Tag: real-time kinematic

Innovation: Doppler-Aided Positioning
Improving Single-Frequency RTK in the Urban Enviornment

By Mojtaba Bahrami and Marek Ziebart

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

INNOVATION INSIGHTS by Richard Langley

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

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

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

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

Correction and Further Details

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

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

Single-Frequency RTK

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

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

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

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

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

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

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

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

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

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

GNSS Doppler Measurement Overview

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

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

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

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

Doppler-Smoothing Algorithm Description

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

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

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

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

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

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

Experimental Results

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

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

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

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

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

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

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

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

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

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

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

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

Conclusion

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

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

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

Acknowledgments

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

Manufacturer

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

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

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

FURTHER READING

• Carrier Smoothing of Pseudoranges

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

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

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

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

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

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

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

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

• Doppler-derived Velocity Information and RTK Positioning

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

• Doppler Smoothing of Pseudoranges and RTK Positioning

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

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

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

• Integer Ambiguity Resolution

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

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

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

“The Least-Squares Ambiguity Decorrelation Adjustment: a Method for Fast GPS Integer Ambiguity Estimation” by P.J.G. Teunissen in Journal of Geodesy, Vol. 70, No. 1–2, 1995, pp. 65–82, doi: 10.1007/BF00863419.
May 1, 2011
Road Talk: Interoperability Considerations for V2X GNSS Receivers
By Chaminda Basnayake

The presence of different types of devices, spanning multiple GNSS receiver types, configurations, hardware, software, and consequent widely varying capabilites, among a user mix of vehicles, cyclists, and pedestrians, poses several engineering challenges for a V2X scheme in which all road users share data with each other and with the road infrastructure.

The use of location awareness for transportation safety, efficiency, and security — a major area of research and development for academics, automotive manufacturers, and organizations such as the U.S. Department of Transportation — has focused attention on enabling communication between vehicles and other road user entities in a concept know as V2X, a term encompassing both vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) systems, so that they can share location and other status information. As a result, any road user entity may see all others around it. This capability is almost always built on GNSS technology.

Future V2X systems will be able to include all road user entities, ranging from vehicles to cyclists to pedestrians, in this information-sharing system. While it sounds natural for everyone to talk to each other and share data for collective benefit, the presence of different types of devices among this user mix poses several engineering challenges. As an example, a V2X device in a vehicle may have a built-in GNSS receiver with a roof-mounted antenna and another vehicle may have a retrofitted V2X device with a passive antenna and relatively limited accuracy capabilities. As the GNSS technology further develops, some vehicles may have multiple-frequency GNSS capability compared to legacy single-frequency devices. In essence, all compatible V2X devices will have to be carefully designed to ensure their interoperability with the rest of the system.

This article investigates positioning challenges arising from multiple GNSS receiver types, configurations, hardware, and software in a V2X operational environment. This produces a clear need to have minimum performance standards for V2X-capable GNSS receivers. The article further investigates the implications of land-based visibility obstructions on relative positioning, and implications on standalone position accuracy both as a result of limited GNSS satellite visibility and WAAS satellite visibility.

V2X Background

V2X systems rely on two critical enabling technologies: communications and positioning. Organizations and industry collaborations have developed and demonstrated various V2X systems over the last few years. These efforts have produced interoperable prototype V2V and V2I systems and over-the-air (OTA) messaging standards.

Figure 1 illustrates the general concept of combined V2V and V2I, or V2X. In a fully operational system, all vehicles and other road users carry short-range communication and positioning technology. At present, these technologies are expected to be based on dedicated short-range communication (DSRC) and GNSS, respectively. This enables each user to be location-aware and capable of sharing their location with others. Vehicles may use built-in systems, retrofitted devices, or those based on the occupant’s personal mobile device. Infrastructure elements and other road users such as pedestrians also form part of the V2X user community.

