Timing Augmented GPS Update

1. Timing Augmented GPS Update Eddie Byrne, Symmetricom January 23, 2008

2. Background • AFIT simulation results indicated that significant improvement in GPS positioning accuracy can be achieved by incorporating precise GPS receiver clock offset information into the GPS position solution. • We have conducted experiments to verify and explore the improvements in GPS positioning accuracy with timing augmented GPS.

3. Briefing Overview • Problem statement • Test setup • How we measure GPS receiver clock offset • GPS receiver selection • Data processing and analysis tools • Results • Performance improvement from timing augmented GPS • Comparison of Novatel and Trimble receivers • Future Work • More receivers to evaluate • Integration Plan

4. Single Point Solution Solver x y z t ~ ~ Single Point Solution Solver x y z ~ ~ Problem Statement • Investigate the benefit of augmenting GPS single point position solutions with external clock bias information. • Conventional Single Point Solution: • Timing Augmented Single Point Solution Pseudorange, Ephemeris From N Satellites Pseudorange, Ephemeris From N Satellites Clock Bias

5. Characteristics of GPS Solution Types • A single point solution uses observations from a single receiver at a single epoch to solve for (x,y,z,t) at that epoch. • Accuracy is limited by the measurement noise on the code phase pseudorange measurements. • Has the advantage of needing only a single GPS receiver. Its accuracy may be improved by: • Averaging multiple solutions over time • Applying methods to reduce the noise on the pseudorange measurement (for example, filtering the dual frequency ionospheric delay measurement) • Applying precise knowledge of GPS receiver’s clock offset • Timing augmented GPS allows for a 3D position solution with observations for only 3 satellites • Carrier phase approaches achieve better positioning accuracy but require a more complex system: • There are one or more ‘base’ GPS receivers at known locations transmitting correction data to ‘rover’ GPS receiver(s). • Requires GPS receiver(s) at base station(s) at known locations • Requires data link between the receivers • Method is effective over a limited baseline

6. Single Point Solution Solver (C++ Executable) x y z t ~ ~ ~ ~ Test Setup • Method for generating single point position solutions with timing augmented GPS: • TWSTT measurement of offset between UTC(USNO) and UTC(TSC) • GPS receiver running with external frequency reference from UTC(TSC) • C++ Single Point Solution Solver, MATLAB for visualization and analysis UTC(USNO) TWSTT Measurement of UTC(USNO) – UTC(TSC) ftp Calibration Constant Clock Bias Single Point Solution Solver (C++ Executable) x y z UTC(UTC) Pseudorange, Ephemeris From N Satellites GPS Receiver 10 MHz Log Files

7. Performance Metrics • Timing augmented GPS performance is evaluated based on: • Position bias: difference between average position from a set of single point position solutions and the reference position. • Reference position calculated using SCOUT (Scripps Coordinate Update Tool), which uses GAMIT post processing engine to implement a differential GPS solution. • Statistics for the magnitude of the error vector. Find the magnitude of the error vector for each single point solution. Calculate the mean and standard deviation of the sequence of error vector magnitudes. • Statistics for the height error. • Note the ordering of magnitude operator and mean operator: • For position bias, take average of positions first, then calculate magnitude • For error vector magnitude stats, calculate magnitude of vectors first, then calculate average and standard deviation

8. GPS Receiver Selection • Dual frequency geodetic quality GPS receivers, preferably with external frequency input • Novatel OEM4-G2, Novatel OEM5 • Trimble BD950 • Magellan ZXW-Sensor (Thales ZXW Eurocard) • Navcom NCT-2030M (NCT-2100d engine) • Status:Novatel OEM4 and Trimble BD950 have been integrated into our test setup. Novatel OEM5, Magellan ZXW-Sensor, and Navcom NCT-2030M are in house and need to be integrated.

9. Timing Augmented GPS Performance Results • The GPS receiver clock bias that we will inject for timing augmented GPS is much cleaner than the clock bias estimate from the conventional (x,y,z,t) single point position solution. • (Green) Result of (x,y,z,t) single point position solution • (Blue) Measured (via TWSTT) UTC(USNO) – UTC(TSC) GPS Receiver Clock Offset vs. Time Clock Offset, 20 ns/div Time, 10 hours/div

10. Timing Augmented GPS Performance Results • The magnitude of the position error is smaller for the timing augmented GPS solution. The height error shows an even larger improvement (distributions and numbers to follow). • (Green) Result of (x,y,z,t) single point position solution • (Blue) Result of (x,y,z) timing augmented single point position solution Position and Height Errors vs. Time Position Error (10 m/div) Height Error (20 m/div) Time (10 hours/div)

11. Timing Augmented GPS Performance Results • Mean and standard deviation of position error magnitude are significantly reduced with timing augmented GPS (mean is reduced by about 40%, std is reduced by about 2X) Position Error Magnitude Distributions Observations Observations Position Error Magnitude (5 m/div)

12. Timing Augmented GPS Performance Results • Height error sigma is reduced by about 4X (data set dependent) with clock bias injection. Height Error Distributions Observations Observations Height Error (10 m/div)

13. Novatel OEM4 Performance Data Summary • Novatel OEM4 receiver data spanning 37 days (split by calendar month in the table below) yields the following performance metrics: • Position bias increases by about 5 cm with timing augmented GPS (see calibration concerns in later slide) • Mean position error magnitude decreases by approximately 40% • Standard deviation of position error magnitude decreases by a factor of 2 • Standard deviation of height error decreases by a factor between 3.5 and 4.5

14. Inject Imperfect Measured Clock Offset • Previous results used ‘perfect’ measured clock offset for clock bias injection • How is performance affected if clock offset measurement suffers from: • Bias • Noise (AWGN)

