Part Va Centimeter-Level Instantaneous Long-Range RTK: Methodology, Algorithms and Application

1. Part Va Centimeter-Level Instantaneous Long-Range RTK: Methodology, Algorithms and Application GS894G

2. Presentation outline • Research Objectives • Methodology • Experiments and Test Results • Newest developments: algorithmic updates • Summary and Outlook

3. Research objectives • Performance analysis of ionosphere modeling techniques, derived from GPS permanent tracking network data • Local • Regional • Global ionospheric models • Feasibility test for ambiguity resolution (AR) in long-range RTK applications • Instantaneous • OTF (on-the-fly) • Study the impact of the model’s accuracy on the positioning results • Study of the impact of the ionospheric conditions on the positioning results

4. Methodology • Compute the reference “truth” ionospheric corrections • Compute model-based corrections • Compare against the reference “truth” • Use model-based corrections to fix ambiguities • On-the-fly (OTF) • Instantaneously • Perform long-range kinematic positioning using model-based corrections interpolated to the user location • Compare AR success ratio • Compare positioning accuracy • Derive performance metrics for long-range RTK GPS • Quiet ionosphere • Active ionosphere

5. Methodology: the ionospheric models • MPGPS-NR — Network (NR) dual-frequency carrier phase-based model, decomposed from DD ionospheric delays • single layer • local – uses reference stations within 100-200 km from the rover • ICON — Absolute model based on undifferenced dual-frequency ambiguous carrier phase data • single layer • regional (~340 CORS stations) • MAGIC — Tomographic model using pseudorange-leveled L1-L2 phase data • 3D • regional (~150 CORS and IGS stations) • IGS GIM — International GPS Service (IGS) global ionospheric map (GIM) • single layer • global (~200 stations)

6. Methodology:ICON and MAGIC models (NGS) • Derived for the continental United States • Provide the ionospheric information for all GPS satellites with a three-day delay • Both models are prototypes • Available to the general public at: http://www.noaanews.noaa.gov/stories2004/s2333.htm • Smith, D.A. (2004), Computing unambiguous TEC and ionospheric delays using only carrier phase data from NOAA´s CORS network, Proceedings of IEEE PLANS 2004, April 26-29, Monterey, California, pp. 527-537. • Spencer, P.S.J., Robertson, D.S. and Mader, G.L. (2004), Ionospheric data assimilation methods for geodetic applications, Proceedings of IEEE PLANS 2004, Monterey, California, April 26-29, 2004, pp. 510-517.

7. Methodology: MPGPS™ - Multi Purpose GPS Processing software (OSU) • Modules • Long-range instantaneous and OTF RTK • Precise point positioning (PPP) • Multi-station DGPS • Local ionosphere modeling and mapping • Troposphere modeling • Operational modes: static, rapid-static, kinematic, instantaneous (single and multi-baseline) The MPGPS™ software was used to derive the “true” DD ionospheric delays (MPGPS-L4) and the network RTK corrections (MPGPS-NR)

8. Mathematical model: network • Sequential generalized least squares model • DD ionosphere estimated from L4 combination every epoch after the ambiguities are fixed • Decomposed to undifferenced iono • TZD estimated every 2 hours per station • Stochastic constraints on tropo and iono • Reference coordinates fixed • Integer ambiguity resolution • LAMBDA method • W-ratio to verify integer selection - receiver indexes - satellite indexes - DD phase observation on frequency n (n=1,2) - DD code observation on frequency n - DD geometric distance - Total zenith delay (TZD) - troposphere mapping function - DD ionospheric delay - GPS frequencies on L1 and L2 - GPS frequency wavelengths on L1 and L2 - carrier phase ambiguities

9. Mathematical model: rover positioning • Mathematical model used for rover positioning is the same as for the network, but • Ionosphere and troposphere are compensated from external models • Stochastic constraints are used on external corrections • LAMBDA AR method and W-ratio • Instantaneous (single-epoch) AR and rover positioning supported by external iono, or • Initial OTF AR using external ionosphere • Processing continues in the instantaneous mode • Iono is predicted from the previous epoch • May continue OTF for the entire rover positioning period • Rover positioning: single- or multi-baseline solution

10. Experiments - test data and model Ohio CORS, August 31, 2003 • 24-h data set was processed in 12 sessions of 2-h • 30-s sampling rate • different reference satellite for each session • varying ionospheric TEC levels • max Kp index = 2o • varying GPS constellation • KNTN CORS station was selected as rover • Known ITRF coordinates from a 24-hour BERNESE solution • October 29, 2003 – significant ionospheric storm

11. 108km KNTN 109km 124km 104km Experiments - test area maps Network map Baseline map 98km LSBN KNTN (rover) 63km The rover station does not contribute to the estimation of the atmospheric corrections The network provides atmospheric corrections to the rover (KNTN)

12. worst best ExperimentsDD ionospheric residuals with respect to the reference “truth”24 h, KNTN-DEFI (~100 km)

13. Residual statistics Ionospheric delay residual statistics 5 and 10 cm cut-off limits for 24 h

14. Statistics-Mean and STD of DD iono residuals wrt the reference “truth”2-h windows

15. Instantaneous RTK positioning analysis KNTN-SIDN ~60 km0 cm constraint (1 sigma) for the ionospheric corrections 0 cm constraint “worst” iono accuracy (MPGPS-NR) 0 cm constraint “best” iono accuracy (MPGPS-NR)