V2X Relative Positioning. Relative positioning of all communicating entities with respect to a given user is a required functional capability of a V2X system. To enable this functionality, positioning information from all communicating entities must be exchanged. For automotive V2X applications, Society of Automotive Engineers (SAE) J2735 DSRC Message Set Dictionary serves as the primary standard for message definitions. Current version of the messages consists of a basic safety message (BSM) , an optional variable rate message (VRM), and an option for including proprietary messages.

With BSM and VRM, vehicle position, speed, heading, and GNSS measurements can be communicated to others. GNSS relative positioning techniques such as real-time kinematic (RTK), code-based differential, or individual position differing (that is, distance between the positions reported by individual vehicles) can be used for relative positioning. The latter method, also known as DPOS, is a particular focus of this article.

Given the above, a system developer may develop a V2X relative positioning system that can operate based on techniques that can be broadly classified as position-based techniques, which include DPOS, and measurement-based differential techniques, including RTK and others.

The Simpler Approach. The SAE J2735 BSM accommodates the simpler approach of using the DPOS method, as it enables the sharing of critical state parameters. This approach is very attractive as it requires minimal OTA data volume compared to sending GNSS measurements. Secondly, DPOS relative position estimation process requires only a fraction of the processing resources required compared to measurement-based differential processing. Thirdly, any GNSS receiver in the market today is capable of outputting a position solution and most of the critical GNSS state parameters required for the V2X BSM. In contrast, most low-cost devices do not output measurements required for other methods.

However, there are quite a few challenges associated with DPOS. A vehicle or any other road-user entity, such as a location-enabled handheld device, will share its location information via BSM only. A relative positioning engine in each entity will use this information to provide lane-level and road-level data (relative distance, speed, and orientation) for its V2X applications. The challenges associated with DPOS method arise from multiple stages in this process.

The presence of many road-user types brings in the possibility of thousands of GNSS receiver types, models, hardware, and software in the user group. Thus the system must be interoperable with devices with a wide range of performance characteristics.

Secondly, each entity will transmit BSM only. This OTA information offers no information about the constellation the GNSS device sees or how the solution was derived in terms of filtering or applied constraints.

Thirdly, the position accuracy reported by each entity is a GNSS device-dependent variable, an estimate of the actual error as derived by a user device.

Finally and most importantly, V2X applications expect relative positioning information for each communicating entity classified in one of three possible accuracy categories: Which Road, Which Lane, or Where-in-Lane (see “Is GNSS up to the V2X Challenge?” GPS World, October 2010). The V2X system must be able to reliably identify this accuracy classification for each communicating entity with the limited information provided via the BSM.

Study Goals. To illustrate the impact of these challenges, several GNSS receiver types, configurations, and operational scenarios were investigated.
- Between multiple receiver types: In a V2X environment, vehicles and other road user entities may have different GNSS receiver types and makes: dual-frequency, single-frequency, and so on.
- Same receivers using different parts of visible constellation: In an urban canyon, it is possible for two adjacent vehicles to see two different parts of the GNSS constellation, due to obstructions.
- WAAS-enabled and non-WAAS receivers.
Data Collection

This data is a combination of field-data collections and a series of RF record playbacks. The field vehicle-mounted test setup included two GPS receivers, a GNSS L1 RF data recording device, and a high quality GPS/INS reference system (Figure 2). Type A receiver is a hi
gh-sensitivity enabled, automotive-grade GPS L1 receiver using a patch antenna, WAAS-capable although WAAS usage was disabled in the real-time data collection. Type B receiver is a high-quality L1/L2 receiver using a geodetic-grade antenna, used with WAAS enabled. The GPS/INS system was connected to the geodetic-grade antenna. The RF recording system was also connected to the automotive-grade GPS L1 antenna.

Figure 2. Vehicle test set-up.

The data was collected on a test route in Detroit, Michigan, that included durations of urban and deep urban canyon (40 miles per hour (mph) or less), freeway (55–70 mph), and suburban/local (30 mph) driving.

