1. Part VI Precise Point Positioning Supported by Local Ionospheric Modeling GS894G

2. Presentation Outline  Research objectives  The Benefits of PPP  MPGPS™ Software  Methodology  Experiments and test results  Summary and Conclusions

3. Research Objectives  Develop precise point positioning (PPP) methodology and algorithms for surveying and navigation applications  Take advantage of the existing IGS products (precise orbits and clock corrections)  Provide local ionospheric maps (LIM) and tropospheric total zenith delays (TZD) from permanent GPS stations to support single-frequency PPP  Evaluate the quality of single and dual-frequency static and kinematic PPP in post processing

4. MPGPS™ - Multi Purpose GPS software  Developed at The Ohio State University (OSU)  Positioning Modules Long-range instantaneous (single epoch) RTK GPS Rapid-static Static Multi-station DGPS Precise point positioning (PPP)  Atmospheric Modules Ionosphere modeling and mapping Troposphere modeling  Positioning Solutions Single-baseline Multi-baseline (network) Stand-alone

5. The Benefits of PPP  Single receiver operation (low-cost)  Can be applied anywhere and anytime under different dynamics (remote areas, space applications, etc)  Not limited by baseline length as relative techniques  Independence on GPS reference stations  Can be applied for static and kinematic platforms

6. Methodology Error Sources in PPP Errors affecting the GPS observations Satellite orbit and clock corrections, (provided by IGS) accuracy < 5 cm and <0.1 ns (3 cm) Relativistic effects (included in the IGS orbits, except for the periodic relativity, which is modeled in MPGPS™) periodic relativity - up to 30 ns (~9 m) Receiver and satellite antenna phase center offsets (provided by IGS or NGS) satellites - up to 1.023 m, receiver up to - 0.2 m Satellite P1  P2 and P1-C1 differential code biases (DCBs) (provided by IGS) up to 2 ns (0.6 m), accuracy 0.1 ns (3 cm) Receiver DCB (GPS receiver calibration in MPGPS™ or IGS) up to 20 ns (6 m), accuracy 0.1 ns (3 cm) Phase wind-up up to 1 cycle (~0.2 m) of carrier phase data

7. Methodology Error Sources in PPP Errors affecting the GPS observations (cont.) Ionospheric refraction Ranges from 100 m Tropospheric refraction TZD = ~ 2.3 m (for standard atmosphere) Errors affecting the station coordinates Atmospheric loading correction: vertical < 1 cm Ocean loading corrections : horizontal < 2 cm, vertical < 5 cm Solid Earth tides correction: horizontal < 5 cm, vertical < 30 cm Earth Rotation Parameters, i.e., pole position and UT1-UTC (included in the IGS orbits)

8. Methodology Adjustment Model  All parameters in the mathematical model are considered pseudo-observations with a priori information (σ = 0 ÷  ) GLS – Generalized Least Squares adjustment - instantaneous parameters (e.g., ionospheric delays) - accumulated parameters (e.g., ambiguities)  Two groups of parameters (pseudo-observations) of interest:  Flexibility, easy implementation of: stochastic constraints fixed constraints weighted parameters filters

9. Methodology PPP Functional Model - undifferenced carrier phase and code observations (in meters) - geometric distance (satellite-receiver) - constant bias, where - integer carrier phase ambiguity and non-zero initial fractional phase - receiver and satellite clock offsets - tropospheric total zenith delay (TZD) - troposphere mapping function - slant ionospheric delay - receiver and satellite code and phase hardware delays - corresponding carrier wavelength - speed of light - random error or residual

10. Methodology PPP - Functional Model Unknowns  Permanent GPS station solution for local ionosphere maps (LIM) receiver clock tropospheric TZD slant ionospheric delays bias parameters (non-integer ambiguities and hardware delays)  Single-frequency positioning solution rover coordinates receiver clock bias parameters  Dual-frequency (ionosphere-free) positioning solution rover coordinates receiver clock tropospheric TZD bias parameters

