and is failsafe even in case of jamming or spoofing of GNSS data.
“Recent events have demonstrated that it is possible to change the course of a ship or force a drone to land in a hostile area by simply spoofing GPS signals,” said CEA-Leti CEO Emmanuel Sabonnadière. “The increasing reliance on a GNSS for the execution of military operations and terrestrial, aeronautic and naval transportation requires using positioning and navigation systems that are able to detect GNSS outages and provide resilient position and navigation features.”
A version of FlexFusion that demands less of the CPU implements a loose coupling algorithm that uses GNSS receiver-output positions as entry of the algorithm. An advanced version implements a tight coupling fusion algorithm of GNSS and IMU data that significantly enhances the resilience of positioning and navigation under real-world conditions.
This novel approach enables total control of treatments and filtering applied to raw signals, which increases performance of the fusion. It also improves positioning performance in particular if there are fewer than four GNSS satellites available, or when there are recurrent multi-trajectories, which sometimes occur in urban canyons.
CEA-Leti has licensed the patented FlexFusion algorithm to Orolia.
“Orolia is integrating FlexFusion in a new version of its VersaPNT product, the first compact, all-in-one and resilient positioning, navigation and timing (PNT) system for vehicles and blue force tracking, tactical UAV navigation and marine applications,” said Thierry Delhomme, EMEA general manager, Orolia. “This powerful algorithm helps deliver on the promise of VersaPNT as an always-accurate PNT system that operates in any environment.”
FlexFusion development was supported and partially funded by the Easytech program of IRT Nanoelec, thanks to the French National Program “Programme d’Investissement d’Avenir” ANR-10-AIRT-05.
How four frequencies help when the ionosphere is disturbed
The authors explore how cycle slips in Galileo carrier-phase measurements can be more effectively detected using four frequencies.
INNOVATION INSIGHTS with Richard Langley
MORE SATELLITES OR MORE SIGNALS? That was the question put to the delegates at GNSS Election ’08, the stimulating and amusing entertainment provided at the GPS World Leadership Dinner held in conjunction with The Institute of Navigation’s meeting in Savannah in September 2008.
During the debate ahead of the election, the Satellite Party advocated that the GNSS user community would be better served by more satellites than more signals. They argued that more satellites (more than those in the operational GPS constellation) would enable more continuous and reliable positioning in cities, mountainous areas and other difficult environments and that the legacy GPS signals were sufficient. Greg Turetsky, one of their candidates, stated, “I would maintain from an economic standpoint that it’s far more cost-effective for our constituents to have more of the same satellites to give them more of the same services that they enjoy today, in more areas, rather than creating new things for which they have no use.”
The Signal Party, on the other hand, advocated for more signals with receivers capable of using them to provide high accuracies for a wide spectrum of GNSS uses. Signal Party candidate Javad Ashjaee opined, “We are the party of building roads, generating accurate maps, growing your food by automating agriculture, synchronizing your power stations. We are even working on automatically landing aircraft to use the air space more efficiently.”
Although contested, the election was won by the Satellite Party, 62 votes to 46. But clearly, both sides offered beneficial advances to the GNSS user community, so why not work together, have the parties enter into an alliance, and provide both more satellites and more signals?
Fast forward to 2016. The alliance has come to pass and we have the best of both worlds. We have two complete GNSS constellations, GPS and GLONASS, with two more, Galileo and BeiDou, on track for completion within the next few years. We also have regional systems either supplying an independent local positioning service or augmenting GPS with NavIC (also known as the Indian Regional Navigation Satellite System) and QZSS, respectively. Not to mention a growing number of satellite-based augmentation system satellites. When I compiled The Almanac for the August issue, there were over 100 GNSS satellites transmitting signals to users. And not only more signals from more satellites, but more technologically advanced signals on more frequencies.
The plethora of signals now being transmitted by GNSS satellites is already leading to further advances in positioning, navigation and timing—even before full constellations transmitting those signals are in place. A good case in point is Galileo’s Open Service, which is transmitted in the E1 and E5 bands. A modified version of binary-offset-carrier (BOC) modulation, called Alternative BOC or AltBOC, is used to generate the wideband E5 signal. Its structure is such that a receiver can track and make measurements on just the lower frequency part of the signal centered on 1176.450 MHz (E5a), just the upper frequency part centered on 1207.140 MHz (E5b), the whole AltBOC signal centered on 1191.795 MHz (E5a+b), or any combination of these including all three. Using all three together with the E1 signal provides us with a four-frequency positioning capability. What’s the benefit of using four frequencies? There are several, but in this month’s column, a recently graduated award-winning Belgian student and her supervisor tell us how cycle slips in Galileo carrier-phase measurements can be more effectively and efficiently detected using four frequencies.
The availability of data offered in the Galileo GNSS Open Service on four carrier frequencies opens the way to new multi-frequency solutions for civil users. In the research reported in this article, we focused on one of the consequences of signal tracking loss, the appearance of cycle slips, and how the use of the four frequencies can help in their detection.
Cycle-slip detection is a key issue for high-precision positioning applications. Any users in need of determining a precise and reliable position must be aware of the potential presence of cycle slips in their data, since they compromise data quality.
Traditionally, two carrier frequencies were used for positioning; for instance, the GPS L1 and L2 frequencies. More recently, three-carrier positioning has allowed enhanced precision and accuracy. Though using a third carrier frequency has allowed us to partially solve the cycle-slip detection issue, existing procedures are still lacking in some aspects. One of today’s main challenges is cycle-slip detection under high ionospheric activity, which is why we focused on this specific case study. And since the use of three frequencies helps to improve reliable cycle-slip detection, might not the use of an additional fourth frequency further improve detection capability? Since Galileo supplies four frequencies in its Open Service, we thought we might be able to improve cycle-slip detection algorithm performance once more.
Framework. In this article, a new quad-frequency cycle-slip detection algorithm is introduced — seemingly, an unexplored track in the literature until now. The algorithm uses undifferenced carrier-phase observations from a single-station static receiver. First developed for post-processing, the algorithm also has been adapted to real-time applications. This algorithm aims to improve cycle-slip detection under high ionospheric activity.
CYCLE SLIPS
Though code (pseudorange) measurements are commonly used for standard positioning, any precise positioning application needs to use carrier-phase measurements, due to their better quality. Unfortunately, the latter are potentially subject to cycle slips, generating a constant bias in data and, if undetected and uncorrected, impacting the inferred positioning.
Carrier-phase measurements are made by observing the beat phase, that is, the difference between the received carrier from the satellite and a receiver-generated replica. At the first observation epoch, only the fractional part of this beat phase can be measured, but the integer offset between the satellite signal and the receiver’s replica is unknown. This integer number of cycles is called the initial phase ambiguity and remains constant during the observation period.
The carrier-phase observable (between a satellite i and a receiver p), in meters, is given by the following equation:
(1)
where the subscript fk indicates the term dependency on the frequency and Φ on the carrier-phase observable. G is the geometric term (that is, a function of the geometric range between the receiver and the tracked satellite, the tropospheric delay, and satellite and receiver clock bias), I is the ionospheric delay, M is the multipath error, HW stands for satellite and receiver hardware delays, c is the vacuum speed of light, N is the initial phase ambiguity, and ε is the random error (also called phase noise).
At the first observation epoch, an integer counter is initialized, and as the tracking goes on, it is incremented by one cycle whenever the beat phase changes from 2π to 0. If the receiver — even briefly — loses track on the signal, the counting is suspended and an integer number of cycles is lost. This loss can result from various causes (signal obstruction, rapid change in the carrier-phase observable, and so on).
In the observation equation, the cycle slip will appear as a change in the value of the initial phase ambiguity. Thus, a one-cycle slip will involve a phase measurement shift of about 20 centimeters (equal to the carrier wavelength), depending on the affected carrier frequency. The cycle-slip size can be any value from one to thousands of cycles.
Ionospheric delay is the only term that could possibly be confused with a small cycle slip. Indeed, during an ionospheric perturbation event, this delay variation between two observation epochs (spaced at 30-second intervals, say) often reaches 20 centimeters (the size of a one-cycle slip in the phase measurement) or more. The ionosphere activity has two main consequences. Firstly, as mentioned before, slips can be hidden in observation noise (including ionospheric variability) and not detected. Secondly, received signal variability can cause loss of lock and thus cycle slips.
A lot of different configurations can arise when the signal is lost. Signal tracking can be interrupted on one single carrier resulting in an isolated cycle slip (ICS) or simultaneously on multiple carriers. In the second case, the slip magnitude on the different carriers can be the same (simultaneous cycle slips of the same magnitude, or SCS-SM) or different (simultaneous cycle slips of different magnitudes, or SCS-DM).
Detection History. The first cycle slip detection algorithm using undifferenced observations, Turbo Edit, was developed in 1990 by Geoff Blewitt. Code and phase measurements from two carrier frequencies are used. It has been implemented in many data preprocessing programs, such as GIPSY-OASIS II, PANDA and Bernese. The Turbo Edit algorithm has been enhanced numerous times. In its latest version, it was adapted to detect cycle slips under high ionospheric activity, but it is still a dual-frequency technique.
Availability of a third, simultaneous signal frequency permits the development of new combinations of observables. A low-noise phase-only combination eliminating geometric as well as first-order ionospheric terms was developed by Andrew Simsky and applied to cycle-slip detection. Studies have also been made to determine the best combinations to be used in triple-frequency positioning, and subsequently in cycle-slip detection and correction algorithms. These algorithms use both code and phase measurements, as well as a triple-frequency method developed by Maria Clara de Lacy and colleagues.
Concern about cycle slips and the relationship with the ionospheric signature in data is trending. In 2011, Zhizhao Liu published a paper on using the rate of change of total electronic content to detect cycle slips. On the other hand, after studying ionospheric cycle slips, Simon Banville and Richard Langley concluded in a paper published in 2013 that the “increased measurement noise associated with an active ionosphere makes correcting cycle slips an ongoing challenge, which requires further investigation,” while Xiaohong Zhang and colleagues, in a paper published in 2014, came to the same conclusion while trying to repair cycle slips during scintillation events. See Further Reading for a list of the highlighted papers in the history of cycle-slip detection and correction.
QUAD-FREQUENCY ALGORITHM
Cycle-slip detection techniques use testing quantities (where the cycle slip is represented by a jump or significant change in the quantity). These are associated with a discontinuity detection algorithm, which aims to locate the jump.
Testing Quantities. Testing quantities are linear combinations of observations. They differ in several aspects: the observables used (in our case, only phase measurements), the number of carrier frequencies used and inner properties of the combination (geometry-free, ionosphere-free and the noise level on the combination).
In our study, we assumed values for the noise on Galileo carrier-phase measurements as given in TABLE 1.
Table 1. Frequencies available in the Galileo Open Service.
Triple-Frequency Simsky Combination. Our algorithm is mainly based on exploiting the triple-frequency Simsky combination. It is a geometry-free and ionosphere-free carrier-phase combination, in meters, as shown in Equation 2.
(2)
When four frequencies are available, four triple-frequency combinations can be computed. Two of them are sufficient to detect slips on any of the four frequencies.
The combination choice must first depend on its precision (given by σS in TABLE 2), obtained by applying the variance-covariance propagation law to raw measurement noise (see Table 1). Precision is not the only factor to be taken into account in the choice of suitable combinations. In each combination, carrier frequencies have different impacts due to their different wavelengths: the impact of a one-cycle-amplitude slip on the E1 frequency will indeed not be the same as the one on E5a, E5b or E5a+b (see Table 2). The smallest impact on a given combination is always the most difficult one to detect.
Table 2. Simsky combinations.
Therefore, the efficiency of a given combination will depend on both the effect of the smallest cycle slip and the combination precision (given by the standard deviation): the higher the ratio between them, the more efficient the combination.
Among the four combination possibilities, the two highest ratios are those formed by the E5a-E5b-E5a+b and E1-E5a-E5b combinations. These will thus be the ones used in our algorithm.
The Simsky combination allows us to detect ICS as well as SCS-DM cycle slips. Nevertheless, this combination is insensitive to SCS-SM slips on all four frequencies (which is a rare phenomenon). We will therefore have to add another testing quantity to our algorithm.
Dual-Frequency, Geometry-Free Combination. The dual-frequency, geometry-free (GF) combination, in meters, allows us to detect SCS-SM slips. It can be computed as follows:
(3)
Unfortunately, the raw dual-frequency, geometry-free combination is affected by ionospheric delay. To mitigate the ionospheric smooth trend, a fourth-order time difference is computed. Still, the result suffers from rapid variations of ionospheric delay.
When four frequencies are available, six dual-frequency combinations can be computed. One is sufficient to detect the presence of simultaneous cycle slips of the same magnitude. The choice will again depend on the ratio between combination precision and the smallest effect of simultaneous one-cycle slips.
On the one hand, differencing the combination results affects precision. On the other hand, the cycle slip, thus the smallest effect to detect, will be amplified by high-order differencing. The best ratio is obtained with a fourth-order difference (see TABLE 3), even if a smooth variation due to the ionosphere is already removed in the second-degree differencing (see Figure 1).
Even if one combination is sufficient, our approach will use two of them to double check their outputs: E1-E5a and E1-E5a+b, since they offer the best ratios.
Detection Method. To detect a discontinuity due to a cycle slip in the testing quantity, it is necessary to establish detection thresholds. Thresholds are one of the key parameters in cycle-slip detection, since they lead to the decision on the presence of a cycle slip or not. If the threshold is too restrictive, some real slips can be missed (a false negative). On the other hand, if it is not restrictive enough, discontinuities that do not match with a cycle slip could be abusively detected (a false positive).
It is important to notice, as our study highlights, that there is no perfect threshold that suits all the needs and constraints. The choice must be made considering the positioning application at hand. Threshold values given in this article are representative and were empirically determined to be optimal with respect to our goal of cycle-slip detection under high ionospheric activity. Results and further discussions about different thresholds can be found in the first author’s thesis (see Further Reading).
Cycle slips will affect the raw Simsky combination by a shift in the mean combination value, whereas the time-differenced one will be affected by a spike.
Detection Using Simsky Combination. Cycle-slip detection on the triple-frequency Simsky combination is performed in two cascading steps (see FIGURE 2).
FIGURE 2. Detection method for the Simsky combination.
The first one uses a time-differenced combination to detect potential cycle slips using a 20-observation-sized forward and backward moving average window, in which the mean and standard deviation statistical parameters are computed. The current epoch is compared to the previous ones to detect a spike, which could correspond to a cycle slip. Two types of thresholds are used: statistical (or relative) and absolute.
As shown in FIGURE 3, using a statistical threshold allows us to adapt detection to the inertia of statistical parameters. Assuming the noise on the observations (here, the Simsky combination results) follows a normal distribution, a confidence interval of 3-sigma around the mean includes 95 percent of the observations. Given the ratio of the two Simsky combinations used (computed earlier), the success rate reaches 100 percent for both combinations, which means any ICS and SCS-DM slips on data will be detected for sure (no false negatives). Nevertheless, false positives may occur because 5 percent of the data is statistically outside the 3-sigma bounds.
FIGURE 3. Statistical and absolute thresholds.
To reduce this rate, an absolute threshold is also applied, equal to 0.4 times the smallest impact of a cycle slip on the combination (see Table 2). If we can take Figure 3 as a suitable example of an extreme ionospheric disturbance leading to unusually high variability in combination results, the absolute threshold will most of the time be far higher than the statistical one and will help to reduce the rate of wrong detections.
As an output of this first step, a flag value is assigned to epochs with larger values than both thresholds, and which are therefore potentially affected by cycle slips.
Once the locations of potential slips are achieved, the second step consists in comparing the mean before and after potential cycle slips for the flagged epochs. A second absolute threshold is applied, equal to 0.8 times the smallest effect. If another potential cycle slip is present in the detection window, the size of the detection window will be reduced to avoid calculation of statistical parameters on partially shifted data.
The goal of the first step is to detect potential slips. Therefore, the priority is to avoid missing a real slip with low threshold values, sometimes leading to false positive detection. On the other hand, the second step aims to separate the potential remaining false positives — outlier spikes in the raw combination — from the real cycle-slip shifts on average. The theoretical performance of this two-step approach is 100 percent: neither false positives nor false negatives should be encountered.
Detection Using Geometry-Free Combination.Since the fourth-order differenced geometry-free combination is affected by a residual ionospheric delay, the previous procedure cannot be applied. Like any time-differenced testing quantity, the slip will appear as a spike in the combination. Therefore, there is no way to distinguish cycle slips from outliers by a mean level comparison (second step).
Consequently, the detection method only consists of a forward-and-backward moving average window, in which a 4-sigma confidence interval is compared to the current epoch combination value. Indeed, in this case, we cannot afford to encounter false positives on 5 percent of epochs (induced by the use of a 3-sigma threshold) since no further step can be set up to eliminate remaining false positives.
The theoretical performances of the geometry-free detection method are also expected to reach 100 percent. Again, neither false positives nor false negatives should be encountered. Note that this calculation only takes ratios into account, neglecting the fact that the geometry-free combination is also sensitive to the variability of the ionosphere.
VALIDATION
We have tested the quad-frequency algorithm on 30-second quad-frequency Galileo observations from stations GMSD (in Nakatane, Japan) and NKLG (in Libreville, Gabon). The GMSD observations were used to test algorithm robustness towards simulated particular cases, whereas the NKLG data were used to assess algorithm behavior for cases met in the equatorial area.
Methodology. Cycle slips were artificially inserted into the GMSD data, simulating the following cycle-slip scenarios: ICS, SCS-DM and SCS-SM. The benefit of such a simulation approach is that the algorithm output can easily be compared to the already-known solution. Moreover, these data had been used to determine whether the use of more carrier frequencies could increase cycle-slip detection performance.
We analyzed a 50-day NKLG dataset, covering observations from Jan. 6 to Feb. 1 and from June 24 to July 19, 2014. This sample is made up of various ionospheric states: calm and extreme days, as well as typical equatorial activity. Since the solar cycle peak happened in 2014, data from that year perfectly fits a study of the effects of high ionospheric activity.
We used NKLG raw data to achieve a dual goal. Firstly, we wanted to determine the proportion of epochs for which small cycle slips (one, two or five cycles) couldn’t be distinguished. This was performed by comparing the impact (in meters) of such scenarios to the instantaneous threshold associated with each epoch. In the case of a high cycle-slip detection threshold, potentially present slips of one, two or five cycles couldn’t be detected. The fraction of epochs in a day for which such small cycle slips would not be detected, for each combination used in the algorithm, seemed to be a suitable indicator of algorithm effectiveness in the equatorial area.
Secondly, we analyzed results by visually assessing algorithm output using combination graphics, and tried to answer the following questions: Do flagged epochs seem to be affected by cycle slips? Are there actual cycle slips that remain undetected?
Results. We looked closely at the results of both our simulations and the analysis of raw data.
Simulation of Particular Cases. Compared to equivalent dual- and triple-frequency methods, our new quad-frequency algorithm gave better results: all inserted cycle slips were successfully detected and no false positive were noticed.
NKLG Raw Dataset Analysis. The validation process using NKLG raw data highlights several trends in algorithm results. First of all, it is interesting to notice that the detection of isolated slips as well as slips of different magnitude (using the Simsky combinations) was guaranteed for every observation epoch of every analyzed day. Indeed, Simsky instantaneous thresholds never exceeded the effect of a slip of one-cycle amplitude.
In addition, in 25 percent of the analyzed days, detection of cycle slips of the same magnitude could also be guaranteed. For the remaining days, detection of simultaneous cycle slips whose amplitudes are less than five cycles could not be guaranteed for a few observation epochs, which can reasonably be neglected because of the very small probability of experiencing such exceptional cases. This is due to the impact of ionospheric variability on the geometry-free combination, inducing high instantaneous threshold values.
However, both the Simsky and geometry-free combinations suffer from false positive detection under extreme ionospheric events: if a cycle slip is detected, it sometimes corresponds to an outlier. This side effect is due to the threshold choices we made to match our initial purpose of detecting all cycle slips for sure, rather than risking missing one of them, even if false positives are part of the results list.