The RF data were subsequently replayed to GNSS receivers that were not a part of the field set-up. RF data was also replayed to receivers with forced sky-visibility obstructions and various WAAS settings. For limited sky-visibility tests, certain satellites were removed from each receiver’s view by receiver-specific configuration software. The satellite selection and restriction was done to mimic typical sky-view obstructions encountered in normal driving.

Type A receiver was chosen to illustrate the impact of visibility differences. A total of 13 satellites were visible in the entire data set (Figure 3). To create obstructed sky-view scenarios, two Type A receivers were configured to not use certain satellites in their position solutions. These configurations were:
- Configuration 1 (C1): PRNs 7, 10, and 13 blocked
- Configuration 2 (C2): PRNs 6, 16, 21, and 31 blocked
C1 mimics a vehicle/receiver with no visibility in the Northwestern part of the sky, whereas C2 mimics a receiver without visibility in the East/Northeastern part of the sky. Sky visibility restrictions do not vary with the heading changes of the vehicle. For example, for C1 receiver, Northwestern sky is always obstructed regardless of the vehicle orientation.

Figure 3. Sky view during the test.

Figure 4 shows an example RF data replay setup. The record and replay system was controlled through a PC and the recorded data was also stored in the controller PC. The output RF signal was split into multiple outputs such that multiple receivers can be tested at the same time. For each replay of the RF data, a benchmark receiver was also used to verify that there is no run-to-run difference as a result of the RF replay.

Outputs from each GPS receiver from field and replay runs were logged to PCs using receiver specific binary formats. The recorded output from each receiver included its position, position error estimate, velocity, satellite-specific measurements and indicators such as pseudorange, carrier phase, and signals-to-noise ratio.

Figure 4. RF data replay set-up.

Data Processing and Analysis

The data was first decoded from the receiver-specific formats to a common format, then corrected for antenna offsets. To simplify the process, the reference system position solution was translated to the position of the test antenna using the known between-antenna distance and orientation of the vehicle as measured by the reference system. As a result, all the receivers and the reference system are reporting the location of the test antenna. Then, data fields such as position and velocity for each receiver were time-matched with the reference solutions, and the actual error was calculated.

For a limited dataset, additional measurement-level differential processing was done to show the difference between a DPOS and an RTK or a code-based differential relative position solution.

Figure 5 shows a plot of the 2D position error observed from each receiver during the test as a function of driving environment. Overall, Type B receiver shows better accuracy as expected from a dual frequency high quality receiver. However, it shows spikes of large error increases at times, mostly observed in the freeway scenario with large error excursions. With Type A receivers, relatively larger errors are observed with the limited-constellation receivers.

Figure 5. Position error (2D) of each receiver as a function of driving environment.

Figure 6 shows the number of satellites used by each receiver in the same environments as in Figure 5. Overall, Type A receiver tracks and uses on average 2–3 satellites more compared to the Type B receiver, likely due to its high-sensitivity capability. Type A C1 and C2 receivers also track and use 2–3 satellites fewer compared to the all-in-view Type A receiver.

Figure 6. GPS satellites used by receivers.

Freeway Data. The vehicle heading in this segment was predominantly north or northwest. The sky view can be considered a combination of urban and open sky conditions. As highlighted in Figure 6, all-in-view Type A receiver was able to use up to 11 GPS satellites with an average of around 9 satellites. Type A C1 and C2 receivers used, on average, about 3 satellites fewer than the all-in-view receiver. All three receivers show satellite count drops down to 4 at certain times in this segment.

The satellite count of the Type B receiver shows the limitations of not using the high-sensitive tracking capability. The satellite count shows frequent drops below 4 satellites and on occasion down to no satellites used.

Although the satellite count difference between all-in-view Type A and C1/C2 receivers was forced by means of receiver configuration, short-term sky visibility restrictions that resemble these conditions are in fact possible. Examples include a passenger car driving next to a semi truck or the side wall of the freeway in below-ground road sections.