11. Methodology Local Ionospheric Model (LIM) Supports PPP in case of single-frequency receiver  Single layer model (SLM) ionosphere approximation Slant ionospheric delays estimation from dual-frequency GPS data at the neighboring permanent stations Slant ionospheric delays conversion to vertical total electron content (VTEC) at ionosphere pierce points (IPPs) Kriging interpolation to produce LIM in a form of a grid using the calculated vertical TEC values at IPPs

12. SLM assumes that all free electrons are contained in a shell of infinitesimal thickness at altitude H z - zenith angle H - SLM height R - Earth radius SLM – Single Layer Model Methodology Local Ionospheric Model (LIM) 1 TECU = 10 16 ellectron/m 2 = 0.162 m delay/advance

13. Methodology PPP Models  Three PPP MPGPS™ models were tested in post processing mode Static PPP – dual-frequency (ionosphere-free) Static PPP – single-frequency supported by LIM Kinematic PPP – single-frequency supported by LIM  Adaptive filter for kinematic solution Follows the dynamic variations of the system estimates and stochastic models Propagates the coordinate and ionosphere residuals together with their stochastic characteristics Forward and backward filters

14. Experiments and test results Data Source  Four stations, IGS/EPN (EUREF permanent network) Three stations were used to derive LIM and TZD (BOR1, GOPE, KRAW) One station was selected as a rover (WROC)  Two three-hour sessions 01 - 04 UTC (nighttime - lowest TEC level) 13 - 17 UTC (daytime - highest TEC level)  30-second sampling rate (i.e., 360 epochs per session)  Phase-smoothed pseudoranges  Distances between permanent stations ~330 km (average)  Distances to the rover ~130–230 km

15. Experiments and test results Test Area Map Czech Republic Poland - LIM/TZD - PPP (rover) N ____________________________________________________ Rover

16. Experiments and test results Satellite Geometry - Station WROC 01-04 UTC nighttime 4-7 satellites 13-17 UTC daytime 4-5 satellites Poor satellite geometry, high GDOP - usually over 5 A short period with very poor geometry occurred in both sessions ____________________________________________________ GDOP = ~80 GDOP =~1000

17. Experiments and test results Example LIM-derived ionospheric delays Station WROC (rover) 01-04 UTC nighttime lowest TEC 13-17 UTC daytime highest TEC _______________________________________________________

18. Experiments and test results Static PPP Analysis – Station WROC Nighttime, dual-frequency (ionosphere-free LC) Daytime, dual-frequency (ionosphere-free LC) Nighttime, single-frequency supported by LIM Daytime, single-frequency supported by LIM ____________________________________________________

19. Experiments and test results Static PPP Analysis – Station WROC  Ionosphere-free solution Horizontal - sub-decimeter-level position accuracy Vertical - decimeter-level Nighttime - convergence after 40 minutes Daytime - convergence after 25 minutes  Single-frequency solution supported by LIM Good agreement with its ionosphere-free counterpart Similar accuracies and convergence times LIM proved to be efficient in removing the ionospheric delays

20. Experiments and test results Kinematic PPP Analysis – Station WROC 01-04 UTC (nighttime) 13-17 UTC (daytime) Unfiltered single- frequency supported by LIM Filtered single- frequency supported by LIM ____________________________________________________

21.  The unfiltered solutions are very noisy in both sessions  In the filtered solution the large residuals were smoothed out after a few iterations (3-4)  The filtered kinematic solutions show similar accuracies as obtained in the static case  Sub-decimeter horizontal and decimeter-level vertical position accuracy was achieved Experiments and test results Kinematic PPP Analysis – Station WROC

22. Summary and Conclusions  The sequential GLS adjustment was successfully applied in the PPP algorithm  Single-frequency static and kinematic PPP solutions, supported by LIM, are comparable to the ionosphere-free solutions  The results prove a good quality of the obtained LIM  The effectiveness of the adaptive filter was presented in the kinematic mode, even under unfavorable satellite geometry  This algorithm may be applied in geodetic applications, where sub-decimeter level accuracy is required