FURTHER IMPROVEMENTS
In addition to post-processing applications, we have also considered a real-time adaptation of the algorithm. The real-time constraint impacts both the Simsky and geometry-free detection methods. In this configuration, the statistical window can indeed only move forward, which neglects cycle-slip detection on the first 20 epochs. Further on, the mean level comparison (see the Simsky detection method described earlier) can no longer be considered because the mean following a potential cycle slip cannot be computed in real-time processing. Even if our quad-frequency detection algorithm suffers from the real-time constraint, it still proves efficient if the latter is taken into account for suitable thresholds choices.
Cycle-slip detection is indeed only a first step, and cycle-slip correction should complete the procedure to avoid discontinuities. It should be pointed out, however, that simply being aware of the presence of a cycle slip in a dataset is precious information for a user, and at the corresponding epoch, the parameters in the solution may be reinitialized.
Enhanced with a suitable cycle slip correction method and a real-time feature, our algorithm could be directly integrated into a software receiver, enabling the supply of continuous and corrected data to the user.
CONCLUSION
In this article, we have introduced the first quad-frequency cycle-slip detection algorithm, with an efficiency that is clearly a step forward.
This innovative detection method opens new doors to numerous research and commercial applications. Every Galileo user, whether civil or military, will be able to benefit from better-quality positioning, especially under harsh ionospheric conditions: not only where the ionosphere is particularly restless such as in the equatorial and polar regions, but also at any latitude during an ionospheric disturbance.
With regard to precise positioning, this is yet another step that reinforces Galileo’s competitiveness against other dual- or triple-frequency systems.
ACKNOWLEDGMENTS
This article is based on the paper “Cycle Slips Detection in Quad-Frequency Mode: Galileo’s Contribution to an Efficient Approach Under High Ionospheric Activity,” the winning submission to the 2014–2015 Students’ Contest of the Comité de Liaison des Géomètres Européens in the Galileo, EGNOS, Copernicus category, which was sponsored by the GSA, the European Global Navigation Satellite Systems Agency.
LAURA VAN DE VYVERE received an M.Sc. in geomatics and geometrology from the Université de Liège, Belgium, in 2015. Her master’s thesis was dedicated to Galileo cycle-slip detection under extreme ionospheric activity. In 2015, she joined M3 Systems Belgium in Wavre as a radionavigation project engineer and is currently involved in GNSS reflectometry and GNSS hybridization projects.
RENÉ WARNANT received an M.Sc. in physics in 1988 and a Ph.D. in physics with a specialty in GNSS in 1996, both from the Université catholique de Louvain, Louvain-la-Neuve, Belgium. He started his career as a geodesist at the Royal Observatory of Belgium in 1988. Since June 2011, he is a full-time professor and head of the Geodesy and GNSS Laboratory at the University of Liège where he is responsible for education in the field of space geodesy and GNSS.
“A New Automated Cycle Slip Detection and Repair Method for a Single Dual-Frequency GPS Receiver” by Z. Liu in Journal of Geodesy, Vol. 85, No. 3, March 2011, pp. 171–183, doi: 0.1007/s00190-010-0426-y.
“An Automated Editing Algorithm for GPS Data” by G. Blewitt in Geophysical Research Letters, Vol. 17, No. 3, March 1990, pp. 199–202, doi: 10.1029/GL017i003p00199.
Cycle Slips and the Ionosphere
“Improved Precise Point Positioning in the Presence of Ionospheric Scintillation” by X. Zhang, F. Guo and P. Zhou in GPS Solutions, Vol. 18, No. 1, Jan. 2014, pp. 51–60, doi: 10.1007/s10291-012-0309-1.
“Cycle Slip Detection and Repair for Undifferenced GPS Observations Under High Ionospheric Activity” by C. Cai, Z. Liu, P. Xia and W. Dai in GPS Solutions, Vol. 17, No. 2, April 2013, pp. 247–260, doi: 10.1007/s10291-012-0275-7.
“Mitigating the Impact of Ionospheric Cycle Slips in GNSS Observations” by S. Banville and R.B. Langley in Journal of Geodesy, Vol. 87, No. 2, Feb. 2013, pp. 179–193, doi: 10.1007/s00190-012-0604-1.
Real-Time Cycle-Slip Detection and Repair
“Real-Time Detection and Repair of Cycle Slips in Triple-Frequency GNSS Measurements” by Q. Zhao, B. Sun, Z. Dai, Z. Hu, C. Shi and J. Liu in GPS Solutions, Vol. 19, No. 3, July 2015, pp. 381–391, doi: 10.1007/s10291-014-0396-2.
“Real-Time Cycle Slip Detection in Triple-Frequency GNSS” by M.C. de Lacy, M. Reguzzoni and F. Sansò in GPS Solutions, Vol. 16, No. 3, July 2012, pp. 353–362, doi: 10.1007/s10291-011-0237-5.
ComNav Technologies has released its new generation Quantum algorithm to international market. The Quantum algorithm can be easily achieved through a firmware upgrade (version 2.5.2 and above), and suits all ComNav OEM boards and OEM-based receivers.
An upgrade to ComNav’s Quan algorithm, the Quantum algorithm dramatically improves the stability and reliability of RTK positioning in complex environments, as well as providing a DP-filter enhancement for the ComNav GNSS products.
Single-point positioning: version 2.30 (left) compared to the new version 2.5.2.
Applications such agricultural guidance and fleet management, where pass-to-pass accuracy is important, will benefit from the advanced smoothing filter in standalone mode. The company’s testing shows smoother and consistent performance, reaching 20-cm pass-to-pass accuracy.
Moreover, the Quantum algorithm provides better CORS compatibility, which means that users can acquire and keep high-accurate solutions even if the CORS network exhibits a poor geometry distribution.
By Ananta Vidyarthi, H. Howard Fan and Stewart DeVilbiss
INNOVATION INSIGHTS by Richard Langley
THE YEAR WAS 1906. On Christmas Eve of that year, Canadian inventor Reginald Fessenden carried out the first amplitude modulation (AM) radio broadcast of voice and music. He used a high-speed alternator capable of rotating at up to 20,000 revolutions per minute (rpm). Connected to an antenna circuit, it generated a continuous wave with a radio frequency equal to the product of the rotation speed and the number of magnetic rotor poles it had. With 360 poles, radio waves of up to about 100 kHz could be generated. However, Fessenden typically used a speed of 10,000 rpm to produce 60 kHz signals. By inserting a water-cooled microphone in the high-power antenna circuit, he amplitude-modulated the transmitted signal. On that Christmas Eve, he played phonograph records, spoke and played the violin with radio operators being amazed at what they heard.
Fessenden had earlier worked with spark-gap transmitters, as these were standard at the time for the transmission of Morse code, or telegraphy, the wireless communication method already in use. But they couldn’t generate a continuous wave and couldn’t produce satisfactory AM signals. But as telegraphy was the chief means of communication, they remained in use for many years along with high-powered alternators and the Poulsen arc transmitter, which could also generate continuous waves.
Although other experimental AM broadcasts were carried out using alternators or arc transmitters, voice transmissions — and in particular sound broadcasting — didn’t take off until the invention of amplifying vacuum tubes. Just before World War I, it was found that they could be used in an oscillator circuit to produce continuous waves, which could be easily modulated to make an AM transmitter. Such transmitters could be used for point-to-point communications but also for broadcasting, and a number of experimental broadcasting stations were established in Europe and North America during and just after the war. Tubes were also instrumental for improvements in receiver technology. “Where there was one licensed station in America in 1920, there were nearly 600 stations just five years later, and the number of radio receivers went from thousands of crystal sets to millions of vacuum-tube circuits.” — from The Science of Radio by Paul J. Nahin, one of my favorite writers on electronics and mathematics.
AM radio broadcasting used frequencies in the long-wave, medium-wave and short-wave frequency bands, and still does. But AM signals often have low audio quality due to bandwidth limitations imposed by regulators and interference from other stations, atmospheric disturbances and electrical noise. So, over the past decade or so, many broadcasters have abandoned long-wave and medium-wave frequencies and moved to the frequency modulation or FM broadcast band with its superior signal capability.
However, this migration pattern might be slowed or stopped if digital broadcasting were to be fully embraced on the AM broadcast bands. A digital technique developed by the iBiquity Digital Corporation is gradually being adopted by broadcasters in the United States and elsewhere. The technique provides FM-quality sound in the medium-wave band by supplementing existing AM signals or replacing them altogether. It can also supply data about the transmitting station and its broadcast. Some 240 AM radio stations in the U.S. already use the technology. (It can also be used in the FM band to provide CD-like quality.)
But these digital signals in the AM broadcast band might serve an additional purpose beyond improving the listening experience. In this month’s column, our authors tell us about some extensive simulation work they have carried out to demonstrate the feasibility of using digital radio signals for navigation. In the future, you may be able to turn on your radio and tune in to get to where you’re going.
“Innovation” is a regular feature that discusses 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, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.
It is well known that the GPS signals are weak and are therefore subject to interference and blockage due to obstruction. Signals of opportunity (SOO), on the other hand, which are designed for other purposes such as communication, may also be used for navigation and have relatively greater signal power than GPS. They are plentiful and relatively more resistant to blockage and jamming compared to GPS. Many authors have presented methods and algorithms utilizing SOO such as AM and FM broadcast signals, TV broadcast signals and 3G/4G wireless communication signals (see Further Reading for examples). These signals are robust and have very good received power levels compared with GPS, and are capable of penetrating through buildings. In addition, these signals are readily available and there is no need for any additional installation of transmitting devices or infrastructure.
In this article, we present the results of a study using AM HD Radio, digital radio in the 540–1700 kHz band of the frequency spectrum, with known transmitter locations, to locate and track receiver locations that are otherwise unknown. HD Radio, originally meaning hybrid-digital radio, is a trademarked term for iBiquity Digital Corporation’s digital radio technology. Unlike analog AM radio signals, digital radio signals are well structured and more immune to co-channel interference, and hence could be better adapted for navigation. In addition, with the proliferation of software-defined radios (SDRs), digital AM radio may eventually replace analog AM radio.
The challenges of navigation using digital radio signals include narrow signal bandwidths, long symbol durations and lack of synchronization among transmitters. Therefore, digital radio signals are not an ideal choice for accurate position estimation, similar to many other SOO that aren’t designed for navigation. Nevertheless, in this work, we have designed algorithms to overcome such difficulties to obtain a good level of location accuracy, making it a feasible alternative for SOO navigation.
Signal Format of Digital AM Radio
Digital AM signals have a well-defined structure called in-band-on-channel (IBOC) that can be exploited for localization purpose. It employs sophisticated digital radio waveforms, which can deliver compact-disc-like sound quality, free of interference and noise, to radio listeners. It uses the existing AM and FM analog broadcasting bands and channel schemes to transmit digital signals. The IBOC digital radio transmitter system encodes analog audio into binary form for transmission.
The design provided by IBOC AM radio has two service modes with two new waveform types: hybrid (denoted by MA1) and all-digital (denoted by MA3). The hybrid waveform retains the analog AM signal, while the all-digital waveform completely replaces the analog AM signal. In the hybrid service mode, the bandwidth of the analog audio signal waveform can be 5 kHz or 8 kHz. The digital signal is transmitted on both sides of the analog host signal in the primary and secondary sidebands. It is also transmitted on the tertiary sidebands, which are 20 dB beneath the analog signal as shown in FIGURE 1.
FIGURE 1. Logical channels and sidebands on the frequency spectrum; hybrid mode with 5-kHz analog signal bandwidth. (After iBiquity.)
For the 8-kHz configuration, the secondary sidebands are also beneath the analog host signal. The greatest system enhancements are realized with the all-digital system, as shown in FIGURE 2. In this system, the analog signal is replaced with the all-digital primary sidebands whose power is increased relative to the hybrid system levels. Secondary and tertiary sideband powers are also increased to the level of the hybrid waveform. Reference subcarriers are also provided to convey system control information. The end result is a higher power digital signal with an overall bandwidth reduction.
FIGURE 2. Logical channels and sidebands on the frequency spectrum; all-digital mode. (After iBiquity.)
Digital radio offers distinct advantages over analog, including mitigation of transmission artifacts and improved audio quality. These changes provide a more robust digital signal that is less susceptible to adjacent channel interference, thereby reducing the noise in the system. An overview of the AM digital system for both the service modes, MA1 and MA3, is given in the following paragraphs. However, in the simulation study we carried out, we used the all-digital AM (MA3) mode. The all-digital AM system has a smaller bandwidth than the hybrid signal. If reasonable localization results can be obtained with it, then we can predict that better localization results may be obtained with the hybrid signal.
IBOC uses an orthogonal frequency-division multiplexing (OFDM) waveform for signal modulation. Each OFDM subcarrier channel has a spacing of 181.7 Hz. The hybrid MA1 service mode comprises 163 subchannels indexed from -81 to 81 over a total bandwidth of 29.4 kHz as shown in Figure 1. The all-digital MA3 service mode has only 105 subchannels indexed from -52 to 52 over a total bandwidth of 18.9 kHz as shown in Figure 2. Therefore, when compared to the all-digital mode, hybrid mode contains more training symbols per OFDM symbol duration. The training symbols are important since these symbols are known and will be used to perform correlation to estimate the signal time of arrival. We predict that since the hybrid mode contains more training symbols than the all-digital mode, detection accuracy will be higher for the hybrid mode. Hence, choosing the all-digital MA3 service mode for the localization will be more challenging, and this is another reason for our decision to use MA3. Demonstrating the capability of the all-digital MA3 service mode for localization would imply that the hybrid mode could be used for the same, with at least the same or better performance.
Interleaving in time and frequency is used to mitigate the effects of burst errors. The interleaver output is according to a structured matrix (not shown here). Each interleaver matrix consists of information associated with a specific portion of the transmitted spectrum, and consists of eight interleaver blocks, with each block of size of 32 × 25. Hence, each block has 800 symbols to be filled, out of which 50 are known training symbols. Since this work entirely relies on training symbols, understanding interleaving is important so we know exactly where the training symbols are in a signal data stream. From the interleaving matrix, the positions of all training symbols are given, which have a periodic appearance of every 16 rows.
The OFDM subcarrier mapping transforms interleaver output into scaled 16 quadrature amplitude modulation (QAM) and 64 QAM and binary phase-shift keying (BPSK) symbols and then maps them to specific OFDM subcarriers. The inputs to OFDM subcarrier mapping are according to the interleaver matrices, which map respective symbols to the primary, secondary, tertiary, Primary IBOC Data Service (PIDS) and reference subcarriers. One row of each active interleaver matrix and one bit of the system control vector are mapped into each OFDM symbol (every Ts seconds) to produce one output vector X, where Ts = 5.805 × 10-3 seconds.
OFDM signal generation takes the complex frequency domain OFDM symbol X as generated above and outputs a time-domain representation of the digital signal. Let Xn be the vector X for the nth OFDM symbol, and Xn[k] be the kth element of Xn, which is the complex scaled constellation points for the subcarrier mapping for the nth symbol, where k = 0, 1,…, L-1 is the subcarrier index in the frequency-domain input to the signal generation for transmission. The input vector Xis transformed into a shaped time-domain baseband pulse yn(t) defining the nth OFDM symbol as
where n = 0, 1, …, ∞, . Note that n indexes consecutive OFDM symbols, L = 105 is the maximum number of OFDM subcarriers, Ts and ∆f are the OFDM symbol period and OFDM subcarrier spacing, respectively, and W(t) is the time-domain pulse shaping function.
Time of Arrival Acquisition
Since the training symbols are known, a local copy can be generated at a receiver to correlate with the received digital AM signal to measure signal time of arrival (TOA). Measuring TOA accurately from a correlation peak is crucial, since any error in TOA measurement directly affects localization accuracy. The relatively narrow bandwidths and hence long symbol durations of the digital AM radio signals pose a challenge as they give rise to potentially large timing errors, thereby greater localization errors. To improve the location accuracy, strong digital AM signal levels are used to our advantage so methods such as curve fitting and time averaging can be performed. Moreover, unlike the structures of the civil GPS signals, which are all known, only the training symbols and their positions in the digital AM signals are known. Other data in the digital AM signals are random and cannot be used for correlation. Therefore, using long correlation vectors will help in detecting peaks as there will be more training symbols.
Sampling. Correlation is performed, of course, after sampling. So we first discuss how to choose an appropriate sampling frequency. After correlation, if we detect the peak and record it as TOA only at the corresponding sampling instant, a maximum distance error of c/2fs can occur between two adjacent samples, where c is the speed of light and fs is the sampling frequency. At the Nyquist sampling frequency, say 40 kHz, this error could be as large as 3,750 meters. Sampling at a frequency much higher than the Nyquist can help to improve accuracy, but this improvement diminishes as the sampling frequency increases beyond a certain value, because the narrow signal bandwidth makes the peak of its correlation function rounded, so detection of the actual peak becomes less accurate. In our simulations, we found that this point of diminishing returns is at about fs = 10 MHz, at which the error between two adjacent samples is 15 meters, much better than that at the Nyquist sampling rate. This high sampling rate is easily doable with today’s digital technologies. However, this 15-meter error is the ranging error between one transmitter and one receiver. Five or more transmitters have to be considered for the location algorithm presented in a later section. Then, the ranging error of 15 meters may magnify to the order of a few kilometers as location errors. Clearly, there is a need to detect TOA of a correlation peak between two adjacent samples; that is, we need interpolation to achieve a smaller TOA error.
Interpolation. To calculate the TOA between two adjacent samples, we interpolate by curve fitting the correlation data and estimate the TOA by solving polynomial functions. It was observed that the correlation peak is asymmetric, so the correlation curve is shaped differently to the left and right of the peak value. This is illustrated in FIGURE 3. Therefore, we need to fit two different curves on each side of the correlation peak. By a trial-and-error process, we determined that a quadratic polynomial is sufficient to fit the correlation values close to the peak. Therefore two simple quadratic functions are fitted for the correlation data points to the left and right of the peak.
FIGURE 3. Asymmetric correlation peak denoting different slopes on either side.
FIGURE 4 shows curve fitting for the correlation of a received signal and a local signal sampled at 10 MHz. The maximum time error due to sampling is Tsamp/2, which equals 5 ×10-8 seconds. This translates into a distance error of 15 meters and localization error of a few kilometers as mentioned before. From Figure 4, it is seen that the intersection point, which is taken as the measured TOA, is much closer to the actual TOA resulting in a much smaller distance error.
FIGURE 4. Enlarged views of Figure 3 near the peak.
Based on the HD Radio documentation, a normal signal-to-noise ratio (SNR) is calculated to be 52 dB. However, in case of adverse channel conditions, lower SNR levels of 30 dB and 10 dB have also been considered. Our simulations show that, with additive white Gaussian noise, the TOA estimation errors are affected by SNR very little above 10 dB, and are improved by an order of magnitude compared with no curve fitting. To make sure the TOA estimation error for the 10 dB SNR case can be used for the purpose of localization, we carried out a Monte Carlo simulation. Twenty-one different random signals were simulated, and the TOA measurement errors after curve fitting were recorded at different delays. The ensemble average of these TOA estimation errors was within 2 ×10-9 seconds. These results confirm that a 10 dB SNR signal can be very well used for localization. Thus, we used an SNR of 10 dB for all the simulations discussed later in this article.
Differential Time-Difference of Arrival
Once all the TOAs from different transmitters are obtained, they are sent to a processing station, which could be one of the receivers. Due to lack of synchronization in digital AM radio transmitters as well as unknown clock offsets in digital AM radio receivers, the obtained TOAs are not aligned, so they cannot be directly used for location determination. A technique called differential time-difference of arrival (dTDOA), which is similar to GPS double differencing and was published by the authors elsewhere (see Further Reading), is employed here to overcome this problem.
Consider the case where there are two transmitters, A and B, and two receivers, C and D, as shown in FIGURE 5.
FIGURE 5. Principle of differential time-difference of arrival (dTDOA).