15. Effect of bias in injected clock offset • Adding a constant bias to the injected clock offset results in a change in the average position. Position Bias vs. Clock Offset Bias Position Bias (0.5 m/div) Bias Applied to Injected Clock Offset (1 ns/div)

16. Effect of noise in injected clock offset • Adding white Gaussian noise to the injected clock offset increases the variation in the magnitude of the position error. σ Position Error magnitude vs. σ Injected Clock Offset Noise σ Position Error Magnitude (0.2 m/div) σ Injected Clock Offset AWGN (1 ns/div)

17. Calibration Challenges • We need to calibrate the offset from the GPS receiver’s clock (based on UTC-TSC) and UTC-USNO. Components of this offset are: • UTC-USNO – UTC-TSC: This is currently measured by a SATRE TWSTT modem. • Delay in distribution network from UTC-TSC to GPS receiver. This delay (cabling and distribution amps) is static and easily measured. • Assuming TWSTT has zero bias over the time intervals of interest, the calibration offset should be constant over time • However, results indicate a time varying relationship between the calibration offset and the bias in the position solution. See next slide. • Does this stem from unmodeled (or unmeasured) changes the UTC-USNO to UTC-TSC offset, or are we up against the performance limit of a single autonomous GPS receiver?

18. Calibration Challenges • One calibration approach is to choose clock offset bias that minimizes the position bias. But we see a data dependent (or time varying) component in this relationship. • If you choose a single clock offset, the position bias can vary by about 0.25m over time. (imaginary vertical line on plot below) • If you repeat the calibration process over different subsets of the overall data set, the resulting clock bias varies by about 1 ns. Position Bias vs. Bias in Clock Offset Position Bias (0.2 m/div) Bias in Injected Clock Offset (1 ns/div)

19. Novatel, Trimble Receiver Comparison • Previously presented results are from data collected with a Novatel OEM4 GPS receiver. We want to evaluate other receivers and choose the one with the best performance. • Testing the Trimble BD950 required hardware and software changes to our test stup. • Hardware • Use ‘same’ antenna as for Novatel OEM4 (take a different output jack on GPS antenna splitter) • Use ‘same’ external frequency reference (a different output jack on a 10 MHz distribution amp driven by UTC(TSC)) • Software • Write new C++ executable to log data packets from GPS receiver’s COM port to a (binary) file • Add Trimble RT17 data format parsing capability to existing GPS single point solution software

20. Novatel, Trimble Receiver Comparison • Compare the position and height error behavior of the Novatel and Trimble receivers. These are conventional single point solutions. • Novatel OEM4 (green), Trimble BD950 (blue) • Similar error magnitudes between the two receivers • Trimble BD950 receiver shows more high frequency noise Position and Height Errors vs. Time Position Error (1 m/div) Height Error (5 m/div) Time (0.05 hours / div)

21. Novatel, Trimble Receiver Comparison • Transient events: This plot shows a ~ 10 minute period where the Trimble’s position error became large (> 10m, peaking at 20m) while the Novatel receiver’s position error remained small (< 5m). • Novatel OEM4 (green), Trimble BD950 (blue) Position and Height Errors vs. Time Position Error (5 m/div) Height Error (10 m/div) Time (0.1 hours / div)

22. Novatel, Trimble Receiver Comparison • Transient events: This plot shows an instance where the Novatel position error was significantly larger than the Trimble’s position error. The Trimble transients (previous slide) occur more frequently than the Novatel transients. Position and Height Errors vs. Time Position Error (5 m/div) Height Error (5 m/div) Time (0.01 hours / div)

23. Novatel, Trimble Performance Comparison Summary • Position error (not bias) performance is very similar between Novatel OEM4 and Trimble BD-950 receivers, for both conventional and timing augmented single point solutions. • Position bias is larger for the Trimble BD950 than the Novatel OEM4 for the conventional single point solution case.

24. Integration into Symmetricom hardware platform • Current implementation of timing augmented GPS is a ‘laboratory’ setup in that it: • Uses the SATRA TWSTT modem to measure UTC(USNO) – UTC(TSC), with updates every 4 hours • Uses post processing of GPS receiver log files to calculate position solutions • We plan to integrate the timing augmented GPS functionality into the timescale portion of our Symmetricom ATS 6XXX products by: • Using the on board Rb oscillator as the GPS receiver’s external frequency reference • Using the existing KAS2 (Kalman filter) algorithm to estimate the GPS receiver’s clock offset from UTC(USNO) • Adding a software application to implement the timing augmented single point position solution • See next slide

25. Integration into Symmetricom hardware platform 10 MHz GPS Receiver Rb Oscillator 10 MHz PPS COM Port Frequency Steering Command GPS Data Parser Existing Software Application Running On x86 KAS2 Kalman Filter GPS Rx Clk Offset Meas. Existing Hardware Configuration (with Novatel receiver) Estimated Clock Offset Pseudorange, Ephemeris Data Timing Augmented Single Point Solution Solver New Software Application Timing Augmented Position Solution

26. Summary of Results • Timing augmented GPS improves performance of single point position solutions • Mean(3D Error Magnitude) reduced by about 40% • σ(3D Error Magnitude) reduced by about 2X • σ(height Error) reduced by 3.5 to 4.5X • Effect on position bias (average 3D position vs. actual position) is mixed: • increase by ~0.5 cm for Novatel OEM4 • improvement for Trimble BD950 • needs further investigation

27. Future Work • Integrate timing augmented GPS into Symmetricom hardware platform • Evaluate calibration strategies (further study of effect of injected clock offset on position bias) • Evaluation of Magellan and NavCom GPS receivers • Resolve problem with integration of Klobuchar ionoshperic delay model (to evaluate timing augmented GPS performance with single frequency receiver)