Figure 7 shows the position outputs of all four receivers on a satellite image of a short segment of the freeway. The true location (reference) is shown in green. Type A, Type B, Type A C1, and Type A C2 are shown in red, black, purple, and blue, respectively. These colors identify the four receiver types in all figures for the rest of this paper. While biases can be seen in the outputs of all four receivers with respect to the reference, the Type A C1 shows the largest offset with the magnitude of more than a lane width.

Figure 7. Freeway positioning accuracy.

Figure 8 illustrates a time series of the positioning error components of all four receivers. It clearly shows error ramp-ups from the Type B receiver at frequent intervals. These coincide with the satellite count drops of Type B shown in Figure 6. No such error ramp-ups are observed for any of the Type A receivers, although relatively large biases of the order of few meters can be seen. As anticipated, larger errors are observed in the height direction.

Figure 8. Freeway positioning accuracy time series.

Local Road, Eastbound. This segment includes data gathered on an eastbound multi-lane local road with 40 mph posted speeds. As shown in Figure 6, a relatively larger number of satellites were continuously tracked in this segment as compared to the freeway. Therefore, this segment is considered to be an open-sky scenario with very limited number of obstructions. As shown in Figure 6, Type B receiver has used about 6 satellites on average, whereas the Type A has used around 3 more satellites most of the time. Type A C1 and C2 have also used around 3 satellites less compared to the all-in-view Type A receiver.

Figure 9 shows the vehicle position as reported by all three receivers and the reference system output for a short road segment in this drive. It clearly illustrates the lateral offsets of both C1 and C2 solutions. The C2 receiver (Blue) generated about a lane width offset towards north whereas the C1 receiver output is biased by around two lane widths to the south. Figure 10 presents a time series look of the positioning biases evident in Figure 9. It clearly shows large (more than 5 meter) biases in North and East position error components for C1 and C2 receivers.

Figure 9. Local (east) positioning accuracy.

Figure 10. Local (east) positioning accuracy time series.

Local Road, Northbound. In roadway characteristics, this resembles Local Eastbound. Figure 6 shows the sky view remained almost unchanged for Type A receivers. For Type A C1, the count remained at 6 throughout. C1 and C2 receivers tracked 2–3 satellites fewer compared to all-in-view Type A. Interestingly, Type B experienced two dropouts of 4 or fewer satellites during the run. Figure 11 shows the position output of all receivers on a short road segment. As in the case of Local (East), significant biases can be readily observed in the output of C1 and C2.

Figure 11. Local (North) accuracy.

Figure 11. Local (North) accuracy.

Figure 12 shows the time series view of the positioning error in this segment, confirming that the biases observed in Figure 11 are not short-term biases, but are in fact vehicle heading-dependent biases. The short-term biases seen in the Type B receiver output coincide with the change in the number of satellites used (shown in Figure 6). This illustrates the implications of different estimation methods used in the two receiver types. For instance, Type B receiver allows stepwise changes in its position estimate whereas Type A output tends to gradually converge to different states.

Figure 12. Local (North) positioning accuracy time series.

Urban Canyon. Results of the urban canyon segment of the drive are shown in Figures 13 and 14. A statistical analysis is not presented for this segment, as receiver type and configuration dependent biases and errors are difficult to isolate from the errors that are the result of multipath and measurement noise. In Figure 14, much larger biases in the order of 10 meters or more can be seen for all three Type A receivers. In comparison, Type B receiver tends to output a relatively accurate position solution whenever it has sufficient satellites visible. In the case of less than optimal satellites availability, Type B receivers tend to show rapidly degrading positioning accuracy, which may be reliably detected using its quality indicators.

Figure 13. Urban canyon accuracy.

Figure 14. Urban canyon positioning accuracy time series.