When transmitter A is transmitting, its signal is received at different time instances by receivers C and D due to different propagation delays. The internal clock of each receiver records the correlation peak with respect to its local time at the corresponding receivers. TOAs of the signal from transmitter A at both receivers C and D are recorded as and , which also contain the unknown transmitter A clock time offset. Differencing these two TOAs , the unknown transmitter A clock time offset is cancelled. But this TDOA is unsynchronized, so it cannot be used for location determination. Then we find the similar unsynchronized TDOA from transmitter B, . To eliminate the unknown receiver clock offsets we difference the two TDOAs, resulting in a dTDOA:
Thus, by using a minimum of two transmitters and two receivers, a dTDOA cancels receiver clock offsets and transmitter clock offsets, thus avoiding the need of precise clock synchronization. The number of independent dTDOA equations required to solve for the locations of n receivers is given by (m-1)(n-1) where m is the number of transmitters, and n is the number of receivers. For two receivers, there are four unknowns in a two-dimensional positioning plane, so we need a minimum of five transmitters to obtain four independent equations to solve for four unknown location parameters. If one of the receivers is permanently stationary with a known location such as in differential GPS, then we only need three transmitters to solve for two unknown horizontal location parameters, or four transmitters for three unknown location parameters in 3-D .
The above dTDOA equations, when expressed in terms of receiver locations, are non-linear. The non-linear over-determined or exact system of equations can be solved using iterative procedures, such as non-linear least squares or the Levenberg-Marquardt (LM) technique. In the simulations we ran, we found that the LM method was more robust than the Gauss-Newton method because it was capable of converging to the solution in the global minimum even if the initial guess was relatively far away. But a reasonable initial estimate of the solution can help with faster convergence. If the initial estimate is too far away, the solution often converges to a local minimum instead of the global minimum.
Therefore, a good initial estimate of the solution is crucial. An approximate initial estimate can be calculated in several ways. For example we can solve linearized equations based on the non-linear dTDOA equations. Or we can use a simple table lookup if we have some a priori knowledge of roughly where the receivers are located.
Once the initial locations are found, the next step is to track the locations of the receivers when they are moving. A Kalman filter should be used for tracking. A Kalman filter can also incorporate the non-linear dTDOA equations with TOA measurement as input for close coupling between localization and tracking. Or, for simplicity, short of using a Kalman filter, the previous locations can be fed into the LM method to find the next locations. The LM method for this kind of tracking has faster convergence than for repeated initialization, so the next locations can be calculated quickly.
Time Averaging. Due to error in tracking, the computed locations are not exact but are usually around the actual location. Time averaging is then used to further improve tracking performance. Time averaging can also be used to smooth the TOA measurements or the locations computed from dTDOA equations as input to a Kalman filter.
Repeated use of the LM method, as shown in FIGURE 6, for estimating a stationary receiver’s coordinates always forms an error ellipsoid because of the noise and computation error. The estimated points are depicted by black points in Figure 6. The small yellow circle in the middle corresponds to the actual location. By simulation, it was found that averaging all the possible estimated locations produced a location much closer to the actual location, as depicted by the red cross in Figure 6. Obviously the more points to average — that is, the larger the time-averaging window — the more accurate the averaged location will be. In general, such time averaging can improve location and tracking performance by an order of magnitude.
FIGURE 6. Image depicting time averaging of a stationary receiver’s location.
For a moving receiver, there is a trade off in choosing the time-averaging window. The larger the time-averaging window, the better the averaged location accuracy, but the larger the resulting time delay in the averaged location. This time delay is also affected by how frequently we update the tracked locations. Receiver velocity and the Doppler effect also affect the choice of the time-averaging window.
Simulation Results
We performed a comprehensive computer simulation study. The primary aim of this simulation study was to prove that the accuracy of digital AM signals for navigation can be improved using the methods introduced in the previous sections, despite the narrow bandwidth of the signals, thereby making digital AM a viable choice for navigation. A number of factors will affect the performance of navigation using digital AM signals including the sampling frequency, SNR, time-averaging window and location update frequency. In this simulation study, these factors have been taken into consideration.
To simulate a realistic environment, we chose the city of Chicago, where there are many digital AM transmitters providing good coverage to the city. We chose the six best transmitters in Chicago based on the power of the signal and location. The working range of the receivers is large enough to perform a detailed study of all the navigation techniques. The locations of the radio station transmitters are shown in FIGURE 7. All figure axes are in kilometers. Colored dots are transmitter locations; colored circles are their ranges. Green tracks are the chosen routes for a fast-moving receiver. Short brown tracks are those of the other receiver, somewhere in the same zone and traveling slowly.
FIGURE 7. Transmitter locations and two different routes considered for simulation with two receivers. (Map courtesy of Google.)
We simulated two receivers moving along the chosen green and brown routes, but we will only show the navigation results of the faster moving receiver along the green routes. A minimum of five transmitters is needed. The entire simulation was done in Matlab. The time-domain digital AM received signals were modeled according to the specifications described previously. Delays corresponding to transmitter and receiver locations were calculated and simulated into the signals received at the two receivers. An SNR of 10 dB was used for all received signals. Along Route 1 (upper left corner of Figure 7), five transmitter signals can be received, whereas along Route 2 (center right in Figure 7), six transmitter signals are received. Simulation conditions and results for these two routes are given in TABLES 1 and 2.
TABLE 1. Simulation parameters and results of Route 1 (five-transmitter zone).TABLE 2. Simulation parameters and results of Route 2 (six-transmitter zone).
In addition, the tracking results for the fast-moving receiver are laid on top of photo maps of the routes, and are shown in FIGURES 8 and 9. The worst-case situation happens when, for example, transition of zones or handover of transmitters happen, for which no specific additional measures were taken in the simulations as shown in Figure 8.
FIGURE 8. Worst-case result for five-transmitter tracking. (Photo map courtesy of Google.)
However, the typical tracking result in Figure 9 happens most of the time. Clearly, the more transmitters that can be used, the better the accuracy results. Use of more than two receivers or use of a stationary receiver with a known location can reduce this demand on the number of transmitters.
The fast sampling frequency, the curve fitting and the time-averaging window are the most important factors affecting the accuracy of this work, and are easily adjustable. In our simulations we used a time-averaging window of 1 second. We expect that the accuracy would further improve as the time-averaging window is increased, but this would result in increased latency. The velocity of the receiver is one limiting factor in choosing the time-averaging window. For a receiver traveling at a maximum speed of 145 kilometers per hour, a time-averaging window of 1 second corresponds to 20.14 meters of tracking lag. Any greater tracking lag may become intolerable. In general, our simulations show that curve fitting alone and time averaging alone each improved localization accuracy by an order of magnitude. When curve fitting and time averaging were combined, the localization accuracy was improved by two orders of magnitude. If a Kalman filter were used for tracking, we would expect further accuracy improvement.
Other challenges that deserve further study to make this concept a mature technology include multipath propagation and its mitigation, incorporation of estimating digital AM carrier phase, and incorporation of a Kalman filter for tracking. Further increased location accuracy is expected by incorporation of these techniques.
Acknowledgment
This article is based, in part, on the paper “A Navigation Solution Using HD Radio Signals” presented at the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif., Jan. 26–28, 2015.
ANANTA VIDYARTHI graduated from Anna University, India, in 2009 with a B. Tech. degree in electronics and communication engineering. She came to the University of Cincinnati in the fall of 2009 and earned her M.S. degree in 2012 in electrical engineering. Currently, she is working with Cummins Inc. in Columbus, Ind.
H. HOWARD FAN graduated from the University of Illinois in Urbana-Champaign with a Ph.D. in electrical engineering in 1985. He has been on the faculty of the University of Cincinnati since then, where he is a professor of electrical engineering and computing systems. His research interests are in digital signal processing, system identification, signal processing for communications, interference mitigation, direction finding, and navigation and location.
STEWART DEVILBISS graduated from Ohio State University with a Ph.D. in electrical engineering in 1994. Since 2007 he has served as the technical advisor for the Navigation and Communication Branch at the Sensors Directorate of the Air Force Research Laboratory, headquartered at Wright-Patterson Air Force Base, Ohio. His primary research interest is in technologies to improve navigation robustness and accuracy.
FURTHER READING
• Authors’ Conference Paper
“Navigation Solution Using HD Radio Signals” by A. Vidyarthi and H.H. Fan in Proceedings of ION ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif., Jan. 26–28, 2015, pp. 285–292.
• HD Radio
The IBOC Handbook: Understanding HD Radio Technology by D.P. Maxson. Published by Focal Press, Burlington, Mass., 2013.
“Asynchronous Differential TDOA for Non-GPS Navigation Using Signals of Opportunity” by C. Yan and H.H. Fan in Proceedings of ICASSP 2008, the IEEE 2008 International Conference on Acoustics, Speech and Signal Processing, Las Vegas, Nev., March 31–April 4, 2008, pp. 5312–5315, doi: 10.1109/ICASSP.2008.4518859.
• Positioning Using Analog AM Signals of Opportunity
“Phase Measurements Using Direct Conversion AM Radio Navigation” by A. Dinh, R. Mason, R. Palmer and K. Runtz in Proceedings of WESCANEX 97, the IEEE 1997 Conference on Communications, Power and Computing, 22–23 May 1997, pp. 280–285, doi: 10.1109/WESCAN.1997.627154.
• Positioning Using TV Signals of Opportunity
“Cooperative position location with signals of opportunity” by C. Yang, T. Nguyen, D. Venable, M. White and R. Siegel in Proceedings of NAECON 2009, the IEEE 2009 National Aerospace and Electronics Conference, Dayton, Ohio, July 21–23, 2009, pp. 18–25, doi: 10.1109/NAECON.2009.5426658.
“A New Positioning System Using Television Synchronization Signals” by M. Rabinowitz and J. J. Spilker, Jr. in IEEE Transactions on Broadcasting, Vol. 51, No. 1, March 2005, pp. 51–61, doi: 10.1109/TBC.2004.837876.
• Positioning Using 3G Cellar Signals of Opportunity
“A Signals of Opportunity Based Cooperative Navigation Network” by M.A. Enright and C.N. Kurby in Proceedings of NAECON 2009, the IEEE 2009 National Aerospace and Electronics Conference, Dayton, Ohio, July 21–23, 2009, pp. 213–218, doi: 10.1109/NAECON.2009.5426626.
The first and best step to combat the growing worldwide problem of GPS jamming is to pursue technologies that can detect and locate the jammers. Signal Sentry 1000 uses arrayed sensors to do just that: look out for jamming and track down its source once sensed.
An array of sensors can be deployed for sensitive and high value entities such as infrastructure installations, including airports, railroads, chemical plants, electric power plants and grids, cargo ports, wireless communication systems and financial transfer centers. The sensors will connect to servers that assimilate the sensor data and provide operator interfaces.
Signal Sentry 1000 is based on a server/client model. The user accesses Signal Sentry using a URL and secure log-in specific to the user’s system. The user’s particular home screen displays a map with each installed sensor displayed with an icon reflecting status. Interferers are displayed as red stars or as error ellipses.
The Signal Sentry web page lists all the interferers stored in the database with their start and end times. The user can manipulate the list by changing the minimum duration of the event to be displayed as well as if the interferer had been geolocated or not, or both. If an interference event was less than a minute long, it may not have a geolocation entry.
Geolocation Methodology. Geolocation of jammers is accomplished through proprietary algorithms running at the network server that utilize digitized, timestamped I and Q samples of received interference waveforms, GPS observables, and other parameters captured by each sensor. This data is processed in a Kalman-filter based location algorithm to determine an initial jammer position and track the position of the jammer throughout the jamming event. This improves performance with moving jammers (that is, vehicle-based) and enables continued jammer location with a limited sensor set (potentially due to signal blockage, erroneous data due to multipath, or out-of-range conditions). Upon detection of an interference event by any sensor, the server polls the entire sensor network for data and determines if the information is sufficient to perform geolocation.
The user receives near-real-time status of event detections and geo-location of the interferer (if possible). Sensor data polling, geolocation processing and GUI updates continue until the interference stops or the emitter goes out of sensor range. Sensor data from each event is stored for later replay and processing using Signal Sentry event analysis tools.
An interference event frequency chart (Figure 1) provides a tool for forensically evaluating the occurrence of interferers. It displays interference events as circles; the size of the circle represents the number of events that occurred at that day of the week and time. When dots are selected on the chart, a map below the chart shows the location of the interference events. More than one dot can be selected at a time. This allows a user to find correlations in time and space, to determine if events occur at specific locations at certain times of the day and/or days of the week.
FIGURE 1. Interference event frequency chart.
Selecting the interferer on the map and then the details button on the popup brings up the interferer details page (Figure 2). Users can sign up for interferer alerts to be sent to their email or phone by text.
FIGURE 2. Interferer details.
Testing
Signal Sentry 1000 was deployed and tested in GPS jamming trials at Sennybridge, United Kingdom, in August 2014. Testing included stationary jammers and mobile jammers moving at up to 50 mph, in open fields and built-up areas.
Sentry Arrayed. The sensors used in these trials were custom units designed and built to Harris specifications by Chronos Technology Ltd. Each consisted of an embedded GPS receiver, an interference signal receiver and a local processor with a network communications interface.
An array of eight sensors was geographically distributed around the test facility. Each sensor and a centralized Signal Sentry processing server were equipped with a mesh data networking capable radio for wireless data communications of commands, status and event data. In other Signal Sentry deployments, the server software is typically hosted on a cloud server, and sensors communicate with the server either via hard-wired internet connections or wirelessly through cellphone network-compatible data adapters.
Jammer Profile. Two jammers performed during the trials, a 150mW and a .5W jammer, used to disrupt the GPS L1 C/A code at 1575.42 MHz.
Open Field. Atest in an area with no obstructions included static jammers and dynamic jammers. Five waypoints along the road, in an area measuring 320 by 444 meters, were surveyed prior to the test using a handheld GPS receiver, to evaluate location accuracy.
Table 1 shows static test results. The accuracy error is the average delta between the Signal Sentry-reported jammer positions versus the actual surveyed jammer positions. The number of points column contains the number of measurements reported by Signal Sentry during the test scenario for each waypoint. The overall average accuracy error for the static jammer test was 17.25 meters.
TABLE 1. Open field static accuracy.
Open Field, Mobile Jammer. In these tests, the jammer was driven in a car on the road through the sensor field. The car was driven at 25 mph north to south, then 50 mph south to north (Figure 3). Cars in the north parking lot caused multipath errors when the jammer came in contact with that area.The overall average accuracy error for the dynamic tracking was 10 meters.
FIGURE 3. Jammer locations detected by Signal Sentry, when jammer was driven at 50 miles per hour, north to south. Green triangles denote sensor locations.
Obstructed Area Test. This test evaluated performance in an urban environment called a FIBUA (Fighting in Built-up Areas), using stationary and dynamic jammers. Seven waypoints in an area 176m x 253m were surveyed for the purpose of evaluating location accuracy. Table 2 shows the results with the 150mW jammer held stationary at the waypoints. Figure 4 provides a graphical view of the jammer position in relation to the waypoints. The overall average accuracy error is 21.40 meters.
TABLE 2. Urban static accuracy.
Obstructed Area, Mobile Jammer. In these tests, the jammer was driven in a car at approximately 20 mph on the road through the sensor field, using a .5W jammer. The overall average accuracy error for this dynamic tracking was 50 meters.
FIGURE 4. Urban area test; jammer locations in yellow, locations delivered by Signal Sentry in red, sensor locations in green.
All figures provided by Jeffrey Coffed and Joseph Rolli.
Precise, Accurate and Multipath-Resistant Distance and Speed Measurements
In this month’s column, we take a look at a short-distance two-way ranging system using a 5.8-GHz carrier to supply not only precise and accurate distance measurements but also complementary measurements of speed.
By Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor
INNOVATION INSIGHTS by Richard Langley
THERE IS A LONG HISTORY of determining distances using radio waves with a large number of techniques being developed over the years for positioning, navigation, situational awareness and other purposes.
Of course, we are all familiar with the latest and greatest distance-measuring technology: GPS and its GNSS brethren. The distance to each observable satellite is determined by measuring the time it takes for the radio signal to travel from the transmitting antenna of the satellite to the receiver’s antenna and then, using the speed of light in a vacuum (which is also the speed of radio waves), converting the signal travel time into a distance. Distances can be determined from either the signal’s modulation (the pseudorandom noise codes) or the carrier phase. Both approaches require modeling and estimation to account for various errors or biases.
GPS is an example of one-way ranging. Other systems, notably radar, are two-way systems relying on reflections (passive ranging) or transponders (active ranging) to return a signal to the point of transmission.
Radar was developed during Word War II although radio-ranging technologies and techniques existed before the war started (to measure the height of the ionosphere, for example) and allowed radar’s rapid development and use during the war.
Besides ranging to terrestrial objects, radar has been used extraterrestrially. Independent experiments in the United States and Hungary in 1946 resulted in the first detections of radar reflections from the moon. Radar has been used subsequently to range to other solar system bodies as well.
Also developed during World War II were several radio-based systems for aircraft navigation. An outgrowth of these were the Loran-C and Omega hyperbolic positioning systems. They operated with networks of coordinated transmitters using frequencies at the low end of the radio spectrum. With widespread GPS availability, Omega was shut down in September 1997 followed by the North American Loran-C chains in 2010. Other chains are threatened with closure. However, there is an ongoing debate about bringing Loran-C back to North America in the form of Enhanced Loran (eLoran) as an autonomous backup for GPS. The United Kingdom has already implemented an eLoran network. Among other improvements, eLoran uses range measurements from multiple transmitters to determine position fixes.
The first terrestrial electromagnetic-distance-measurement or EDM device using microwave signals was the Tellurometer. Developed for surveying in 1954, it initially used a 3-GHz carrier modulated by frequencies near 10 MHz and was capable of accurately measuring distances up to at least 50 kilometers (line of sight).
Ranging can be performed with virtually any radio signal, and viable positioning techniques have been developed to use so-called signals of opportunity such as AM, FM and TV signals. And purpose-designed systems have been developed using ultra-wideband and other short-distance radio technologies.
An issue with any radio-based ranging system is multipath where, in addition to a direct line-of-sight signal, interfering signals are received after being reflected off nearby structures. Multipath degrades the system’s achievable precision and accuracy. Better performance can be obtained by using measurements on the signal’s carrier rather than on its modulation, and the higher the carrier frequency, generally the smaller will be the multipath error in the distance measurement. In this month’s column, we take a look at a short-distance two-way ranging system using a 5.8-GHz carrier to supply not only precise and accurate distance measurements but also complementary measurements of speed.
“Innovation” is a regular feature that discusses 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, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.
Reliable measurements of distance and speed are a critical aid to integrated positioning and navigation systems. Several different sensor technologies can provide such measurements including a variety of radio frequency (RF) ranging techniques. Previous work by the authors based on round-trip time-of-flight RF ranging using the baseband code phase of direct sequence spread spectrum (DSSS)-modulated signals achieves centimeter-level distance estimation performance. This DSSS ranging implementation approaches the Cramér-Rao lower bound in a benign RF channel (the theoretical lower bound on the variance or corresponding standard deviation of any unbiased estimator of a deterministic parameter — the best we can ever expect to achieve). A distance measuring radio (DMR) produced by our company is shown in FIGURE 1.
FIGURE 1. Distance measuring radio. The dimensions of the radio are 160 × 69 × 13.3 millimeters with a mass of 180 grams. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
Our baseband ranging capability has been demonstrated on a direct conversion radio operating in the unlicensed 5.8-GHz industrial, scientific and medical (ISM) band with approximately 20 MHz RF signal bandwidth, and has been previously implemented in the 2.4 GHz and 915 MHz ISM bands. The system uses an 11-megachip-per-second chipping rate and a symbol rate of about 687 kHz per channel (16 chips per symbol). This method has been implemented with both binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) modulation. The same signal that is used for ranging is also used for data communications. A decentralized asynchronous carrier-sense multiple access with collision avoidance (CSMA/CA) networking layer supports networked operation.
The DMR performs real-time digital signal processing on a Kintex-7 field-programmable gate array (FPGA) baseband processor to compute ranging observables on the received baseband packet structure. A round-trip measurement duration under three milliseconds allows for approximately 350 measurements per second for a single pair of DMRs. Measurements do not require a priori synchronization of the remote radios nor high-performance reference oscillators, as remote oscillator behavior is observed in the ranging operation. The measurement is highly compatible with frequency agility techniques. A system of ranging radios provides networked operation for measurements between multiple platforms.
The primary limitation of DSSS code-phase ranging is degraded accuracy and reliability in challenging multipath environments. This is somewhat mitigated by a “quality factor” observation on the characteristics of the received DSSS baseband signal, which can be used to de-weight or exclude corrupted baseband ranging measurements from an integrated navigation or positioning filter. However, it is desirable to provide a ranging measurement that has improved robustness against multipath corruption in all environments.
