Ionospheric Parameter Estimation Using GPS

1. Ionospheric Parameter Estimation Using GPS Attila Komjathy, Lawrence Sparks and Anthony J. Mannucci Jet Propulsion Laboratory California Institute of Technology M/S 238-600 4800 Oak Grove Drive Pasadena CA 91109 Email: Attila.Komjathy@jpl.nasa.gov

2. This lecture covers: Why? Topics IONOSPHERE ESTIMATION USING GPS Using GPS signals to measure the ionosphere Understand purpose and operation of reference stations Understand how ionospheric corrections are formed Forming ionospheric measurements from GPS observables Data quality and editing Calibration of GPS data

3. Introduction • Currently the largest error sources in GPS positioning is that of ionospheric refraction causing signal propagation delays L What can be done? • If we have a dual-frequency GPS receiver, then the ionospheric effect can be almost totally accounted for J • What if we have a single-frequency receiver? • We can ignore the effect and live with the consequences M • We can minimize it using various processing techniques J • We can model it using empirical ionospheric models such as the GPS single-frequency Broadcast model, IRI2000 model, PIM, etc. J • We can measure it using nearby dual-frequency receiver observations (pseudorange only, carrier-phase only, pseudorange/carrier-phase combined) and apply it as a correction to the single-frequency observations. J • What is the error in positioning accuracy caused by the ionosphere and how can we reduce it?

4. IRI-95 profile Illustration for GPS and Ionosphere

5. Broadcast Ionospheric Model

6. Broadcast Model: Seasonal Variation

7. Broadcast Model: Solar Cycle Dependence

8. International Reference Ionosphere

9. IRI Model: Seasonal Dependence

10. The Accuracy of Broadcast Model

11. GPS Observation Equations GPS pseudorange observation equation: GPS carrier phase observation equation: Range, clock, ambiguity, ionosphere, troposphere, satellite bias, receiver bias, multipath, noise

12. Generating GPS Ionospheric Observables phase-leveled ionospheric observable precise but ambiguous less precise but unambiguous

13. GPS Ionospheric Measurements Code measurement Phase measurement

14. Leveling the Phase Using Code Measurements The level is computed by averaging PI-LI using an elevation-dependent weighting. Higher elevation data is weighted more heavily. (The weighting is based on historical Turborogue PI-LI noise/ multipath data giving a historical PI-LI scatter of th(E) where E is elevation.) The level is computed as: where E is the elevation angle. The uncertainty on the level is computed in a rather rough way using a combination of th(E) and observed pseudorange scatter: The TEC sigma in the JPL Processed Data files are the level uncertainty.

15. Supertruth Data for Three Threads

16. The Impact of Arc Lengths

17. Major Error Source: The Code Multipath

18. Global Ionospheric Mapping: GIM For three shells, our model is For single shell, our model is where is the slant TEC; is the thin shell mapping function for shell 1, etc; is the horizontal basis function (C2, TRIN, etc); are the basis function coefficients solved for in the filter, indexed by horizontal (i) and vertical (1,2,3 for three shells) indices; are the satellite and receiver instrumental biases.

19. WAAS Ionospheric Models WAASplanar fit ionospheric model is Pseudo-IGP approach: IPP treated as if it were collocated with IGP where are the planar fit parameters, are the distances from the IGP to the IPP in the eastern and northern directions, respectively. WAAS-type quadratic fit ionospheric model is are the additional planar fit parameters describing quadratic and cross terms.

20. All-Site GPS Data Processing Algorithm Bias Fixing Algorithm using all available GPS stations worldwide: GIM TEC prediction Biased TEC observation GIM satellite bias estimate is the biased phase-levelled ionospheric observable is the thin shell mapping function for shell 1, etc; is the horizontal basis function (C2, TRIN, etc); are the basis function coefficients solved for in the filter, indexed by horizontal (i) and vertical (1,2,3 for three shells) indices; are the satellite and receiver instrumental biases.

21. Single Vs. Three-Shell Model Limitations The concept of multi-shell GIM: Single-shell 2-D maps Does not capture small-scale variations in the ionosphere Multi-shell is more realistic and accurate than the single-shell approximation

22. Receiver Bias Estimation Precision

23. Slant TEC Bias-Fixing Method Estimated bias time series: errors caused by GIM, multipath, noise, sub-daily bias drift Bias-removed slant TEC Location of station

24. Coverage of Daily IGS Network and Regional Networks (10 degree elevation mask; 450 km shell height)

25. Example for Single Shell Model Results An Example of the Diurnal Variation of TEC for a Geomagnetically Quiet Day Components in TECU, TECU/hour, TECU/km