Position Error Distributions

Position error probability distribution functions were generated for the first three road segments using the time series data above. Figures 15-17 show these functions for Freeway, Local (East), and Local (North) segments, respectively. They lead to these general conclusions:
- Based on the mean and the spread of the distributions, Type B receiver has consistently provided the most unbiased and accurate positioning performance out of all the receivers considered. Overall, the output appears to be unbiased, as should be the case for a high quality dual frequency receiver with WAAS capability.
- Type A all-in-view receiver shows the next best overall accuracy statistics with some biases in certain cases. These biases can be time-of-day-dependent and may differ for different times of the day or if observed over a longer time.
- Type A C1 and C2 receivers show very significant vehicle-heading-dependent biases/errors. This is with very limited sky view obstructions (that is, C1 only restricts less than 1/8 of the entire sky view whereas C2 covers around 1/4) and with the same type of the receiver.
- Although enabling WAAS should theoretically help minimize the biases observed in these tests, the availability (open line-of-sight) of WAAS satellites for automotive applications in these environments must be taken into consideration for WAAS accuracy benefits to be applicable. For these datasets, WAAS signals availabilities for a Type B receiver were 58 percent of total driving time in urban canyon, 60 percent in the freeway scenario, 95 percent and 99 percent in the local road scenarios.
Figure 15. Freeway position error distribution.

Figure 16. Local road (east) position error distribution.

Figure 17. Local road (north) position error distribution.

Velocity Domain Performance. For each test segment, velocity estimates from each receiver were logged at the default data rate of 4 Hz. For analysis purposes, North and East velocity readings from each receiver were converted to 2D speed estimates. These were used with reference system speed estimates to generate 2D speed error statistics (Table 1).

Based on Table 1, no significant biases or errors were observed from any particular receiver or configuration. The only exception was the increased errors in the Urban Canyon segment, particular for C1 and C2. This is expected .to be a result of limited satellite availability in a challenging environment with additional forced satellite eliminations.

Table 1. Receiver Velocity Error Statistics (meters/second).

Virtual Two-Vehicle Analysis. Assume that Type A and Type A C1 receivers were located in two vehicles. Ideally, both receivers should report the same location, as they were both connected to the same antenna on a single vehicle, creating a zero-baseline scenario. However, as shown in the previous section, a meter-level separation was observed between the two solutions.

In this virtual two-vehicle scenario, relative position of one receiver (Type A) with respect to the other (Type A C2) was estimated by three methods, using GNSS data processing software in post-mission. The methods were:
- Differenced Positions (DPOS). Latitude and longitude reported by each vehicle were time-matched; distance between the two points was calculated.
- Code and Carrier. Single frequency (L1) GPS RTK positioning with float ambiguity estimation.
- Code Only. GPS code measurements generated a relative position solution.
The 2D receiver separation results of this processing are shown in Figure 19 as three subplots for freeway (top), local/east (middle), and local/north (bottom) scenarios. The 2D separation results for local scenarios show clear performance benefits for the GNSS measurements-based methods. In both east and north local scenarios, around a 5-meter bias is observed in the DPOS solution whereas this is reduced to around a meter in both code-only and code and carrier methods. The freeway scenario shows relatively smaller difference potentially due to measurement noise, multipath, and frequent interruption of sky view. Table 2 shows mean values of these results.

Figure 18. Position separation for processing methods.

Table 2. Mean Accuracy (meters) using processing methods.

Discussion

OTA transfer of certain GNSS measurement data elements appears to be a critical requirement for reliable lane-level positioning capability. However, the method must be capable of supporting a certain level of performance even in challenging environments for GNSS. The solution for such challenging environments is likely to be GNSS integration methods with vehicle-based sensors (that is, GNSS/INS) for the foreseeable future.

Given these facts, a reliable and accurate V2X relative position method will require the OTA transfer of a combination of critical vehicle states which include the vehicle location, a confidence measure, and certain GNSS measurement data elements. With its ability to support all of these needs, the SAE J2735 provides a basic framework for further refinement of relative positioning technologies for automotive applications.