16. Instantaneous RTK positioning analysis KNTN-SIDN ~60 km5 cm constraint (1 sigma) for the ionospheric corrections 5 cm constraint “worst” iono accuracy (MPGPS-NR) 5 cm constraint “best” iono accuracy (MPGPS-NR)

17. Instantaneous RTK positioning analysis KNTN-DEFI ~100 km1 and 5 cm constraint for the ionospheric corrections 5 cm constraint “worst” iono accuracy (MPGPS-NR) 1 cm constraint “best” iono accuracy (MPGPS-NR)

18. OTF Ambiguity Resolution: number of epochs needed to resolve the integers: ~100 km baseline; the worst window • * means that the correct ambiguity was found at the first epoch, however the method requires a minimum of three epochs to validate the choice • Shown are different solutions with varying stochastic constraints applied to the externally provided ionosphere in the rover positioning solution • Processing was restarted every 10 minutes, continued for 100 epochs

19. OTF Ambiguity Resolution: number of epochs needed to resolve the integers: ~100 km baseline; the best window • * means that the correct ambiguity was found at the first epoch, however the method requires a minimum of three epochs to validate the choice • Shown are different solutions with varying stochastic constraints applied to the externally provided ionosphere in the rover positioning solution • Processing was restarted every 10 minutes, continued for 100 epochs

20. OTF Ambiguity Resolution: summary • Different number of epochs needed to resolve the integers as a function of: • Ionospheric model type • Level of stochastic constraints applied to the external ionosphere • Ionospheric activity and baseline length (to some extent) • Level of local details recovered by the model • MPGPS-NR needs 7.4 (6.5)* epochs on average during the higher ionospheric variability and 3 (3) epochs during the period of lowest ionospheric variability, using 5 cm constraints on ionosphere; similarly for 1 cm constraint • MAGIC requires 12 (10) and 4 (3) epochs, respectively • ICON and GIM need more epochs • Stochastic constraints of 10 cm for MAGIC and GIM and 20 cm for ICON • 8 (18) and 4 (3) for MAGIC • 24 (68) and 22 (11) for ICON • 15 (25) and 18 (22) for GIM * The number in parenthesis correspond to the longer baseline

21. Position residuals with respect to the known reference coordinates: summary statistics, MPGPS-NR MPGPS-NR model

22. Algorithmic updates: ICON and MAGIC • ICON solution can be fitted to MAGIC solution to provide the best of both methods: correct biases from MAGIC and ionospheric details from ICON • MAGIC solution can use carrier phase fit after the biases have been fixed • L2-L1 data are fitted to the estimated MAGIC values, and the constant mean difference (bias) along the satellite arc is removed • Result: high accuracy ionospheric corrections matching the DD reference “truth” with 5-10 cm level of accuracy >90% of the time • Both models are, therefore, suitable for instantaneous and/or fast OTF AR

23. ICON and MAGIC: original vs. modified DD ionosphere [meters] Original MAGIC solution ~100 km baseline Original ICON solution: ~100 km baseline Modified ICON solution: ~100 km baseline Modified MAGIC solution ~100 km baseline

24. Modified MAGIC solution: rover data (KNTN) fit included(Applicable to high-accuracy analysis in post-processing) m Modified MAGIC solution ~60 km baseline m Modified MAGIC solution ~100 km baseline

25. Modified ICON and MAGIC: summary statistics * in post-processing

26. Reference network and test baseline: October 29, 2003 – severe ionospheric storm Baseline map Network map ~120 km base-rover separation ~200 km reference station separation

27. Quality of ionospheric corrections during highly disturbed ionospheric conditions (storm): baseline COLB-LEBA, 121 km MPGPS-NR solution October 29, 2003

28. Summary statistics: active vs. quiet ionosphere “True” DDionospheric delays(absolute values) within selected ranges, 24 h DD ionospheric delayresidualswith respect to the reference “truth”within selected ranges, 24 h Earlier findings show that 10-cm or better accuracy should assure instantaneous AR

29. Ambiguity resolution success ratio as a function of ionospheric activity: instantaneous solution Success ratio is defined as the ratio of the number of correctly resolved epochs to the number of all processed epochs 1. During the quiet day, the success ratio was over 94% 2. During the disturbed period, as expected, it dropped dramatically to 31%

30. OTF ambiguity resolution statistics: October 29, 2003 Number of epochs required to fix the integers with different levels of constraints on external ionosphere Note: Quiet day data were processed with 10 cm stochastic constraints imposed on the network-derived DD ionospheric corrections. All the ambiguities (in each of the 24 shifted solutions) were solved using the required minimum of three epochs

31. Summary and Outlook • Different ionospheric models were analyzed • Varying TEC levels, benign and severe ionosphericconditions • Varying GPS constellation • 10 cm or better fit to the reference “truth” assures instantaneous AR and high-accuracy cm-level positioning • Over 90% success ratio for benign ionosphere conditions • 31% success ratio for severe storm • OTF AR time-to-fix vary with the model type, stochastic constraints and ionospheric activity • Stochastic constraints depend on the ionospheric activity level • Needs significant relaxation under severe storms (from 5-10 to 40 cm) • MPGPS-NR, modified MAGIC and ICON – almost equivalent quality • MPGPS provides high accuracy kinematic positioning with all ionospheric models presented • Algorithmic modification towards real-time applications