26. JPL’s GIM Multi-Shell Model

27. TOPEX Validation for 12 Oct 2001, Track 10

28. Recent GIM Validation Using Jason-1

29. Global Point Plots

30. Point Plot Differences

31. October 30, 2003 2nd Interplanetary Coronal Mass Ejection DST -390 nT at 2315 UT on October 30

32. November 20, 2003 Storm Details are difficult to interpret 5-day average of quiet ionosphere removed: structures are easier to detect Quiet ionosphere following the storm

33. An Example for Repeatibility of Estimated Satellite Biases: Multi-Shell versus Single-Shell • Multi-shell significantly improves repeatibility in daily bias estimates • We compare bias averages over 7–10 days • Scatter (std. dev.) over a week improved by factor of 2 to 4 • Satellite biases • 7-day scatter improved from 2–6 cm to 8–24 mm • This may indicate reduction of systematic errors in bias estimation 6 cm 0 cm

34. An Example for Repeatibility in Estimated Receiver Biases:Multi-Shell versus Single-Shell 0.6 m • Receiver biases • 7-day scatter improved from 8–64 cm to 0.5–19 cm • Larger scatter due to stations in low latitude sector • Systematic error? • Examine long time-series of biases • Look for shifts in ionospheric delay level for all biases simultaneously 0 m

35. Comparison of Single and Multi-Shell Results for ENG1 Postfit Residuals ENG1 = English Turn, LA Improvement at low elevation angles Prediction Residuals

36. Comparison of Single and Multi-Shell Results for MBWW Postfit Residuals Improvement at low elevation angles MBWW = Medicine Bow, WY Prediction Residuals

37. Low-Earth Orbiter GPS COSMICIonospheric Weather Constellation Electron Density Profile COSMIC coverage: 2500 profiles/day Six-satellite COSMIC constellation Launched April 14, 2006

39. State and covariance Analysis State and covariance Forecast Adjustment Of Parameters Kalman Filter 4DVAR Global Assimilative Ionospheric Model Data Assimilation Process Driving Forces Physics Model Mapping State To Measurements Innovation Vector • Kalman Filter • Recursive Filtering • Covariance estimation and state correction Optimal interpolation Band-Limited Kalman filter • 4-Dimensional Variational Approach • Minimization of cost function by estimating driving parameters • Non-linear least-square minimization • Adjoint method to efficiently compute the gradient of cost function • Parameterization of model “drivers”

40. Input Data Types • Ground GPS Data (Absolute TEC) • >200 5-min. to Hourly Global GPS Ground Stations • Assimilate >300,000 TEC points per day (@ 5 min rate) per day • Space GPS Data (Absolute or Relative TEC) • CHAMP (@ 440 km) • SAC-C (@ 700 km) • IOX (@ 800 km) • GRACE (@ 350 km) • Topex/Poseidon (@1330 km) (Upward looking only) • Jason 1 (@1330 km) (Upward looking only) • C/NOFS & COSMIC constellation • UV airglow data (135.6 nm radiance) • LORAAS on ARGOS, GUVI on TIMED • SSUSI/SSULI on DMSP • TIP on COSMIC • Other Data Types • TEC from TOPEX/JASON Altimeters • Ionosonde bottomside profiles • DMSP in situ • CHAMP in situ • GRACE cross-links

41. Kalman Assimilation Runs for June 26, 2006 • Three runs: • GAIM Climate (no data) • Ground GPS TEC (200 sites) • Ground + COSMIC links (upward & occultation) • Resolution: 2.5 deg. Lat. 10 deg. Lon. 40 km Alt. • No. of grid cells: 100,000 • Sparse Kalman filter: • Update & propagate covariance • Truncate off-diagonal covariance that is beyond physical correlation lengths

42. GAIM Assimilation Using Ground and COSMIC Data

43. GAIM Validation Using Jason-2 Vertical TEC Ground-data only Ground and space data

44. GAIM vs. Abel HmF2 Comparison

45. GAIM Driven By Ground GPS Onlyversus JASON VTEC June – Nov. 2004: 137 days

46. COSMIC Demo 2007 Global ground network data: 5-minute and 1-hour latency COSMIC data: 120+ minutes latency GAIM 3-D global electron density grids 15-minute cadence Start of orbit End of orbit; data downloaded Limb TEC available Data received at CDAAC Profiles (Abel) available CDAAC: COSMIC Data Analysis and Archiving Center at UCAR

47. What You Have Learned Ionosphere is the largest error source in GPS positioning Empirical models can be used to mitigate effects Dual-frequency GPS data can be used to solve for the ionospheric effect Error sources affecting GPS-based ionospheric estimation: arc length,leveling, biases, multipath, noise, etc. Global Ionospheric Mapping techniques: single vs multi-shell approaches: ionospheric delay and biases estimation Validation of maps, point plots, movies, etc.