Multipath Effects on Carrier Phase
The carrier phase of the DSSS ranging signal in space can be used as an additional ranging measurement. Each 5.8-GHz RF carrier-wave cycle has a length of about 52 millimeters. Phase measurements on the received carrier phase in a round-trip ranging exchange are proportional to the propagation distance of the RF signal over the air. These measurements of the carrier phase can be made precisely, and they are inherently more tolerant to multipath than baseband phase measurements.
Consider a simplified two-ray RF channel model, where there is a direct RF line-of-sight (LOS) path and a multipath (MP) reflection. The two signals will have a phase difference between MP and LOS of θm and an amplitude ratio of MP to LOS of α, which lumps together the attenuation due to the additional path length of the MP signal, the reflection coefficient of the reflecting surface, the difference in antenna gain at the incidence angles and other factors. The received signal will be a superposition of the two signals with a phase difference between this composite and the original LOS of θc. This phase difference is the multipath-induced error on the received carrier phase. The worst-case error will occur when there is a small difference in total path length. In this case, the LOS and MP are inseparable by the DSSS receiver, and the error is bounded by Equation 1. The error is reduced for MP with much longer path length due to both a reduced amplitude coefficient α of the MP signal, as well as separation by the DSSS receiver due to the baseband spreading codes.
(1)
The multipath carrier-phase error bounds are ±90 degrees for α ≤ 1, which is satisfied when there is an RF LOS signal present. In practice, α is typically much less than 1. For a more practical case of α = 0.1, the maximum carrier-phase error is less than ±6 degrees. At 5.8 GHz RF, ±6 degrees corresponds to about 0.1 millimeters. A plot of this response for various values of α is shown in FIGURE 2.
FIGURE 2. Carrier-phase error due to multipath interference for various values of relative multipath amplitude. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
As a physical interpretation, the carrier-phase error goes to zero when there is zero phase difference between LOS and MP signals as the signals happen to be in phase already, and at ±180 degrees where the MP signal is in phase with the LOS signal but with inverted polarity, and serves to reduce the magnitude of the received signal, which is the case in a deep multipath fade. MP signals arrive at a dynamic receiver with an unpredictable distribution of relative phase to the LOS signal due to platform motion. This resistance to multipath is highly desirable for use in an RF ranging system. The following sections will present a ranging method that leverages this useful behavior.
Carrier-Phase Ranging Measurement
Each DMR round-trip ranging exchange consists of transmission and reception of a packet between two cooperating DMR devices, typically termed “originator” and “transponder” with roles determined by software configuration. For baseband ranging, the code phase is computed on the oversampled shape of the DSSS correlator output and exchanged in the round-trip measurement. The number of elapsed baseband clock periods between receive and transmit on the transponder and between transmit and receive on the originator are also observed to compute a round-trip coarse time. These measurements, plus a calibration offset due to cabling and other systematic delays, are used to perform baseband ranging.
Two additional observations are required for carrier-phase ranging: the carrier phase of the received DSSS signal in space and the carrier-frequency offset of the received carrier with respect to the local oscillator on the receiving radio. These observables are exchanged in a round-trip transaction, generating carrier-phase range (CPR), the magnitude of carrier-phase velocity (CPV) and clock-offset measurements. This section will describe the background of the CPR and CPV measurements.
Assuming the communicating DMRs operate with identical carrier frequencies, the round-trip carrier-phase ranging measurement is a function of the RF carrier wavelength λC = c/fC and the received phase on each DMR (φO and φT) in units of radians. The measurement is ambiguous by Namb half-wavelengths, as shown in Equation 2.
(2)
The frequency offsets measured at each receiver (SO and ST) in units of hertz will reflect the Doppler-based velocity offset between the two receivers, as shown in Equation 3.
(3)
While the velocity measurement is absolute, the carrier-phase ranging measurement is ambiguous within a half-wavelength in a round-trip measurement. There are several ways to overcome this limitation including using the velocity measurement to “unwrap” sequential carrier-phase observations, using baseband phase measurements to establish absolute offsets, by aiding the measurement with a strapdown inertial measurement unit (IMU) and by other means. The primary error source for carrier-phase ranging in practice is the solution of integer ambiguity, not the actual phase measurements. The quality of the phase measurements becomes the limiting factor when the integer ambiguity is resolved perfectly. An analysis of the Cramér-Rao lower bound (CRLB) for carrier-phase ranging and carrier-frequency velocity measurements along with measured performance is presented in the following section.
Measurement Performance Bounds
The CRLB for estimation of phase and frequency of a sinusoid based on a number of data samples in additive white Gaussian noise has been previously treated in the literature and can be interpreted to provide a best case, lower bound on how well the measurements could perform. The CRLBs for carrier-frequency and phase estimation are computed in terms of the sinusoid’s signal-to-noise ratio, SNR, the number of observed samples of the phase of the signal NS and the sample rate of the measurement system fS.
The CRLB for the standard deviation of carrier-phase ranging measurements is presented in Equation 4 in units of radians. In general, the standard deviation of carrier-phase measurements improves with the square root of NS and the square root of SNR.
(4)
The CRLB for carrier-phase estimation can be used to compute the CRLB for carrier-phase ranging by scaling each measurement by λC
(5)
This CRLB can be interpreted for the carrier-phase ranging observable generation process used in this DMR system. NS can be expanded to Equation 6, with NC = 12 chips out of a 16-chip pseudorandom noise code, α = 400 symbols typically tracked (assuming 100 symbrols are consumed in automatic gain control out of a 512-symbol preamble), and fSample/fChip = 44 MHz/11 MHz = 4. [Note different use of the character α here than in the section on multipath.] This gives NS = 400 · 12 · 4 = 19,200 in a typical usable DMR preamble as currently implemented.
(6) FIGURE 3 shows the CRLB for carrier-phase ranging measurement evaluated over a range of SNR and with a varying number of symbols used in the ranging preamble, with typical α = 400 in the current implementation. Evaluating the phase CRLB at a conservatively low SNR = 10 dB and typical NS = 19,200 on a 5.8-GHz RF carrier yields a lower bound of about 27 micrometers standard deviation for a round-trip carrier-phase ranging measurement.
FIGURE 3. Cramér-Rao lower bound for carrier-phase ranging with different numbers of symbols used in the ranging preamble. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
The CRLB for the standard deviation of carrier-frequency-offset measurements is presented in Equation 7 in units of hertz. In general, the standard deviation of carrier-frequency observation improves with NS3/2 and the square root of SNR.
(7)
The CRLB for carrier-frequency estimation can be used to compute the CRLB for carrier-phase velocity by scaling each measurement by λC to convert to meters per second, and reducing the standard deviation by the square root of 2 due to the two independent phase measurements being conducted in the round-trip experiment as shown in Equation 8.
(8)
Evaluating the round-trip carrier-phase velocity CRLB at a conservatively low SNR = 10 dB and typical NS = 19,200 on a 5.8-GHz RF carrier yields a lower bound of about 10 centimeters per second velocity standard deviation. FIGURE 4 shows the CRLB for velocity measurement evaluated over a range of SNR and with varying number of symbols used in the ranging preamble.
FIGURE 4. Cramér-Rao lower bound for carrier-phase velocity with different numbers of symbols used in the ranging preamble. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
These CRLB levels predict that excellent CPR with precision much better than millimeter level and CPV precision much better than a meter per second should be achievable with the designed system assuming a perfect carrier-frequency generation circuit operating in additive white Gaussian noise. The practical limiting factor for these measurements at high SNR is typically the phase-noise performance of the reference oscillators themselves.
Measurement Results
CPR measurements have been implemented in our DMRs and tested in a variety of environments. In a static data collection, CPR demonstrates a stationary precision of approximately 0.1 millimeters at one sigma as shown in the histogram in FIGURE 5. The red line indicates the best-fit to a Gaussian curve of the measurement data, showing very well behaved data.
FIGURE 5. Histogram showing carrier-phase range precision. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
A static collection of CPV measurements demonstrates a precision of approximately 15 centimeters per second at one sigma as shown in the histogram of CPV data in FIGURE 6, which also has the best fit Gaussian distribution overlaid. The performance of these measurements approaches the CRLB.
FIGURE 6. Histogram showing carrier-phase velocity precision. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
To further quantify the accuracy of CPR, a test was conducted comparing CPR to the distance measured by a survey-grade total station laser rangefinder. The transponding radio was mounted on a tripod and moved to varying distances away from the originating radio, which was located near the total station. FIGURE 7 shows the distance-measurement results. The blue dots are the baseband distance measurements and the red dots are the unwrapped carrier-phase range distance measurements. The mean distance and scatter within each stationary period were used to evaluate the precision and accuracy of CPR versus the total station rangefinder values.
FIGURE 7. Distance determined from baseband ranging (blue) and carrier-phase ranging (red) data collected during a test with varying distances between originating and transponding radios and using a total station to provide ground-truth. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
FIGURE 8 shows the outcome of the laser-based total station ground-truth validation of the carrier-phase distance measuring performance in an outdoor LOS environment. The red lines indicate the ±8 millimeter experimental accuracy of the laser ground-truth test setup. The error from each surveyed point is within the uncertainty of the test, with an experimental precision of 0.6 millimeters at one sigma indicated by the vertical error bars on each data point.
FIGURE 8. Range comparison between CPR and a total station. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
System Integration
CPR and CPV measurements have been successfully integrated into a pedestrian tracking dual boot-mounted inertial system. In this configuration, one industrial-grade microelectromechanical systems IMU operating at 400 Hz (three-axis accelerometer, three-axis gyro and three-axis magnetic compass) is mounted on the heel of each boot, and a DMR with CPR/CPV capability is attached to the medial side of each boot. The DMRs perform inter-boot ranging and velocity measurements at 360 Hz throughout system operation. The walking motion generates a very high-dynamic, high-multipath environment that is challenging for RF systems.
FIGURE 9 shows four strides of walking data collected in this configuration. Periodic walking motion is clearly visible on CPR and CPV as the range between boots increases up to 0.6 meters at the extents of strides and passes near zero during foot crossings. CPV measurements are internally consistent with CPR. The first difference of CPR is equivalent to the independent Doppler-based CPV measurement. A significant benefit of the CPV measurement as opposed to the first difference of CPR is that CPV is an absolute measurement with no integer ambiguity.
FIGURE 9. CPR and CPV data for four strides from boot-mounted distance measuring radios. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
For this system, IMU data is integrated using both interpreted zero-velocity updates (ZUPTs) and ranging measurements to determine dead-reckoning motion of each individual boot. The high-precision, multipath-tolerant CPR and CPV measurements are used to constrain inter-boot position and velocity in a centralized extended Kalman filter (CEKF). CPR and CPV residuals from the CEKF are shown in FIGURE 10 and FIGURE 11, representing measurement accuracy in a challenging, high-dynamic environment. All system errors including antenna phase response, integrated IMU errors, and others are included in these histograms, so the true CPR and CPV measurement errors are likely significantly lower, even for this high-multipath environment. This is why we believe our results are a good estimate of the system’s accuracy capability.
FIGURE 10. Histogram showing carrier-phase range accuracy. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)FIGURE 11. Histogram showing carrier-phase velocity accuracy. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
While the overall CPR measurement accuracy of about 11 millimeters is two orders of magnitude worse than the stationary measurement precision of 0.1 millimeters, it should be noted that this includes all measurement biases in the system and various error sources.
CPV achieves an in-system measurement accuracy of 0.31 meters per second, which is approximately a factor of two degraded from the stationary, LOS collection (0.15 meters per second). In this sense, CPV is shown to be an extremely robust measurement in the presence of multipath and non-ideal antenna patterns throughout actual walking motion.
Conclusions
This article presents a new method to perform highly precise, accurate and multipath-resistant measurements of distance and velocity using a small portable radio. Measurements that are as accurate as a laser require only milliseconds to complete and are insensitive to multipath interference. This opens up a wide range of applicability as an aiding sensor to integrated navigation systems. Performance has been demonstrated in the high-dynamic and high-multipath environment between the boots of a walking pedestrian, and similar performance is expected in industrial and military applications. By employing a conventional communications link, measurements of CPR and CPV should be scalable to longer distances with the availability of the measurements roughly comparable to the availability of the communications link.
CPR and CPV achieve stand-alone measurement precision of much better than 1 millimeter standard deviation, and about 15 centimeters per second velocity respectively at a rate of hundreds of measurements per second. In-system performance of CPR and CPV measurement residuals demonstrates 1-centimeter CPR accuracy and 30 centimeters per second CPV accuracy. The measurements presented in this article are typically 100 times more precise than typical baseband round-trip RF measurements in a similarly challenging RF environment.
Acknowledgments
The work described in this article was sponsored by ENSCO Inc.
Manufacturers
The distance measuring radio is manufactured by ENSCO Inc. The inertial measurement unit used in the boot test was a Memsense LLC model H3, while the total station used for calibration was a Leica Geosystems AG model TS30.
BRADLEY D. FARNSWORTH is the chief engineer for positioning, navigation and timing (PNT) at ENSCO Inc., Springfield, Va. He holds several U.S. patents and has expertise in real-time signal processing, autonomous systems and mixed-signal design. He received his B.S. summa cum laude and M.S. degrees in electrical engineering from Case Western Reserve University, Cleveland, Ohio.
E.J. KREINAR is with ENSCO Inc. and holds B.S. and M.S. degrees in electrical engineering from Case Western Reserve University. He has expertise in optimal estimation using Kalman filters, real-time signal processing and autonomous systems.
DAVID W.A. TAYLOR is the director of technology development and business area lead for PNT at ENSCO Inc., where he leads R&D programs developing sensors and systems for national security applications. He holds several U.S. patents and is an expert in GPS-denied navigation technologies. Taylor holds a B.S. in physics from Rhodes College, Memphis, Tenn. and a Ph.D. in geophysics from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, Va.
FURTHER READING
Authors’ Conference Paper on which the Article is Based
“Precise, Accurate, and Multipath-Resistant Networked Round-Trip Carrier Phase RF Ranging” by B.D. Farnsworth, E.J. Kreiner and D.W.A. Taylor in Proceedings of ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif. January 26–28, 2015, pp. 651–656.
RF Ranging for Location Awareness by S.M. Lanzisera and K. Pister, Technical Report No. UCB/EECS-2009-69, Dept. of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, Calif., May 19, 2009.
Direct Sequence Spread Spectrum Radio Frequency Ranging
“High-Precision 2.4 GHz DSSS RF Ranging” by B.D. Farnsworth and D.W.A. Taylor in Proceedings of ITM 2011, the 2011 International Technical Meeting of The Institute of Navigation, San Diego, Calif., January 24–26, 2011, pp. 178–183.
“High Precision Narrow-Band RF Ranging” by B.D. Farnsworth and D.W.A. Taylor in Proceedings of ITM 2010, the 2010 International Technical Meeting of The Institute of Navigation, San Diego, Calif., January 25–27, 2010, pp. 161–166.
Handling the Biases for Improved Triple-Frequency PPP Convergence
By Denis Laurichesse
Precise point positioning (PPP) can be considered a viable tool in the kitbag of GPS positioning techniques. One precision aspect of PPP is its use of carrier-phase measurements rather than just pseudoranges. But there is a catch. Often many epochs of measurements are needed for a position solution to converge to a sufficiently high accuracy. In this month’s column, we look at how using measurements from three satellite frequencies rather than just two can help.
INNOVATION INSIGHTS by Richard Langley
PPP? WHAT’S THAT? This acronym stands for precise point positioning and, although the technique is still in development, it has evolved to a stage where it can be considered another viable tool in the kitbag of GPS positioning techniques. It is now supported by a number of receiver manufacturers and several free online PPP processing services. You might think, looking at the name, that there’s nothing particularly special about it. After all, doesn’t any kind of positioning with GPS give you a precise point position including that from a handheld receiver or a satnav device? They key word here is precise.
The use of the word precise, in the context of GPS positioning, usually means getting positional information with precision and accuracy better than that afforded by the use of L1 C/A-code pseudorange measurements and the data provided in the broadcast navigation messages from the satellites. A typically small improvement in precision and accuracy can be had by using pseudoranges determined from the L2 frequency in addition to L1. This permits the real-time correction for the perturbing effect of the ionosphere. Such an improvement in positioning is embodied in the distinction between the two official GPS levels of service: the Standard Positioning Service provided through the L1 C/A-code and the Precise Positioning Service provided for “authorized” users, which requires the use of the encrypted P-code on both the L1 and L2 frequencies. Civil GPS users will have access to a similar level of service once a sufficient number of satellites transmitting the L2 Civil (L2C) code are in orbit. However, this capability will only provide meter-level accuracy. The PPP technique can do much better than this.
It can do so thanks to two additional precision aspects of the technique. The first is the use of more precise (and, again, accurate) descriptions of the orbits of the satellites and the behavior of their atomic clocks than those included in the navigation messages. Such data is provided, for example, by the International GNSS Service (IGS) through its global tracking network and analysis centers. These so-called precise products are typically used to process receiver data after collection in a post-processing mode, although real-time correction streams are now being provided by the IGS and some commercial entities.
Now, it’s true that a user can get high precision and accuracy in GPS positioning using the differential technique where data from one or more base or reference stations is combined with data from the user receiver. However, by using precise products and a very thorough model of the GPS observables, the PPP technique does away with the requirement for a directly accessed base station.
The other precision aspect of PPP is its use of carrier-phase measurements rather than just pseudoranges. Carrier-phase measurements have a precision on the order of two magnitudes (a factor of 100) better than that of pseudoranges. But there is a catch to the use of carrier-phase measurements: they are ambiguous by an integer multiple of one cycle. Processing algorithms must resolve the value of this ambiguity and ideally fix it at its correct integer value. Unfortunately, it is difficult to do this instantaneously, and often many epochs of measurements are needed for a position solution to converge to a sufficiently high accuracy, say better than 10 centimeters. Researchers are actively working on reducing the convergence time, and in this month’s column, we look at how using measurements from three satellite frequencies rather than just two can help.
“Innovation” is a regular feature that discusses 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, University of New Brunswick. He welcomes comments and topic ideas. To contact him, see the “Contributing Editors” section on page 6.
While carrier-phase measurements typically have very low noise compared to pseudorange (code) measurements, they have an inherent integer cycle ambiguity: the carrier phase, interpreted as a range measurement, is ambiguous by any number of cycles. However, integer ambiguity fixing is now routinely applied to undifferenced GPS carrier-phase measurements to achieve precise positioning. Some implementations are even available in real time. This so-called precise point positioning (PPP) technique permits ambiguity resolution at the centimeter level.
With the new modernized satellites’ capabilities, performing PPP with triple-frequency measurements will be possible and, therefore, the current dual-frequency formulation will not be applicable. There is also a need for a generalized formulation of phase biases for Radio Technical Commission for Maritime Services (RTCM) State Space Representation (SSR) needs. In this RTCM framework, the definition of a standard is important to allow interoperability between the two components of a positioning system: the network side and the user side.
Classical Formulation
In this section, we review the formulation of the observation equations. We will use the following constants in the equations:
where f1 and f2 are the two primary frequencies transmitted by all GPS satellites and c is the vacuum speed of light. For the GPS L1 and L2 bands, f1 = 154f0 and f2 = 120f0, where f0 = 10.23 MHz.
The pseudorange (or code) measurements, P1 and P2, are expressed in meters, while phase measurements, L1 and L2, are expressed in cycles. In the following, we use the word “clock” to mean a time offset between a receiver or satellite clock and GPS System Time as determined from either code or phase measurements on different frequencies or some combination of them.
The code and phase measurements are modeled as:
(1)
where:
D1 and D2 are the geometrical propagation distances between the emitter and receiver antenna phase centers at f1 and f2 including troposphere elongation, relativistic effects and so on.
W is the contribution of the wind-up effect (in cycles).
e is the code ionosphere elongation in meters at f1. This elongation varies with the inverse of the square of the carrier frequency and is applied with the opposite sign for phase.
Δh = hi – hj is the difference between receiver i and emitter j ionosphere-free phase clocks. Δhp is the corresponding term for code clocks.