A reliable position confidence measure broadcast over-the-air is also a critical need, particularly if GNSS measurement data is not broadcasted on a regular basis. This also holds true for conditions under which a vehicle may be operating in a GNSS and vehicle sensor integrated mode or with less than optimal number of satellites in view. However, estimating such a parameter that can be trusted with high degree of confidence can be challenging given the presence of various biases that can depend on the environment, vehicle, GNSS receiver, and sensors and methods used. Potential examples are time-of-day, vehicle heading, vehicle speed, GNSS receiver/sensor type, model, and configuration. However, developing a parameter similar to the RTCA Horizontal Uncertainty Level (HUL) for automotive applications is an important consideration.

While there are many other candidate receivers to be considered for a study of this nature, only two receiver types were used in this analysis. Analysis of more receiver types can be beneficial to identify the desired characteristics for a certain applications. A consideration could be achieving a desirable balance between accuracy and the sensitivity of the GNSS receivers, as increased sensitivity often produces higher solution availability at the cost of degrading accuracy.

Another area to investigate in related work is the benefits of using WAAS under the test conditions given in this paper. The general expectation is to see less bias in the position solution with WAAS as the ranging errors are likely to be smaller as a result of WAAS corrections. However, for automotive applications in particular, availability of WAAS signals to land vehicles need to be investigated.

CHAMINDA BASNYAKE is a senior research engineer at General Motors Global Research and Development and GNSS technology expert for GM OnStar. He leads GNSS-based vehicle navigation technology R&D efforts at GM and holds a Ph.D. in geomatics engineering from the University of Calgary.
March 1, 2011
On the Edge: Lost Graves, Trail of Tears

By Steven M. Di Naso, Vincent P. Gutowski, Harvey Henson, and Ryan Leonard

During the winter of 1838–39, the great Native American Cherokee Nation trekked across southern Illinois, in a forced removal by the U.S. government from their ancestral homeland in Tennessee. Harried, unequipped, and unsupported by their captors, thousands died on the Trail of Tears. Burial records were not kept, and burial locations remain lost to this day. Local history suggests that some Illinois settlers allowed the Cherokee to bury their dead on small plots of land adjacent to their own family cemeteries. One such plot, the Campground Presbyterian Church cemetery near Anna, Illinois, may contain unmarked Cherokee graves.

Researchers from Southern Illinois University and Eastern Illinois University used GPS to navigate and precisely map probes of a ground-penetrating radar (GPR) instrument in the cemetery. We monumented the geophysical survey grids using real-time kinematic (RTK) DGPS. Site topography was also mapped using GPS, as were the individual cemetery headstones. Adding geographic information systems (GIS) software to our mix to map cemetery headstone distribution and record headstone attributes (dates of death, names), we could determine chronological gaps within the cemetery that coincide with the probable emigration of the Cherokee.

GPR and electromagnetic conductivity produced contour plots of high-resolution magnetic gradient data. Small dipolar anomalies detected are typically related to disruptions within near-surface soil horizons and may correspond to locations of shallow graves: the lost final resting places of many Cherokee.

By close examination of the geophysical survey data and the anomalies produced from them, we were able to present plausible if not possible locations of several gravesites. However, at this time, and for obvious reasons, the actual location must remain secure and cannot be published.

The figure below shows a mosaic of amplitude depth slices at .30–.70 meter intervals from processed interpolated 250-MHz GPR profile data. White rectangles denote known graves. Most marked graves were imaged, although some were represented as more subtle anomalies on this display. Some possible unmarked graves were interpreted at UTM coordinates xxxx, yyyy.

The cemetery is within working distance of CORS station ILCB at Southern Illinois University. Two RTK GPS units communicating with the station via CDMA cellular radio used real-time differential corrections along a variable baseline length of approximately 28.5 kilometers, enabling mapping of the site at centimeter-accuracy resolution.

Survey data were edited, mapped, and analyzed with a GIS. Family genealogy polygons were generated using last names, to produce family distribution plots throughout the cemetery.

Manufacturers

The study, supported by a National Park Service grant with Southern Illinois University at Carbondale, used two Leica 1250 RTK GPS units, a Leica TC802 robotic total station, and Esri ArcGIS ArcInfo. Equipment was provided by Kara Company of Countryside, Illinois.

March 27, 2010