Δτ = τi – τj is the difference between receiver i and emitter j offsets between the phase clocks at f1 and the ionosphere-free phase clocks. By construction, the corresponding quantity at f2 is γΔτ. Similarly, the corresponding quantity for the code is Δτp (time group delay).
N1 and N2 are the two carrier-phase ambiguities. By definition, these ambiguities are integers. Unambiguous phase measurements are therefore L1 + N1 and L2 + N2.
Equations (1) take into account all the biases related to delays and clock offsets. The four independent parameters, Δh, Δτ, Δhp, and Δτp, are equivalent to the definition of one clock per observable. However, our choice of parameters emphasizes the specific nature of the problem by identifying reference clocks for code and phase (Δhp and Δh) and the corresponding hardware offsets (Δτp and Δτ). These offsets are assumed to vary slowly with time, with limited amplitudes.
The measured widelane ambiguity, , (also called the Melbourne-Wübbena widelane) can be written as:
(2)
whereNwis the integer widelane ambiguity,μ jis the constant widelane delay for satellite j and μiis the widelane delay for receiver i (which is fairly stable for good quality geodetic receivers). The symbolmeans that all quantities have been averaged over a satellite pass.
Integer widelane ambiguities are then easily identified from averaged measured widelanes corrected for satellite widelane delays. Once integer widelane ambiguities are known, the ionosphere-free phase combination can be expressed as
(3)
whereis the ionosphere-free phase combination computed using the known Nw ambiguity,Dcis the propagation distance,hiis the receiver clock and h jis the satellite clock. N1is the remaining ambiguity associated to the ionosphere-free wavelengthλc(10.7 centimeters).
The complete problem is thus transformed into a single-frequency problem with wavelengthλcand without any ionosphere contribution. Many algorithms can be used to solve Equation (3) using data from a network of stations. IfDcis known with sufficient accuracy (typically a few centimeters, which can be achieved using a good floating-point or real-valued ambiguity solution), it is possible to simultaneously solve for N1 ,hiand h j. The properties of such a solution have been studied in detail. A very interesting property of theh jsatellite clocks is, in particular, the capability to directly fix (to the correct integer value) the N1values of a receiver that was not part of the initial network.
The majority of the precise-point-positioning ambiguity-resolution (PPP-AR) implementations are based on the identification and use of the two quantitiesμ jand h j. These quantities may be called widelane biases and integer phase clocks, a decoupled clock model or uncalibrated phase delays, but they are all of the same nature.
A Real-Time PPP-AR Implementation
A PPP-AR technique was successfully implemented by the Centre National d’Etudes Spatiales (CNES) in real time in the so-called PPP-Wizard demonstrator in 2010 and has been subsequently improved. In this demonstrator and in the framework of the International GNSS Service (IGS) Real-Time Service (RTS) and the RTCM, the GPS and GLONASS constellation orbits and clocks are computed. Additional biases for GPS ambiguity resolution are computed and broadcast to the user. The demonstrator also provides an open-source implementation of the method on the user side, for test purposes. Centimeter-level positioning accuracy in real time is obtained on a routine basis.
Limitations of the Bias Formulations. The current formulation works but it has several drawbacks:
The chosen representation is dependent on the implemented method. Even if the nature of the biases is the same, their representation may be different according to the underlying methods, and this makes it difficult for a standardization of the bias messages.
The user side must implement the same method as the one used on the network side. Otherwise, the user side would have to convert the quantities from one method to another, leading to potential bugs or misinterpretations.
It is limited to the dual-frequency case. There are only two quantities to be computed in the dual-frequency case ( and ), but in the triple-frequency case, there are many more possible combinations. For example, one can have (this is a non-exhaustive list) , , ,, , , where the indices refer to different pairs of frequencies, and other ionosphere-free combinations such as phase widelane-only or even phase ionosphere-free and geometry-free combinations are possible.
New RTCM SSR Model
The new model, as proposed by the RTCM Special Committee 104 SSR working group for phase bias messages is based on the idea that the phase bias is inherent to each frequency. Thus, instead of making specific combinations, one phase bias per phase observable is identified and broadcast.
It is noted that this convention was adopted a long time ago for code biases. Indeed, in the RTCM framework, and unlike the standard differential code bias (DCB) convention where code biases are undifferenced but combined, the RTCM SSR code biases are defined as undifferenced and uncombined. The general model for uncombined code and phase biases is therefore:
(4)
Time group delays, τ, and phase clocks, h, in Equation (1) are replaced by code and phase biases (ΔbP andΔbLrespectively). RTCM SSR code and phase biases correspond to the satellite part of these biases. The prime notation denotes the “unbiasing” process of the measurements. Here, the clock definition is crucial. As the biases are uncombined, they are referenced to the clocks. The convention chosen for the standard is natural: it is the same as the one used by IGS, that is,ΔhPin our notation.
This new model can be extended to the triple-frequency case very easily, as it does not involve explicit dual-frequency combinations:
(5)
This new model simplifies the concept of phase biases for ambiguity resolution. This representation is very attractive because no assumption is made on the method used to identify phase biases on the network side. All the implementations are valid if they respect this proposed model. It also allows convenient interoperability if the network and user sides implement different ambiguity resolution methods.
TABLE 1 summarizes the different messages used for PPP-AR in the context of RTCM SSR:
TABLE 1. RTCM SSR messages for PPP-AR.
Bias Estimation in the Dual-Frequency Case. The new phase biases identification in the dual-frequency case is straightforward. There are two biases (, ) to be estimated using two combinations (µ and h). The problem to be solved is described in FIGURE 1.
FIGURE 1. Phase biases estimation in the dual-frequency case.
It can be solved very easily on the network side by means of a 2 × 2 matrix inversion:
(6)
with
Note: All the quantities denote the satellite part of the Δ operator defined above.
Bias Estimation in the Triple-Frequency Case. The triple-frequency bias identification is tricky due to the need, using only three biases, to keep the integer nature of phase ambiguities on all viable ionosphere-free combinations, and in particular combinations that were not used in the identification process. At this level, one cannot make assumptions on what kind of combinations will be employed by a user. The problem to be solved is described in FIGURE 2.
FIGURE 2. Phase biases estimation in the triple-frequency case.
As an example, a naïve solution would be to identify the extra-widelane phase biases,, using the dual-frequency widelane approach, and then identify thebias. Given the large wavelength of the extra-widelane combination, such identification would be very easy. However, the corresponding bias would be only helpful for extra-widelane ambiguity identification, and its noise would prevent its use for widelane 15 (L1/L5) ambiguity resolution or other useful combinations available in the triple-frequency context.
Each independent phase bias can be directly estimated in a filter; however, in order to keep ascending compatibility with the dual-frequency case during the deployment phase of the new modernized satellites, we have chosen to stay in the old framework, that is, to work with combinations of biases. The resolution method is the following:
The widelane biases, that is, the identification of all thebLi – bLj quantities, are solved. For this computation and in order to have an accurate estimate of these biases, the two MW-widelane biasesµ12andµ15are used coupled to an additional phase bias, which is given by the triple-frequency ionosphere-free phase combination with the integer widelane ambiguities already fixed. This last combination using only phase measurements is much more accurate than MW-widelanes. The system to be solved is redundant and the noise of the different equations has to be chosen carefully.
The remaining bias (bLi ) is estimated using the traditional ionosphere-free phase combination of L1 and L2.
This computation has been implemented in the CNES real-time analysis center software, and since September 15, 2014, CNES broadcasts phase biases compatible with this triple-frequency concept on the IGS CLK93 real-time data stream.
Real Data Analysis
To prove the validity of the concept, at CNES, we compute several ambiguity combinations using real data. The process is the following:
Look for good receiver locations having a large number of GPS Block IIF satellites (transmitting the L5 signal) in view for a period of time exceeding 30 minutes, and choose among them, one participating in the IGS Multi-GNSS (MGEX) experiment. The station CPVG (Cape Verde) in the Reseau GNSS pour l’IGS et la Navigation (REGINA) network was chosen for the time span on September 28, 2014, between 19 and 20 hours UTC. During this period, four Block IIF satellites were visible simultaneously (PRNs 1, 6, 9, 30) for a total of 14 GPS satellites in view.
Record a compatible phase-bias stream. The CLK93 stream is recorded during the time span of the experiment.
Perform a PPP solution using the measurements, CLK93 corrections and biases to estimate the propagation distance, the troposphere delay and the receiver clock and phase ambiguity estimates according to Equation (5).
For different ambiguity estimates, compute and plot the obtained residuals.
We present in the following graphs various ambiguity residuals for the four Block IIF satellites in view. The values of each ambiguity are offset by an integer value for clarity purposes.
Melbourne-Wübbena Extra-Widelane.FIGURE 3 represents the MW extra-widelane (between frequencies L2 and L5) ambiguity estimation using our process. The MW extra-widelane ambiguity has a wavelength of 5.86 meters. The noise of the combination expressed in cycles is very low, and the integer nature of ambiguities in this combination is clearly visible.
FIGURE 3. Ambiguity residuals for the extra-widelane 5-2 combination.
Melbourne-Wübbena Widelanes.FIGURE 4 represents the MW-widelanes (the regular 1-2 and 1-5 combinations). Here again, the integer nature of the four ambiguities is clearly visible.
Widelane-Only Ionosphere-Free Phase. In the triple-frequency context, there is a possibility of forming an ionosphere-free combination of the three phase observables. This combination has an important noise amplification factor (>20), but would allow us to perform decimeter-accuracy PPP using only the solved widelane integer ambiguities and if the corresponding phase biases are accurate. In addition, it can be shown that the wavelength of the widelane ambiguity when the extra-widelane ambiguity is solved is about 3.4 meters. It means that the remaining widelane using this combination can be solved if the position is accurate enough (a few tens of centimeters) and the extra-widelane is known. FIGURE 5 shows such a case, that is, the residuals of the widelane ambiguity using this combination and assuming that the extra-widelane is already solved for.
FIGURE 5. Ambiguity residuals for widelane-only 1-2-5 ionosphere free combinations.
Such a case where the solution is the most biasedis shown (the dark blue curve). This behavior is mainly due to the difficulty in estimating the phase biases on this combination accurately using only a few Block IIF satellites. We hope that in the future the increasing number of modernized satellites will help such bias estimation.
N1 Ionosphere-Free Phase.FIGURES 6 to 8 show the three possible ambiguity estimates using the ionosphere-free phase combination with two measurements (we assume that the corresponding widelane has already been solved). In each case, the computed biases allow us to easily retrieve the integer nature of the N1 ambiguity.
FIGURE 6. Ambiguity residuals for the N1 combination using a fixed 1-2 widelane.FIGURE 7. Ambiguity residuals for the N1 combination using a fixed 1-5 widelane.FIGURE 8. Ambiguity residuals for the N1 combination using a fixed 2-5 widelane.
Application to Triple-Frequency PPP
The results presented above show that the integer ambiguity nature of phase measurements is conserved for various useful observable combinations and prove the validity of the model. Another experiment has been carried out to estimate the impact of ambiguity convergence in the triple-frequency context. For that, in order to maximize the observability of the GPS Block IIF constellation and thus the accuracy of the biases, a network of ten stations across Europe has been chosen for the phase biases computation (see FIGURE 9). The station REDU (in green) was the test station to be positioned. The test occurred on January 10, 2015, around 11:00 UTC. At that time, four Block IIF satellites were visible simultaneously (PRNs 1, 3, 6, 9) for a total of 10 satellites in view.
FIGURE 9. Network used for the triple-frequency PPP study.
The PPP-Wizard open source client was used to perform PPP in real time. The advantage of this implementation is that it directly follows the uncombined observable formulation described in Equations (5). The strategy for ambiguity resolution is a simple bootstrap approach.
Convergence of the Widelane-Only Solution. In this test, a PPP solution was performed, but only the fixing of the widelane ambiguities was implemented. As noted in the previous section, the wavelength of the widelane ambiguity when the extra-widelane ambiguity is solved is about 3.4 meters, so it is expected that all the widelanes can be fixed in a very short time. Despite the amplification factor of about 20 of the equivalent unambiguous phase combination, we expect to obtain an accuracy of about 10 centimeters with such a solution.
FIGURE 10 shows the convergence time of several PPP runs in this context (16 different runs of five minutes are superimposed), in terms of horizontal position error.
FIGURE 10. Widelane-only triple-frequency PPP convergence (horizontal position error).
The extra-widelanes are fixed instantaneously; the remaining widelanes are fixed in about two minutes on average to be below 30 centimeters (this is represented by the different sharp reductions of the errors). This new configuration, available in the triple-frequency context, is very interesting as it provides an intermediate class of accuracy, which converges very quickly and which is suitable for applications that do not demand centimeter accuracy. Another interesting aspect of this combination is the gap-bridging feature. In PPP, gap-bridging is the functionality that allows us to recover the integer nature of the ambiguities after a loss of the receiver measurements over a short period of time (typically a pass through a tunnel or under a bridge). This is done usually by means of the estimation of a geometry-free combination (ionosphere delay estimation) during the gap. Realistic maximum gap duration in the dual-frequency case is about one minute. In the triple-frequency case, the wavelength of the geometry-free combination involving the widelane (if the extra-widelane is fixed) is 1.98 meters. With such a large wavelength, the gaps are much easier to fill, and we can safely extend the gap duration to several minutes. In addition, the widelane combinations are wind-up independent, so there is no need to monitor a possible rotation of the antenna during the gap, as in the dual-frequency case.
Overall Convergence (All Ambiguities). Another PPP convergence test has been carried out with all ambiguities fixing activated (four different runs of 15 minutes are superimposed). Results are shown in FIGURE 11.
FIGURE 11. All ambiguities triple-frequency PPP convergence (horizontal position error).
The centimeter accuracy is obtained in this configuration within eight minutes, which is a significant improvement in comparison to the dual-frequency case. Further improvement of this convergence time is expected with an increase in the number of Block IIF satellites and, subsequently, GPS IIIA satellites.
Convergence Time Comparison Between the Dual- and Triple-Frequency Contexts. Thanks to these new results, a realistic picture for PPP convergence in the dual- and triple-frequency contexts can be drawn. To do so, polynomial functions have been fitted over the data points obtained in the previous studies. Two data sets were used:
Standard dual-frequency convergence (GPS only, 10 satellites in view).
Triple-frequency convergence (GPS only, 10 satellites in view, four Block IIF satellites).
FIGURE 12 represents the comparison between the two polynomials (horizontal error).
FIGURE 12. Realistic PPP convergence comparison between dual- and triple-frequency contexts (horizontal position error).
Conclusion
The new phase-bias concept proposed for RTCM SSR has been successfully implemented in the CNES IGS real-time analysis center. This new concept represents the phase biases in an uncombined form, unlike the previous formulations. It has the advantage of the unification of the different proposed methods for ambiguity resolution, and it prepares us for the future; for example, for a widely available triple-frequency scenario. The validity of this concept has been shown; that is, the integer ambiguity nature of phase measurements is conserved for various useful observable combinations.
In addition, we have also shown that the triple-frequency context has a significant impact on ambiguity convergence time. The overall convergence time is drastically reduced (to some minutes instead of some tens of minutes) and there is an intermediate combination (widelane-only) that has some interesting properties in terms of convergence time, accuracy and gap-bridging for non-demanding centimeter-level applications.
Acknowledgments
The contributions of colleagues contributing to the IGS services are gratefully acknowledged. Geo++ is thanked for useful discussions on the standardization of phase bias representation.
DENIS LAURICHESSE received his engineering degree and a Diplôme d’études appliquées (an advanced study diploma) from the Institut National des Sciences Appliquées in Toulouse, France, in 1988. He has worked in the Spaceflight Dynamics Department of the Centre National d’Etudes Spatiales (CNES, the French Space Agency) in Toulouse since 1992, responsible for the development of the onboard GNSS Diogene navigator. He was involved in the performance assessment of the EGNOS and Galileo systems and is now in charge of the CNES International GNSS Service real-time analysis center. He specializes in navigation, precise satellite orbit determination and GNNS-based systems. He was the recipient of The Institute of Navigation Burka Award in 2009 for his work on phase ambiguity resolution.
“Undifferenced GPS Ambiguity Resolution Using the Decoupled Clock Model and Ambiguity Datum Fixing” by P. Collins, S. Bisnath, F. Lahaye, and P. Héroux in Navigation, Journal of The Institute of Navigation, Vol. 57, No. 2, Summer 2010, pp. 123–135, doi: 10.1002/j.2161-4296.2010.tb01772.x.
“Integer Ambiguity Resolution on Undifferenced GPS Phase Measurements and Its Application to PPP and Satellite Precise Orbit Determination” by D. Laurichesse, F. Mercier, J.-P. Berthias, P. Broca, and L. Cerri in Navigation, Journal of The Institute of Navigation, Vol. 56, No. 2, Summer 2009, pp. 135–149, doi: 0.1002/j.2161-4296.2009.tb01750.x.
“Resolution of GPS Carrier-Phase Ambiguities in Precise Point Positioning (PPP) with Daily Observations” by M. Ge, G. Gendt, M. Rothacher, C. Shi, and J. Liu in Journal of Geodesy, Vol. 82, No. 7, pp. 389–399, doi: 10.1007/s00190-007-0187-4. Erratum: 10.1007/s00190-007-0208-3.
“The CNES Real-time PPP with Undifferenced Integer Ambiguity Resolution Demonstrator” by D. Laurichesse in Proceedings of ION GNSS 2011, the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation, Portland, Ore, September 20–23, 2011, pp. 654–662.
“The RTCM Multiple Signal Messages: A New Step in GNSS Data Standardization” by A. Boriskin, D. Kozlov, and G. Zyryanov in Proceedings of ION GNSS 2012, the 25th International Technical Meeting of The Satellite Division of the Institute of Navigation, Nashville, Tenn., September 17–21, 2012, pp. 2947-2955.
Improved Convergence for GNSS Precise Point Positioning by S. Banville, Ph.D. dissertation, Department of Geodesy and Geomatics Engineering, Technical Report No. 294, University of New Brunswick, Fredericton, New Brunswick, Canada. Recipient of The Institute of Navigation 2014 Bradford W. Parkinson Award.
Analysis of new Galileo signals at an experimental ground-based augmentation system (GBAS) compares noise and multipath in their performance to GPS L1 and L5. Raw noise and multipath level of the Galileo signals is shown to be smaller than those of GPS. Even after smoothing, Galileo signals perform somewhat better than GPS and are less sensitive to the smoothing time constant.
By Mihaela-Simona Circiu, Michael Felux, German Aerospace Center (DLR), and Sam Pullen, Stanford University
Several ground-based augmentation system (GBAS) stations have become operational in recent years and are used on a regular basis for approach guidance. These include airports at Sydney, Malaga, Frankfurt and Zurich. These stations are so-called GBAS Approach Service Type C (GAST C) stations and support approaches only under CAT-I weather conditions; that is, with a certain minimum visibility. Standards for stations supporting CAT-II/III operations (low visibility or automatic landing, called GAST D), are expected to be agreed upon by the International Civil Aviation Organization (ICAO) later this year. Stations could be commercially available as soon as 2018.
However, for both GAST C and D, the availability of the GBAS approach service can be significantly reduced under active ionospheric conditions. One potential solution is the use of two frequencies and multiple constellations in order to be able to correct for ionospheric impacts, detect and remove any compromised satellites, and improve the overall satellite geometry (and thus the availability) of the system.
A new multi-frequency and multi-constellation (MFMC) GBAS will have different potential error sources and failure modes that have to be considered and bounded. Thus, all performance and integrity assumptions of the existing single-frequency GBAS must be carefully reviewed before they can be applied to an MFMC system. A central element for ensuring the integrity of the estimated position solution is the calculation of protection levels. This is done by modeling all disturbances to the navigation signals in a conservative way and then estimating a bound on the resulting positioning errors that is valid at an allocated integrity risk probability.
One of the parameters that is different for the new signals and must be recharacterized is the residual uncertainty attributed to the corrections from the ground system (σpr_gnd). A method to assess the contribution of residual noise and multipath is by evaluating the B-values in GBAS, which give an estimate of the error contribution from a single reference receiver to a broadcast correction. Independent data samples over at least one day (for GPS) are collected and sorted by elevation angle. Then the mean and standard deviations for each elevation bin are determined.
Here, we evaluate the E1 and E5a signals broadcast by the operational Galileo satellites now in orbit. In the same manner as we did for GPS L5 in earlier research, we determine the σpr_gnd values for these Galileo signals. As for GPS L5, results show a lower level of noise and multipath in unsmoothed pseudorange measurements compared to GPS L1 C/A code.
DLR GBAS Facility
DLR has set up a GBAS prototype at the research airport in Braunschweig (ICAO identifier EDVE) near the DLR research facility there. This ground station has recently been updated and now consists of four GNSS receivers connected to choke ring antennas, which are mounted at heights between 2.5 meters and 7.5 meters above equipment shelters. All four receivers are capable of tracking GPS L5 (in addition to GPS L1 and L2 semi-codeless) and Galileo E1 and E5a signals. Figure 1 gives an overview of the current ground station layout, and Table 1 gives the coordinates of the antennas.
Figure 1. DLR ground facility near Braunschweig Airport, also shown in opening photo at left.Table 1. Ground receiver antenna coordinates.
Smoothing Techniques
The GBAS system corrects for the combined effects of multiple sources of measurement errors that are highly correlated between reference receivers and users, such as satellite clock, ephemeris error, ionospheric delay error, and tropospheric delay error, through the differential corrections broadcast by the GBAS ground subsystem. However, uncorrelated errors such as multipath and receiver noise can make a significant contribution to the remaining differential error. Multipath errors are introduced by the satellite signal reaching the antenna via both the direct path from the satellites and from other paths due to reflection. These errors affect both the ground and the airborne receivers, but are different at each and do not cancel out when differential corrections are applied.
To reduce these errors, GBAS performs carrier smoothing. Smoothing makes use of the less noisy but ambiguous carrier-phase measurements to suppress the noise and multipath from the noisy but unambiguous code measurements.
The current GBAS architecture is based on single-frequency GPS L1 C/A code measurements only. Single-frequency carrier smoothing reduces noise and multipath, but ionospheric disturbances can cause significant differential errors when the ground station and the airborne user are affected by different conditions. With the new available satellites (GPS Block IIF and Galileo) broadcasting in an additional aeronautical band (L5 / E5), this second frequency could be used in GBAS to overcome many current limitations of the single-frequency system.
Dual-frequency techniques have been investigated in previous work. Two dual-frequency smoothing algorithms, Divergence Free (Dfree) and Ionosphere Free (Ifree), have been proposed to mitigate the effect of ionosphere gradients.
The Dfree output removes the temporal ionospheric gradient that affects the single-frequency filter but is still affected by the absolute difference in delay created by spatial gradients. The main advantage of Dfree is that the output noise is similar to that of single-frequency smoothing, since only one single-frequency code measurement is used as the code input (recall that carrier phase noise on both frequencies is small and can be neglected).
Ifree smoothing completely removes the (first-order) effects of ionospheric delay by using ionosphere-free combinations of code and phase measurements from two frequencies as inputs to the smoothing filter. Unlike the Dfree, the Ifree outputs contain the combination of errors from two code measurements. This increases the standard deviation of the differential pseudorange error and thus also of the position solution.
Noise and Multipath in New GNSS Signals
GBAS users compute nominal protection levels (H0) under a fault-free assumption. These protection levels are conservative overbounds of the maximum position error after application of the differential corrections broadcast by the ground system, assuming that no faults or anomalies affect the position solution. In order to compute these error bounds, the total standard deviation of each differentially corrected pseudorange measurements has to be modeled. The standard deviation of the residual uncertainty (σn, for the nth satellite) consists of the root-sum-square of uncertainties introduced by atmospheric effects (ionosphere, troposphere) as well as of the contribution of the ground multipath and noise. In other words, these error components are combined to estimate σn2 as described in the following equation:
(1)
The ground broadcasts a value for σpr_gnd (described later in the section) associated with the pseudorange correction for each satellite. These broadcast values are based on combinations of theoretical models and actual measurements collected from the ground receivers that represent actual system characteristics. Unlike the ground, σpr_air is computed based entirely on a standardized error model. This is mainly to avoid the evaluation of multipath for each receiver and each aircraft during equipment approval.
In addition to the characteristics of nearby signal reflectors, multipath errors are mainly dependent on signal modulation and other signal characteristics (for example, power, chip rate). In earlier research, we showed that the newly available L5 signals broadcast by the GPS Block IIF satellites show better performance in terms of lower noise and multipath. This mainly results from an increased transmitted power and a 10 times higher chip rate on L5 compared to the L1 C/A code signal.
In this work, we extend this evaluation to the new Galileo signals and investigate their impact on a future multi-frequency, multi-constellation GBAS. Characterization of these new signals is based on ground subsystem measurements, since no flight data with GPS L5 or Galileo measurements are available at the moment. We assume that the improvements observed by ground receivers are also applicable to airborne measurements. This assumption will be validated as soon as flight data are available.
The measurements used were collected from the DLR GBAS test bed over 10 days (note that Galileo satellite ground track repeatability is 10 sidereal days) between the December 14 and 23, 2013. In that period, four Galileo and four Block IIF GPS satellites were operational and broadcast signals on both aeronautical bands E1 / L1 and E5a / L5.
In Figure 2, the suppression of multipath and noise on the Galileo signals can be observed, where the code multipath and noise versus elevation for GPS L1 C/A BSPK(1), Galileo E1 (BOC (1,1)) and Galileo E5a (BPSK(10)) signals are shown. The code multipath and noise was estimated using the linear dual-frequency combination described in equation (2), where MPi represents the code multipath and noise on frequency i, ρi the code measurement, and ϕi,and ϕj represent the carrier-phase measurements on frequencies i and j, respectively. Carrier phase noises are small and can be neglected.
(2)
Figure 2. Raw multipath function of elevation for GPS L1, Galileo E1 (BOC (1,1)) and Galileo E5a (BPSK(10)) signals.
The multipath on the Galileo E1 (BOC(1,1)) signal (the magenta curve) is lower than the GPS L1 C/A (BPSK(1))(black curve), especially for low elevation, where the advantage of the E1 BOC(1,1) is more pronounced. The lower values can be explained by the wider transmission bandwidth on E1 and the structure of the BOC signal. Galileo E5a (green data in Figure 2) again shows a better performance than Galileo E1. This was expected due to the higher chip rate and higher signal power. A comparison of the raw multipath and noise standard deviations for GPS L1, L5 and Galileo E1, E5a signals is presented in Figure 3.
Figure 3. Ratios of the multipath and noise standard deviation function of elevation.
The curves there show the ratios of the standard deviations for each elevation bin. The values for GPS L1 are almost 1.5 times larger than those for Galileo E1 BOC(1,1) (green curve) for elevations below 20°. For high elevations, the ratio approaches 1.0. This corresponds to the observations in the raw multipath plot ( Figure 2). With the same signal modulation and the same chip rate, E5a and L5 have very similar results (red curve), and the ratio stays close to 1.0 for all elevations.
The blue and the purple curves in Figure 3 show the ratio of GPS L1 C/A (BPSK(1)) and GPS L5 (BPSK(10)), and Galileo E1 (BOC(1,1)) and Galileo E5a (BPSK(10)), respectively. The ratio of GPS L1 to GPS L5 (blue curve) increases with elevation from values around 2.5 for low elevations, reaching values above 3.5 for elevations higher than 60°. As Galileo E1 performs better, the ratio between Galileo E1 and Galileo E5a (purple curve) is smaller, from a value of 1.5 for elevations below 10 degrees to a value of 3.0 for high elevations.
Until now, we have presented the evaluation of raw code noise and multipath. However, in GBAS, carrier smoothing is performed to minimize the effect of code noise and multipath. The value that describes the noise introduced by the ground station is represented by a standard deviation called σpr_gnd and is computed based on the smoothed pseudoranges from the reference receivers. In the following section, we focus on the evaluation of σpr_gnd using different signals and different smoothing time constants. Note that, in this study, σpr_gnd contains only smoothed multipath and noise; no other contributions (for example, inflation due to signal deformation or geometry screening) are considered.
B-values and σpr_gnd
B-values represent estimates of the associated noise and multipath with the pseudorange corrections provided from each receiver for each satellite, as described in Eurocae ED-114A and RTCA DO-253C. They are used to detect faulty measurements in the ground system. For each satellite-receiver pair B(i,j), they are computed as:
(3)
where PRCTX represents the candidate transmitted pseudorange correction for satellite i (computed as an average over all M(i) receivers), and PRCSCA(i,k) represents the correction for satellite i from receiver k after smoothed clock adjustment, which is the process of removing the individual receiver clock bias from each reference receiver and all other common errors from the corrections. The summation computes the average correction over all M(k) receivers except receiver j. This allows detection and exclusion of receiver j if it is faulty. If all B-values are below their thresholds, the candidate pseudorange correction PRCTX is approved and transmitted. If not, a series of measurement exclusions and PRC and B-value recalculations takes place until all revised B-values are below threshold. Note that, under nominal conditions using only single-frequency measurements, the B-values are mainly affected by code multipath and noise.
Under the assumption that multipath errors are uncorrelated across reference receivers, nominal B-values can be used to assess the accuracy of the ground system. The standard deviation of the uncertainty associated with the contribution of the corrections (σpr_gnd) for each receiver m is related to the standard deviation of the B-values by:
(4)
where M represents the number of the receivers and N represents the number of satellites used. The final sigma takes into account the contribution from all receivers and is computed as the root mean square of the standard deviation of the uncertainties associated with each receiver (Equation 4).
Figure 4 shows the evaluation of (σpr_gnd) for the Galileo E1, BOC(1,1) signal and the GPS L1 C/A signal for increasing smoothing time constants (10, 30, 60, and 100 seconds). Starting with a 10-second smoothing constant, Galileo E1 shows much better performance than GPS L1. The difference shrinks as the smoothing constant increases due to the effectiveness of smoothing in reducing noise and short-delay multipath. However, even with 100-second smoothing (the purple curves), Galileo E1 BOC(1,1) shows lower values of (σpr_gnd).
Figure 4. σ(pr_gnd) versus elevation for Galileo E1 (dotted lines) and GPS L1 (solid lines for different smoothing constants: red (10s), green (30s), cyan (60s), purple (100s).
A similar comparison is presented in Figure 5, of the performance of GPS L1 and Galileo E5a. The Galileo E5a signal is significantly less affected by multipath, and the difference stays more pronounced than in the Galileo E1 – GPS L1, even with 100-second smoothing. It can be also observed that the Galileo signals have a lower sensitivity to the smoothing constant. The Galileo E1 signal shows an increase of sensitivity for low elevations (below 40°), while on E5a, a smoothing constant larger than 10 seconds has almost no impact on the residual error. Thus, a shorter smoothing constant on Galileo E5a generates approximately the same residual noise and multipath a 100-second smoothing constant on GPS L1.
Figure 5. σ(pr_gnd) versus elevation for Galileo E5a (dotted lines) and GPS L1 (solid lines) for different smoothing constants: red (10s), green (30s), cyan (60s), purple (100s).
The values for (σpr_gnd) are, however, impacted by the number of satellites which are used to determine a correction. Since only a very limited number of satellites broadcasting L5 and Galileo signals are currently available, these results should be considered preliminary. The first evaluations strongly indicate that with the new signals, we get better ranging performance. Based on the performance advantage of the new signals, a decrease of the smoothing constant is one option for future application. This would reduce the time required (for smoothing to converge) before including a new satellite or re-including a satellite after it was lost.
In the current GAST-D implementation, based on GPS L1 only, guidance is developed based on a 30-second smoothing time constant. A second solution, one with 100 seconds of smoothing, is used for deriving the Dv and Dl parameters from the DSIGMA monitor and thus for protection level bounding (it is also used for guidance in GAST-C). During the flight, different flight maneuvers or the blockage by the airframe can lead to the loss of the satellite signal.
Figure 6 shows the ground track of a recent flight trial conducted by DLR in November 2014. The colors represent the difference between the number of satellites used by the ground subsystem (with available corrections) and the number of satellites used by the airborne subsystem in the GAST-D position solution. One of the purposes of the flight was to characterize the loss of satellite signals in turns. In turns with a steeper bank angle, up to 3 satellites are lost (Turns 1, 3, and 4), while on a wide turn with a small bank angle (Turn 2), no loss of satellite lock occurred. It is also possible for airframe to block satellite signals, leading to a different number of satellites between ground and airborne even without turns.
Figure 6. Ground track of a flight trial conducted by DLR. The colors represent difference between number of SVs used by the ground system and number of SVs used by the airborne.
With this in mind, a shorter smoothing constant would allow the satellites lost to turns or to airframe blockage to be re-included more rapidly in the position solution. However, a new smoothing constant would have to be validated with a larger amount of data. Data from flights trials has to be evaluated as well to confirm that similar levels of performance are reresentative of the air multipath and noise.
In a future dual-frequency GBAS implementation, an important advantage of lower multipath and noise is to improve the Ifree position solution. In earlier research, we demonstrated that the error level of the Dfree solution is almost the same as for single-frequency, but an increase in error by a factor of 2.33 was computed for the Ifree standard deviation based on L1 C/A code and L2 semi-codeless measurements.
If the errors on L1 (E1) and L5 (E5a) code and carrier phase measurements are statistically independent the standard deviation of the σIfree can be written as,
(5)
where α=1−f 21 ∕ f 25, and σL1,σL5 represent the standard deviations of the smoothed noise and multipath for L1 (E1) and L5 (E5a), respectively. Considering σpr_gnd,L1(E1)) = σpr_gnd,L5(E5a)) in equation (5), the noise and multipath error on Ifree (σIfree) increases by a factor of 2.59.
Figure 7 shows the ratio σIfree/σL1 using measured data. We observe that the measured ratio (the black curve) is below the theoretical ratio computed based on the assumption of statistically independent samples (the constant value of 2.59). This is explained by the fact that the multipath errors in the measurements are not independent but have some degree of statistical correlation. The standard deviations are computed based on the same data set used in the raw multipath and noise assessment using 100-second smoothed measurements sorted into elevation bins of 10° spacing.
Figure 7. Measured ratio σIfree/σL1 function of elevation.
Conclusion
We have shown how GBAS can benefit from the new signals provided by the latest generation of GPS and Galileo satellites. We have demonstrated improved performance in terms of lower noise and multipath in data collected in our GBAS test bed. When GBAS is extended to a multi-frequency and multi-constellation system, these improvements can be leveraged for improved availability and better robustness of GBAS against ionospheric and other disturbances.
Acknowledgment
Large portions of this work were conducted in the framework of the DLR internal project, GRETA.
Manufacturers
The ground facility consists of four JAVAD GNSS Delta receivers, all connected to Leica AR 25choke ring antennas.
Mihaela-Simona Circiu is is a research associate at the German Aerospace Center (DLR). Her research focuses on multi-frequency multi-constellation Ground Based Augmentation System. She obtained a 2nd level Specialized Master in Navigation and Related Applications from Politecnico di Torino.
MIchael Felux is is a research associate at the German Aerospace Center (DLR). He is coordinating research in the field of ground-based augmentation systems and pursuing a Ph.D. in Aerospace Engineering at the Technische Universität München.
Sam Pullen is a senior research engineer at Stanford University, where he is the director of the Local Area Augmentation System (LAAS) research effort. He has supported the FAA and others in developing GNSS system concepts, requirements, integrity algorithms, and performance models since obtaining his Ph.D. from Stanford in Aeronautics and Astronautics.
Positioning in Challenging Environments Using Ultra-Wideband Sensor Networks
By Zoltan Koppanyi, Charles K. Toth and Dorota A. Grejner-Brzezinska
INNOVATION INSIGHTS by Richard Langley
QUICK. WHO WAS THE FIRST TO PREDICT THE EXISTENCE OF RADIO WAVES? If you answered James Clerk Maxwell, you are right. (If you didn’t and have an electrical engineering or physics degree, it’s back to school for you.) In the mid-1800s, Maxwell developed the theory of electric and magnetic forces, which is embodied in the group of four equations named after him. This year marks the 150th anniversary of the publication of Maxwell’s paper “A Dynamical Theory of the Electromagnetic Field” in the Philosophical Transactions of the Royal Society of London.
Interestingly, Maxwell used 20 equations to describe his theory but Oliver Heaviside managed to boil them down to the four we are familiar with today. Maxwell’s theory predicted the existence of radiating electromagnetic waves and that these waves could exist at any wavelength. Maxwell had speculated that light must be a form of electromagnetic radiation. In his 1865 paper, he said “This velocity [of the waves] is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.”
That electromagnetic waves with much longer wavelengths than those of light must be possible was conclusively demonstrated by Heinrich Hertz who, between 1886 and 1889, built various apparatuses for transmitting and receiving electromagnetic waves with wavelengths of around 5 meters (60 MHz). These waves were, in fact, radio waves. Hertz’s experiments conclusively proved the existence of electromagnetic waves traveling at the speed of light. He also famously said “I do not think that the wireless waves I have discovered will have any practical application.” How quickly he was proven wrong.
Beginning in 1894, Guglielmo Marconi demonstrated wireless communication over increasingly longer distances, culminating in his bridging the Atlantic Ocean in 1901 or 1902. And, as they say, the rest is history. Radio waves are used for data, voice and image one-way (broadcasting) and two-way communications; for remote control of systems and devices; for radar (including imaging); and for positioning, navigation and time transfer. And signals can be produced over a wide range of frequencies from below 10 kHz to above 100 GHz.
Conventional radio transmissions use a variety of modulation techniques but most involve varying the amplitude, frequency and/or phase of a sinusoidal carrier wave. But in the late 1960s, it was shown that one could generate a signal as a sequence of very short pulses, which results in the signal energy being spread over a large part of the radio spectrum. Initially called pulse radio, the technique has become known as impulse radio ultra-wideband or just ultra-wideband (UWB) for short and by the 1990s a variety of practical transmission and reception technologies had been developed.
The use of large transmission bandwidths offers a number of benefits, including accurate ranging and that application in particular is being actively developed for positioning and navigation in environments that are challenging to GNSS such as indoors and built-up areas. In this month’s column, we take a look at the work being carried out in this area by a team of researchers at The Ohio State University.
“Innovation” is a regular feature that discusses 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, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.
GNSS technology provides position, navigation and timing (PNT) information with high accuracy and global coverage where line-of-sight between the satellites and receivers is assured. This condition, however, is typically not satisfied indoors or in confined environments. Emerging safety, military, location-based and personal navigation applications increasingly require consistent accuracy and availability, comparable to that of GNSS but in indoor environments.
Most of the existing indoor positioning systems use narrowband radio frequency signals for location estimation, such as Wi-Fi, or telecommunication-based positioning (including GSM and UMTS mobile telephone networks). All these technologies require dedicated infrastructure, and the narrowband RF systems are subject to jamming and multipath, as well as loss of signal strength while propagating through walls. In contrast, using ultra-wideband (UWB) signals can, to some extent, remediate those problems by offering better resistance against interference and multipath, and they feature better signal penetration capability. Due to these properties, the use of UWB has the potential to support a broad range of applications, such as radar, through-wall imagery, robust communication with high frequency, and resistance to jamming. Furthermore the impulse radio UWB (IR-UWB), the subject of this article, can be an efficient standalone technology or a component of positioning systems designed for multipath-challenged, confined or indoor environments, where GNSS signals are compromised.
IR-UWB positioning can be useful in typical emergency response applications such as fires in large buildings, dismounted soldiers in combat situations, and emergency evacuations. In such circumstances, the positioning/navigation systems must determine not only the exact position of any individual firefighter or soldier to facilitate their team-based mission, but also navigate them back to safety. Under these scenarios, a temporary ad hoc network has to be quickly deployed, as the existing infrastructure is usually non-functional, damaged or destroyed at that point. The UWB-based systems may easily satisfy these criteria: (1) nodes placed in the target area can rapidly establish the network geometry even if line-of-sight between nodes is not available, (2) the communication capability allows for sharing measurements, and (3) the node positions may be calculated based on these measured ranges in a centralized or distributed way. Once the node coordinates have been determined, the tracking of the moving units can start. Obviously, the resistance against jamming makes this solution attractive for military applications.
Ad Hoc Network Formation for Emergency Response
Quick deployment
Sufficient positioning accuracy
Robustness against interference (jamming)
Signal penetration through solid structures
Generally, positioning systems, both local and global, require an infrastructure, which defines the implementation of a coordinate frame. For example, the national reference frames and their realizations support conventional land surveying, or the satellite and the GPS tracking subsystems, as well as the beacons in Wi-Fi systems. UWB positioning also follows the same logic; the network infrastructure defines a local coordinate system and allows for range measurements between the network nodes and the tracked unit(s).
Ad Hoc Sensor Network: Ad hoc networks are temporary, and thus, the node coordinates are not expected to be known or measured a priori; consequently, they are calculated based on measuring the ranges between the units in the initial phase, and can be updated subsequently if the network configuration changes.
Anchored Networks: The network nodes’ coordinates are known. If only local coordinates are known, then to connect to a global coordinate frame, at least one node’s global coordinates and a direction vector must be known to anchor and orient the network.
Anchor-Free Networks: No node coordinates are known, thus the localization problem is underdetermined. Nevertheless, the problem is still solvable, if it is extended with additional constraints.
Tracking: Once a network is established, static/moving objects can be positioned in the network coordinate system.
Ultra-Wideband Ranging
At the beginning of the 21st century, the Federal Communications Commission (FCC) introduced new regulations that enabled several commercial applications and initiated research on UWB application to PNT. The current FCC rules for pulse-based positioning or localization implementations require the applied bandwidth be between 3.1 and 10.6 GHz and the bandwidth to be higher than 500 MHz or the fractional bandwidth to be more than 0.2.
The typical IR-UWB ranging system consists of multiple transceiver units, including the transmitter and the receiver components. The transmitter emits a very short pulse (high bandwidth) with low energy, and the receiver detects the signal after it travels through the air, interacting with the environment. After reaching objects, the emitted pulse is backscattered as several signals, which likely reach the receiver at different times. In contrast, conventional RF signals are longer in duration, thus the backscattered waves overlap each other at the receiver, forming a complex waveform, and may not be distinguishable individually. Due to the shortness of the UWB signals, measurable peaks are nicely separated, representing different signal paths.
The wave shape of the impulse response of the transmission medium highly depends on the environment complexity due to multipath. Detections in the received wave are determined by a peak-detecting algorithm. Note that the travel time is generally determined from the first detection, as it is assumed to be from the shortest path, although other peak detection algorithms also exist.
In the experiments discussed in this article, a commercial UWB radio system was used. This sensor’s bandwidth is between 3.1 and 5.3 GHz, with a 4.3-GHz center frequency. Three methods are available to obtain ranges: (1) coarse range estimation, based on the received signal strength with dynamic recalibration; (2) precision range measurement (PRM), which uses the two-way time-of-flight technique; and (3) the filtered range estimates (FRE) method that refines the PRM solution using Kalman filtering. In our investigations, PRM data were used in static situations, when both the unit to be positioned and the reference units were static (such as when determining network node coordinates), and FRE was logged in kinematic scenarios.
Localization in a UWB Network
Commercial UWB products usually provide capabilities for all three applications: communication, ranging and radar imaging. In positioning applications, identical units are used for both the rovers — that is, the units to be localized — and the static nodes of the network. The general terminology, however, is that the rover unit with unknown position is called the receiver, and units deployed at known locations are called transmitters. We will also use the terms rover and stations. The positions are typically defined in a local coordinate system. The usual ranging methods used in RF technologies, including signal strength and fingerprinting, time of arrival, angle of arrival, and time difference of arrival, are also applicable to UWB systems. TABLE 1 lists the ranging methods and typical performance levels; the achievable accuracies are based on external references. Note that the accuracy depends on the sensor hardware and network configuration, applied bandwidth, signal-to-noise ratio, peak detection algorithm, experiment circumstances, formation and the environment complexity.
TABLE 1. Typical accuracy of the different UWB localization techniques. Note that the results depend on the hardware, antenna, applied bandwidth, experiment circumstances and geometric configuration; * denotes indoor environment with area coverage of a few times 10 × 10 meters, with line-of-sight conditions, and ** refers to the maximum error in the outdoor test area of about 100 × 100 meters).
Signal Strength. The received signal strength (RSS) requires modeling of the signal loss, which is a challenging problem since signals at different frequencies interact with the environment in different ways, and thus the resulting accuracy is generally inadequate for most applications. The fingerprinting approach is also applied to UWB positioning; the signal-strength vector received from the transmitters identifies a location by the best match, where the vector-location pairs are measured in a calibration/training phase and stored in a database.
Time of Flight. The time-of-flight method requires the synchronization of the clocks of the UWB units, which is difficult, in particular, in the low-cost systems. Therefore, most UWB systems are based on the two-way time-of-flight method, which eliminates the unknown clock delay between the sensors, although it also has its own challenges. The range between two units is obtained by measuring the time difference of the transmitted and received pulses plus knowing the fixed response time of the responding unit.
Computing Position in a Network. Once the ranges are known in a network environment, the position is determined by circular lateration. The principle for the 2D case with three stations is shown in FIGURE 1. Note that each range determines a circle around the known stations (stations 1, 2 and 3 in the figure), thus, if the stations’ coordinates are known, the unknown position can be calculated as the intersection of these circles. The problem is treated as a system of non-linear equations; note that the lateration requires at least three or four nodes in an adequate spatial distribution for 2D and 3D positioning, respectively. The measured ranges, characterized by the error terms usually modeled with a normal distribution, are depicted by the dotted parallel circles around the solid “perfect” range in Figure 1. Note that this is an optimization problem, which can be solved with direct numerical approximation, such as gradient methods, or by solving the respective linear system after linearizing the problem with close initial position values.
FIGURE 1. Circular lateration.
Time Difference and Angle of Arrival. The time difference of arrival (TDoA) approach is useful when the time synchronization is not established. The unknown time delays are eliminated by subtracting the travel times between the rover and the stations, and the response time of the responding unit must be known. The location estimation is similar to the time of arrival case, but rather than the intersection of the circles, hyperbolic function curves representing constant TDoA values are used to determine the rover position. Also, if errors are present in the measurements, the position calculation becomes an optimization problem instead of finding the root of an equation. The TDoA can be combined with the angle of arrival (AoA). This method assumes that the set of UWB antennas are arranged in an array, and the angle can be calculated as the time difference of the first and the last detection from different antennas of the array.
Calibration
The ranges obtained by UWB sensors could be further improved by calibration — for example, by estimating antenna and hardware delays. In our outdoor tests, the joint calibration model (see Two Calibration Models box) was used, and coefficients of various model functions were estimated. During these tests, the UWB units were placed at the corners of a 15× 15 meter area (see FIGURE 2).
FIGURE 2. Outdoor test configuration.
At two diagonal corners, two UWB units with a 1.5-meter vertical separation were installed on poles, while at the two other corners only one unit was used. These six units formed the nodes or the stations of the network. In all cases, a GPS antenna was fixed to the top of the poles to provide reference data. A pushcart with two UWB units, a logging laptop computer, a GPS antenna and a receiver formed the rover system. The reference solution was obtained by using the GPS measurements, with the accuracy around 1 centimeter after kinematic post-processing using precise satellite orbit and clock data. During calibration, the pushcart was collecting stationary data at points 1 to 12, marked on a 5 × 5 meter grid, as shown in Figure 2.
Two Calibration Models
Individual sensor calibration is the approach where the sensor delays are determined separately, for example, , where is the measured range between stations A and B, and are the calibration functions, and is the corrected range.
Joint calibration model is the approach where the calibration function does not provide the offset per station, but rather gives the relative offset between the two stations, where .
The calibration model as a function of the measured distance can be constant, linear or a higher-order polynomial.
After acquiring range data between the rover and network stations, three types of joint calibration functions were investigated: constant, linear and polynomial models. The coefficients of these functions were estimated from the measured ranges and GPS-provided reference positions at all grid points. The estimated functions with respect to the six network nodes are shown in FIGURE 3. Our hypothesis was that the accuracy is assumed to depend on the rover-station distance, and thus, the detected discrepancies between the rover and reference points are expected to be higher if the distance is larger. The results indicate that a constant correction (that is, an antenna delay) is generally sufficient, indicating that the calibration may be applicable to similar installations. In some cases, a linear trend (a distance dependency) may be recognized due to slight data changes, but the observed regression lines are either increasing or decreasing, which clearly rejects the distance-dependency hypothesis. The linear and second-order polynomial functions likely model only local effects. The corrections provided by these functions depend on the environment, and consequently, are valid only in that configuration and where they were observed.
FIGURE 3. Calibration models.
Error surfaces, derived as the approximation of a second-order surface from the residuals at the grid points between the receiver and the six station units, show that the discrepancies can be as large as 0.5 meter. Calibrated results using the constant model show that all the discrepancies are less than 10 centimeters with an empirical standard deviation of 3.6 centimeters. This suggests that, at least, the constant-model-based calibration is needed.
Tracking Outdoors and Indoors
If the coordinates of the network nodes and the calibration parameters are known, the location of the moving rover can be calculated with circular lateration. The experiment described in this section is based on the same field test as presented earlier. For assessing the outdoor tracking performance, a random trajectory of the pushcart inside and outside of the rectangle defined by nodes was acquired (see FIGURE 4). The reference trajectory was obtained by GPS and the UWB trajectory was calculated with circular lateration.
FIGURE 4. Trajectory solutions.
TABLE 2 presents a statistical comparison of the coordinate component differences between the GPS reference and the UWB trajectory based on calibrated ranges. The mean of the X and Y coordinate differences are around 0 centimeters, and their standard deviations are 9.7 and 13.2 centimeters, respectively, with the largest differences being less than half a meter in both coordinate components. Note that the vertical coordinates have large errors due to the small vertical angle, which translates to weak geometric conditions for error propagation.
TABLE 2. Statistical results for the coordinate components.
Indoor UWB positioning is more challenging than outdoor, as propagation through walls modifies the RF signals resulting in attenuations and delays. Furthermore, the geometric error propagation conditions (that is, the shape of the network) may also reduce the quality of positioning. In the indoor tests, a personal navigation system demonstration prototype built in our lab (shown in FIGURE 5) was used as a rover. During the tests, the person was moving at a normal pace, and the rover unit recorded the ranges from the reference stations. Concerning the network, two point types are defined: (1) network nodes depicted by a double circle in the figure, which are used in the tracking phase; and (2) reference points marked by a single circle, which support the validation of the positioning results.
FIGURE 5. Indoor test configuration.
Since no reference solution was available during the indoor testing, the calibration method’s consistency was evaluated based on the relative or internal accuracy metric, which is the a posteriori reference standard deviation error:
where v is the vector of residual errors andr=dim(ATA) – rank(ATA) is the degrees of freedom of the network with A being the design matrix describing the geometry of the network. The m0 values are shown in FIGURE 6. This parameter describes the statistical difference of the measurements from the assumed model (circular lateration). The average m0 is 7.6 centimeters without calibration, and higher if any of the outdoor calibration models are used.
FIGURE 6. The indoor test results showing values of m0 at the epochs.
To estimate the absolute or external accuracy without a reference trajectory, points 1002 and 1004 were used as checkpoints with known coordinates. Obviously, these points were not part of the network. The UWB rover unit was placed at these points, and data were acquired in a static mode. The coordinates were continuously calculated after measuring at least three ranges. TABLE 3 presents the statistical results. Note that the average is not 0, thus the result is biased, indicating that the signal penetration and/or multipath effects are present in this complex indoor environment. Also, note that no calibration was performed, as no indoor calibration results were available, and using the outdoor calibration models only decreased the positioning accuracy. In addition, the standard deviations indicate the average m0 is consistent with the external error for point 1002, while this hypothesis is rejected for point 1004.
TABLE 3. Differences between the UWB position estimations and the correct coordinates at points 1002 and 1004.
Taking a closer look at the results of point 1004, the ambiguity problem of the circular lateration can be observed. The random measurement error can be large enough to cover two possible intersections in circular lateration, thus the estimator may oscillate between two solutions. Two main causes for this ambiguity are a weak network configuration and the large ranging errors (see FIGURE 7).
FIGURE 7. Ambiguity of lateration.
Ad Hoc UWB Sensor Network
We have also carried out tests on an indoor ad hoc sensor network using different coordinate estimation methods. Indoor distance measurements typically do not follow a normal or Gaussian error distribution but rather a Gaussian mixture distribution, which demands the use of a robust estimation method. Our results showed that the maximum likelihood estimation technique performs better than conventional least squares for this type of network.
Conclusion
Ultra-wideband technology is an effective positioning method for short-range applications with decimeter-level accuracy. The coverage area can be extended with increasing network size. The technology can be used independently or as a component of an integrated positioning/navigation system. GPS-compromised outdoor situations and indoor applications can be supported by UWB in permanent and ad hoc network configurations. While UWB technology is relatively less affected by environmental conditions, signal propagation through objects or other non-line-of-sight conditions can reduce the reliability and accuracy.
Acknowledgments
This article is based, in part, on the paper “Performance Analysis of UWB Technology for Indoor Positioning,” presented at the 2014 International Technical Meeting of The Institute of Navigation, held in San Diego, Calif., Jan. 27–29, 2014.
Manufacturer
The experiments discussed in the article used a Time Domain Corp. PulsON 300 UWB radio system.
ZOLTAN KOPPANYI received his B.Sc. degree in civil engineering in 2010 and his M.Sc. in land surveying and GIS in 2012, both from Budapest University of Technology and Economics (BME), Hungary. He also received a B.Sc. in computer science from the Eötvös Loránd University, Budapest, in 2011. He is a Ph.D. student at BME and was a visiting scholar at the Ohio State University (OSU), Columbus, in 2013. His research area is human mobility pattern analysis and indoor navigation.
CHARLES K. TOTH is a research professor in the Department of Civil, Environmental and Geodetic Engineering at OSU. He received an M.Sc. in electrical engineering and a Ph.D. in electrical engineering and geo-information sciences from the Technical University of Budapest, Hungary. His research expertise covers broad areas of 2D/3D signal processing; spatial information systems; high-resolution imaging; surface extraction, modeling, integrating and calibrating of multi-sensor systems; multi-sensor geospatial data acquisition systems, and mobile mapping technology.
DOROTA A. GREJNER-BRZEZINSKA is a professor in geodetic science, and director of the Satellite Positioning and Inertial Navigation (SPIN) Laboratory at OSU. Her research interests cover GPS/GNSS algorithms, GPS/inertial and other sensor integration for navigation in GPS-challenged environments, sensors and algorithms for indoor and personal navigation, and Kalman and non-linear filtering.
Further Reading
• Authors’ Conference Paper
“Performance Analysis of UWB Technology for Indoor Positioning” by Z. Koppanyi, C.K. Toth, D.A. Grejner-Brzezinska, and G. Jozkow in Proceedings of ITM 2014, the 2014 International Technical Meeting of The Institute of Navigation, San Diego, Calif. January 27–29, 2014, pp. 154–165.
• U.S. Regulations on Ultra-Wideband
“Ultra-Wideband Operation” in Code of Federal Regulations, Title 47, Chapter I, Subchapter A, Part 15, U.S. National Archives and Records Administration, Washington, D.C., October 1, 2014. Available online.
• Introduction to Ultra-Wideband
“History and Applications of UWB” by M.Z. Win, D. Dardari, A.F. Molisch, W. Wiesbeck, and J. Zhang in Proceedings of the Institute of Electrical and Electronics Engineers, Vol. 97, No. 2, February 2009, pp. 198–204, doi: 10.1109/JROC.2008.2008762.
“Ultra-Wideband Range Estimation: Theoretical Limits and Practical Algorithms” by I. Guvenc, S. Gezici, and Z. Sahinoglu in Proceedings of ICUWB2008, the 2008 Institute of Electrical and Electronics Engineers International Conference on Ultra-Wideband, Hannover, Germany, September 10–12, 2008, Vol. 3, pp. 93–96, doi: 10.1109/ICUWB.2008.4653424.
• Received Signal Strength Fingerprinting
“Increased Ranging Capacity Using Ultrawideband Direct-Path Pulse Signal Strength with Dynamic Recalibration” by B. Dewberry and W. Beeler in Proceedings of PLANS 2012, the Institute of Electrical and Electronics Engineers / Institute of Navigation 2012 Position, Location and Navigation Symposium, Myrtle Beach, S.C., April 23–26, 2010, pp. 1013–1017, doi: 10.1109/PLANS.2012.6236843.
“Indoor Ultra-Wideband Location Fingerprinting” by H. Kröll and C. Steiner in Proceedings of IPIN 2010, the 2010 International Conference on Indoor Positioning and Indoor Navigation, Zurich, September 15–17, 2010, pp. 1–5, doi: 10.1109/IPIN.2010.5648087.
• Ultra-Wideband Time-of-Arrival and Angle-of-Arrival“Ultra-Wideband Time-of-Arrival and Angle-of-Arrival Estimation Using Transformation Between Frequency and Time Domain Signals” by N. Iwakiri and T. Kobayashi in Journal of Communications, Vol. 3, No. 1, January 2008, pp. 12–19, 10.4304/jcm.3.1.12-19.
• Maxwell’s Equations
“The Long Road to Maxwell’s Equations” by J.C. Rautio in IEEE Spectrum, Vol. 51, No. 12, December 2014, North American edition, pp. 36–40 and 54–56, doi: 10.1109/mspec.2014.6964925.
A Student’s Guide to Maxwell’s Equations by D. Fleisch, Cambridge University Press, Cambridge, U.K., 2008.
Testing the Feasibility of Positioning Using Ambient Light
By Jingbin Liu, Ruizhi Chen, Yuwei Chen, Jian Tang, and Juha Hyyppä
INNOVATION INSIGHTS by Richard Langley
AND THEN THERE WAS LIGHT. Well, the whole electromagnetic (EM) spectrum, actually. Visible light occupies only a small portion of the spectrum, which extends from below the extremely low frequency (ELF) 3 to 30 hertz band with equivalent wavelengths of 100,000 to 10,000 kilometers through infrared, visible, and ultraviolet light and x-rays to gamma rays in the 30 to 300 exahertz band (an exahertz is 1018 hertz) with wavelengths of 10 to 1 picometers and beyond. The radio part of the spectrum extends to frequencies of about 300 gigahertz or so, but the distinction between millimeter radio waves and long infrared light waves is a little blurry.
Natural processes can generate electromagnetic radiation in virtually every part of the spectrum. For example, lightning produces ELF radio waves, and the black hole at the center of our Milky Way Galaxy produces gamma rays. And various mechanical processes can be used to generate and detect EM radiation for different purposes from ELF waves for communication tests with submerged submarines to gamma rays for diagnostic imaging in nuclear medicine.
Various parts of the EM spectrum have been used for navigation systems over the years. For example, the Omega system used eight powerful terrestrial beacons transmitting signals in the range of 10 to 14 kilohertz permitting global navigation on land, in the air, and at sea. At the other end of the spectrum, researchers have explored the feasibility of determining spacecraft time and position using x-rays generated by pulsars — rapidly rotating neutron stars that generate pulses of EM radiation.
But the oldest navigation aids, lighthouses, used the visible part of the EM spectrum. The first lighthouses were likely constructed by the ancient Greeks sometime before the third century B.C. The famous Pharos of Alexandria dates from that era. And before the construction of lighthouses, mariners used fires built on hilltops to help them navigate. The Greeks also navigated using the light from stars, or celestial navigation. Records go back to Homer’s Odyssey where we read “Calypso, the lovely goddess had told him to keep that constellation [the Great Bear] to port as he crossed the waters.” By around 1500 A.D., the astrolabe and the cross-staff had been developed sufficiently that they could be used to measure the altitudes of the sun or stars to determine latitude at sea. Celestial navigation was further advanced with the introduction of the quadrant and then the sextant. And determining longitude was possible by observing the moons of Jupiter (but not easily done at sea), measuring distances between the moon and other celestial bodies and, once it was developed, using a chronometer to time altitude observations.
How else is light used for positioning and navigation? Early in the space age, satellites were launched with flashing beacons or with large surface areas to reflect sunlight so that they could be photographed from the ground against background stars with known positions to determine the location of the camera. We also have laser ranging to satellites and the moon and the related terrestrial LiDAR technology, as well as the total stations used by surveyors. And in this month’s column, we take a look at the simple, innovative method of light fingerprinting: the use of observations of the artificial light emitted by unmodified light fixtures as well as the natural light that passes through windows and doorways in a technique for position determination inside buildings.
“Innovation” is a regular feature that discusses 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, University of New Brunswick. He welcomes comments and topic ideas.
Over the years, various localization technologies have been used to determine locations of people and devices in an absolute or relative sense. Relative positioning methods determine a location relative to another one in a local coordinate framework, while absolute positioning techniques fix an absolute location in a specific coordinate framework.
In the past, people observed the positions (orientation angles) of a celestial body (such as the sun, the moon, or a star) to determine their locations on the Earth, which is known as celestial navigation (see FIGURE 1). The locations are resolved by relating a measured angle between the celestial body and the visible horizon to the Nautical Almanac, which is a knowledge base containing the coordinates of navigational celestial bodies and other relevant data. Other than an observation device, celestial navigation does not rely on any infrastructure, and hence it can be used virtually anywhere on the globe at anytime, weather permitting. Nowadays, an increasing number of applications, location-based services, and ambient intelligence largely require positioning functions across various environments due to increasing mobility of people and devices. In particular, the development of robotics for a number of purposes requires the support of localization capability in various conditions where positioning infrastructure may be missing.
Various positioning technologies share an intrinsic characteristic that a positioning solution is resolved by using the dependency between spatial locations and a set of physical observables. The dependency may be expressed in the form of either a deterministic function model or a probabilistic model. A deterministic model expresses the dependency between locations and observables in a closed-form function, while a probabilistic model defines the dependency between locations and observables in the Bayesian sense. Depending on the form of dependency, different mathematical models have been used for position resolution.
For example, satellite-based GNSS positioning derives the location of a user’s receiver based on radio frequency (RF) signals transmitted by the satellite systems. GNSS positioning is grounded in accurate time determination: the time differences between the transmitted and the received radio signals denote signal travel times (observables), which are then converted into distance measurements between the satellite and the user antenna. Using the distance measurements between the user antenna and four different satellites, the receiver can obtain three-dimensional receiver coordinates in a global reference frame and the time difference between the receiver and satellite clocks. The dependency between user location and a set of distance observables can be expressed in a simplified equation:
(1)
where ρi is an observed range between the ith satellite and the receiver, (x,y,z)i is the position of the ith satellite, (x,y,z) is the position of the receiver to be estimated, γ denotes errors in the range observable, δt and c are receiver clock error and the speed of light, respectively (the sign of the clock term is arbitrary, but must be used consistently).
It is obvious that GNSS positioning relies strongly on the visibility of the GNSS constellation — the space infrastructure — as it requires line-of-sight visibility of four or more satellites. The positioning capability is degraded or totally unavailable in signal-blocked environments, such as indoors and in urban canyons.
An example of Bayesian positioning is to use various signals of opportunity (SOOP) — signals not originally intended for positioning and navigation. They include RF signals, such as those of cellular telephone networks, digital television, frequency modulation broadcasting, wireless local area networks, and Bluetooth, as well as naturally occurring signals such as the Earth’s magnetic field and the polarized light from the sun. Indicators of these signals, such as signal strengths and signal quality, are dependent on locations in the Bayesian sense. The dependency between signal indicators and locations is expressed in a probabilistic model:
(2)
where signifies a dependency between a set of physical signals and locations, I denotes indicators of SOOP signals, L denotes location, and P(i|l) is the probability that signal indicators (i) are observed at location (l).
Positioning resolution involves finding a location that yields the maximum a posteriori probability given a specific set of observables. Bayes’ Rule for computing conditional probabilities is applicable in the positioning estimation, and a family of Bayesian inference methods has been developed (see Further Reading).
An inertial navigation system (INS) is a typical relative positioning technology, and it provides the estimation of moved distance, direction, and/or direction change. A commonly used INS consists of accelerometers, gyroscopes, and a compass. It is self-contained and needs no infrastructure in principle to operate. However, the sensors yield accumulated positioning errors, and they need extra information for calibration. For example, in a GNSS/INS combined system, the INS needs to be calibrated using GNSS positioning results. To achieve an enhanced positioning performance in terms of availability, accuracy, and reliability, different positioning technologies are commonly integrated to overcome the limitations of individual technologies in applicability and performance.
This article discusses the feasibility of ambient light (ambilight) positioning, and we believe it is the first time that ambilight has been proposed as a positioning signal source. We propose the use of two types of observables of ambient light, and correspondingly two different positioning principles are applied in the positioning resolution. Our solution does not require any modifications to commonly used sources of illumination, and it is therefore different from other indoor lighting positioning systems that have been proposed, which use a modulated lighting source.
Ambilight positioning does not require extra infrastructure because illumination infrastructure, including lamps and their power supply and windows, are always necessary for our normal functioning within spaces. Ambilight exists anywhere (indoor and outdoor), anytime, if we consider darkness as a special status of ambient light. Ambilight sensors have been sufficiently miniaturized and are commonly used. For example, an ambilight sensor is used in a modern smartphone to detect the light brightness of the environment and to adaptively adjust the backlight, which improves the user vision experience and conserves power. Additionally, ambilight sensors are also widely used in automotive systems to detect the light intensity of environments for safety reasons. Therefore, ambilight positioning can use existing sensors in mobile platforms. This article presents the possibilities and methods of ambilight positioning to resolve both absolute and relative positioning solutions, and which can be integrated as a component in a hybrid positioning system.
Absolute Positioning Using Ambilight Spectral Measurements
The essence of localization problems is to resolve the intrinsic dependency of location on a set of physical observables. Therefore, a straightforward idea is that the type of observables applicable to positioning can be determined once the location-observables dependency is established. The feasibility is validated when the location-observables dependency is confirmed in the sense of necessary and sufficient conditions.
Ambient light is a synthesis of artificial light sources and natural light. The light spectrum is defined by the distribution of lighting intensity over a particular wavelength range. Researchers have reported development of sensor technology that has a spectral response from 300 to 1450 nanometers (from ultraviolet through infrared light). The spectrum of ambient light is mainly determined by colors of reflective surfaces in the circumstance, in addition to that of artificial and natural light sources. Therefore, intensity spectrum measurements are strongly correlated with surrounding environments of different locations. The traditional fingerprinting method can be used to resolve the positioning solution.
The fingerprinting approach makes use of the physical dependency between observables and geo-locations to infer positions where signals are observed. This approach requires the knowledge of observable-location dependency, which comprises a knowledge database. The fingerprinting approach resolves the most likely position estimate by correlating observed SOOP measurements with the knowledge database. The related fingerprinting algorithms include K-nearest neighbors, maximum likelihood estimation, probabilistic inference, and pattern-recognition techniques. These algorithms commonly consider moving positions as a series of isolated points, and they are therefore related to the single-point positioning approach. In addition, a “hidden Markov” model method has been developed to fuse SOOP measurements and microelectromechanical systems (MEMS) sensors-derived motion-dynamics information to improve positioning accuracy and robustness.
In the case of ambilight positioning, prior knowledge is related to structure layout information, including the layout of a specific space, spatial distribution of lighting sources (lamps), types of lighting sources, and windows and doors where natural light can come through. Spatial distribution of lighting sources is normally set up together with power supplies when the structure is constructed, and their layout and locations are not usually changed thereafter. For example, illumination lamps are usually installed on a ceiling or a wall in fixed positions, and the locations of doors and windows, through which light comes, are also typically fixed throughout the life of a building. Therefore, the knowledge database of lighting conditions can be built up and maintained easily through the whole life cycle of a structure.
In practice, a specific working region is divided into discrete grids, and intensity spectrum measurements are collected at grid points to construct a knowledge database. The grid size is determined based on the required spatial resolution and spatial correlation of spectrum measurements. The spatial correlation defines the degree of cross-correlation of two sets of spectrum measurements observed at two separated locations.
We measured the spectrum of ambient light with a two-meter grid size in our library. The measurements were conducted using a handheld spectrometer. FIGURE 2 shows a set of samples of ambilight spectrum measurements, and the corresponding photos show the circumstances under which each spectrum plot was collected. These spectral measurements show strong geo-location dependency. Spectrum differences of different locations are sufficiently identifiable. TABLE 1 shows the cross-correlation coefficients of spectral measurements of different locations. The auto-correlation coefficients of spectral measurements of a specific location are very close to the theoretical peak value of unity, and the cross-correlation coefficients of spectra at different locations are significantly low. Therefore, the correlation coefficient is an efficient measure to match a spectrum observable with a geo-referred database of ambilight spectra.
FIGURE 2. Ambilight spectral measurements of nine locations in the library of the Finnish Geodetic Institute (arbitrary units). The photos below the spectrum plots show the circumstances under which the corresponding spectral measurements were collected.TABLE 1. Correlation coefficient matrix of spectral measurements of different locations.
Relative Positioning Using Ambilight Intensity Measurements
Total ambilight intensity is an integrated measure of the light spectrum, and it represents the total irradiance of ambient light. In general, a lamp produces a certain amount of light, measured in lumens. This light falls on surfaces with a density that is measured in foot-candles or lux. A person looking at the scene sees different areas of his or her visual field in terms of levels of brightness, or luminance, measured in candelas per square meter. The ambilight intensity can be measured by a light detector resistor (LDR), and it is the output of an onboard 10-bit analog-to-digital converter (ADC) on an iRobot platform, which is the platform for a low-cost home-cleaning robot as shown in FIGURE 3.
FIGURE 3. The iRobot-based multi-sensor positioning platform, which is equipped with a light sensor and other versatile positioning sensors as marked in the figure.
We designed a simple current-to-voltage circuit based on an LDR and a 10-kilohm resistor, and the integrated analog voltage is input into the iRobot’s ADC with a 25-pin D-type socket, which is called the Cargo Bay Connector. FIGURES 4 and 6 show that the LDR sensor was not saturated during the test whenever we turned the corridor lamps on or off. Since the output of the light sensor was not calibrated with any standard light source, the raw ADC output rather than real values of physical light intensity was used in this study. During the test, the iRobot platform ran at a roughly constant speed of 25 centimeters per second, and the response time of the LDR was 50 milliseconds according to the sensor datasheet. The sampling rate of light intensity measurements was 5 Hz. Thus, the ADC could digitalize the input voltage in a timely fashion.
FIGURE 4. Total irradiance intensity measurements of ambient light in a closed space. The estimated lamp positions (magenta points) can be compared to the true lamp positions (green points).FIGURE 6. Total irradiance intensity measurements of ambient light in the open corridor of the third floor.
We conducted the experiments with the iRobot platform in two corridors in the Finnish Geodetic Institute building. The robot was controlled to move along the corridors, and it collected measurements as it traveled. The two corridors represent two types of environment. The corridor of the first floor is a closed space where there is no natural light, and the corridor of the third floor has both natural light and artificial illuminating light. The illuminating fluorescent lamps are installed in the ceiling. In a specific environment, fluorescent lamps are usually installed at fixed locations, and their locations are not normally changed after installation. Therefore, the knowledge of lamp locations can be used for positioning.
Ambilight positioning is relatively simple in the first case where there is no natural light in the environment and all ambilight intensity comes from artificial light. Because the fluorescent lamps are separated by certain distances, the intensity measurements have a sine-like pattern with respect to the horizontal distance along the corridor. The sine-like pattern is a key indicator to be used for detecting the proximity of a lamp. As shown in Figures 4 and 6, raw measurements of ambilight intensity and smoothed intensity have a sine-like pattern. Because raw intensity measurements have low noise, either raw measurements or smoothed intensity can be used to detect the proximity of a lamp. Figure 4 also shows the results of detection and the comparison to the true lamp positions. There are four fluorescent lamps in this corridor test. The first three were detected successfully, and the estimated positions are close to true positions with a root-mean-square (RMS) error of 0.23 meters. The fourth lamp could not be detected because its light is blocked by a shelf placed in the corridor just below the lamp as shown in FIGURE 5. Figure 4 shows the sine-like intensity pattern of the fourth lamp did not occur due to the blockage.
FIGURE 5. The light of the fourth lamp in the corridor is blocked by shelves, and the corresponding sine-like light pattern does not appear.
On the third floor, the situation is more complicated because there is both natural light and incandescent lamps in the corridor. Natural light may come in from windows, which are located at multiple locations on the floor. In addition, the light spectrum in the corridor may be interfered with by light from office rooms around the floor. To recover the sine-like intensity pattern of the lamps, the intensity of the background light was measured when the incandescent lamps were turned off. Therefore, the calibrated intensity measurements of illuminating lamps can be calculated as follows:
(3)
where Ia is the intensity measurements of composite ambient light, Ib is the intensity measurements of background light, and Ic is the intensity measurements of the calibrated ambient light of the illuminating lamps.
Figure 6 shows the intensity measurements of composite ambient light, background light, and calibrated lamp light. In addition, the intensity measurements of calibrated lamp light are smoothed by an adaptive low-pass filter to mitigate noise and interference. The intensity measurements of smoothed lamp light were used to estimate the positions of the lamps according to the sine-like pattern. The estimated lamp positions were compared to the true lamp positions, and the errors are shown in FIGURE 7. The estimated lamp positions have a mean error of 0.03 meters and an RMS error of 0.79 meters. In addition, for the total of 15 lamps in the corridor, only one lamp failed to be detected (omission error rate = 1/15) and one lamp was detected twice (commission error rate = 1/15).
Discussion and Conclusion
Ambilight positioning needs no particular infrastructure, and therefore it does not have the problem of infrastructure availability, which many other positioning technologies have, limiting their applicability. For example, indoor positioning systems using Wi-Fi or Bluetooth could not work in emergency cases when the power supply of these devices is cut off. What ambilight positioning needs is just the knowledge of indoor structure and ambilight observables. The lighting conditions of an indoor structure can be reconstructed based on the knowledge of the layout structure whenever illuminating lamps are on or off. Thus, ambilight observables can be related to the layout structure to resolve positioning estimates as we showed in this article.
Besides indoor environments, the methods we have presented are also applicable in many other GNSS-denied environments, such as underground spaces and long tunnels. For example, the Channel Tunnel between England and France has a length of 50.5 kilometers, and position determination is still needed in this kind of environment. In such environments, there is usually no natural light, and the intensity of illuminating lamps has a clear sine-like pattern.
In particular, ambient light positioning is promising for robot applications when a robot is operated for tasks in a dangerous environment where there is no infrastructure for other technical systems such as Wi-Fi networks. Given the knowledge of the lighting infrastructure acquired from the construction layout design, the method of ambilight positioning can be used for robot localization and navigation. Our tests have shown also that the proposed ambilight positioning methods work well with both fluorescent lamps and incandescent lamps, as long as the light intensity sensor is not saturated.
A clear advantage of the technique is that the illuminating infrastructure and the structure layout of these environments are kept mostly unchanged during their life cycle, and the lighting knowledge can be constructed from the structure design. Hence, it is easy to acquire and maintain these knowledge bases. The hardware of ambient light sensors is low-cost and miniature in size, and the sensors can be easily integrated with other sensors and systems.
Although a spectrometer sensor is not currently able to be equipped with a mobile-phone device, the proposed ambilight positioning techniques can still be implemented with a modern mobile phone in several ways. For example, an economical way would be to form a multispectral camera using a selection of optical filters of selected bands or a miniature adjustable gradual optical filter. The spectral resolution then is defined by the bandwidth of the band-pass optical filters and the optical characteristics of the gradual optical filter. Other sensors, such as an acousto-optic tunable filter spectrometer and a MEMS-based Fabry-Pérot spectrometer, could also be used to measure the spectrum of ambilight in the near future. With such techniques, ambilight spectral measurements can be observed in an automated way and with higher temporal resolution.
Acknowledgments
The work described in this article was supported, in part, by the Finnish Centre of Excellence in Laser Scanning Research (CoE-LaSR), which is designated by the Academy of Finland as project 272195. This article is based on the authors’ paper “The Uses of Ambient Light for Ubiquitous Positioning” presented at PLANS 2014, the Institute of Electrical and Electronics Engineers / Institute of Navigation Position, Location and Navigation Symposium held in Monterey, California, May 5–8, 2014.
JINGBIN LIU is a senior fellow in the Department of Remote Sensing and Photogrammetry of the Finnish Geodetic Institute (FGI) in Helsinki. He is also a staff member of the Centre of Excellence in Laser Scanning Research of the Academy of Finland. Liu received his bachelor’s (2001), master’s (2004), and doctoral (2008) degrees in geodesy from Wuhan University, China. Liu has investigated positioning and geo-reference science and technology for more than ten years in both industrial and academic organizations.
RUIZHI CHEN holds an endowed chair and is a professor at the Conrad Blucher Institute for Surveying and Science, Texas A&M University in Corpus Christie. He was awarded a Ph.D. degree in geophysics, an M.Sc. degree in computer science, and a B.Sc. degree in surveying engineering. His research results, in the area of 3D smartphone navigation and location-based services, have been published twice as cover stories in GPS World. He was formerly an FGI staff member.
YUWEI CHEN is a research manager in the Department of Remote Sensing and Photogrammetry at FGI. His research interests include laser scanning, ubiquitous LiDAR mapping, hyperspectral LiDAR, seamless indoor/outdoor positioning, intelligent location algorithms for fusing multiple/emerging sensors, and satellite navigation.
JIAN TANG is an assistant professor at the GNSS Research Center, Wuhan University, China, and also a senior research scientist at FGI. He received his Ph.D. degree in remote sensing from Wuhan University in 2008 and focuses his research interests on indoor positioning and mapping.
JUHA HYYPPA is a professor and the head of the Department of Remote Sensing and Photogrammetry at FGI and also the director of the Centre of Excellence in Laser Scanning Research. His research is focused on laser scanning systems, their performance, and new applications, especially those related to mobile laser scanning and point-cloud processing.
FURTHER READING
• Authors’ Conference Paper
“The Uses of Ambient Light for Ubiquitous Positioning” by J. Liu, Y. Chen, A. Jaakkola, T. Hakala, J. Hyyppä, L. Chen, R. Chen, J. Tang, and H. Hyyppä in Proceedings of PLANS 2014, the Institute of Electrical and Electronics Engineers / Institute of Navigation Position, Location and Navigation Symposium, Monterey, California, May 5–8, 2014, pp. 102–108, doi: 10.1109/PLANS.2014. 6851363.
• Light Sensor Technology
“High-Detectivity Polymer Photodetectors with Spectral Response from 300 nm to 1450 nm” by X. Gong, M. Tong, Y. Xia, W. Cai, J.S. Moon, Y. Cao, G. Yu, C.-L. Shieh, B. Nilsson, and A.J. Heeger in Science, Vol. 325, No. 5948, September 25, 2009, pp. 1665–1667, doi: 10.1126/science.1176706.
• Light Measurement
“Light Intensity Measurement” by T. Kranjc in Proceedings of SPIE—The International Society for Optical Engineering (formerly Society of Photo-Optical Instrumentation Engineers), Vol. 6307, Unconventional Imaging II, 63070Q, September 7, 2006, doi:10.1117/12.681721.
• Modulated Light Positioning
“Towards a Practical Indoor Lighting Positioning System” by A. Arafa, R. Klukas, J.F. Holzman, and X. Jin in Proceedings of ION GNSS 2012, the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, September 17–21, 2012, pp. 2450–2453.
• Application of Hidden Markov Model Method
“iParking: An Intelligent Indoor Location-Based Smartphone Parking Service” by J. Liu, R. Chen, Y. Chen, L. Pei, and L. Chen in Sensors, Vol. 12, No. 11, 2012, pp. 14612-14629, doi: 10.3390/s121114612.
• Application of Bayesian Inference
“A Hybrid Smartphone Indoor Positioning Solution for Mobile LBS” by J. Liu, R. Chen, L. Pei, R. Guinness, and H. Kuusniemi in Sensors, Vol. 12, No. 12, pp. 17208–17233, 2012, doi:10.3390/s121217208.
“Hybrid Positioning with Smartphones” by J. Liu in Ubiquitous Positioning and Mobile Location-Based Services in Smart Phones, edited by R. Chen, published by IGI Global, Hershey, Pennsylvania, 2012, pp. 159–194.
“Non-GPS Navigation for Security Personnel and First Responders” by L. Ojeda and J. Borenstein in Journal of Navigation, Vol. 60, No. 3, September 2007, pp. 391–407, doi: 10.1017/S0373463307004286.
