From dual- to triple-frequency PPP: method, problems and application in California

1. From dual- to triple-frequency PPP: method, problems and application in California Jianghui Geng, Yehuda Bock Scripps Institution of Oceanography University of California San Diego

2. Precise point positioning ambiguity resolution (PPP-AR) • PPP-AR has been developed since 2008 • “Uncalibrated phase delay” by GFZ/Nottingham/Wuhan • “Integer clock” or “decoupled clock model” by CNES/NRCan • Single receiver ambiguity resolution by JPL • etc. Clocks Atmospheric corrections Ambiguities Equipment biases, etc. GIPSY 6.0 by JPL CNES/NRCan GFZ/Nottingham/Wuhan Augmented PPP-RTK

3. Real-time PPP-AR system in Scripps for earthquake early warning Predicted orbits from IGS ITRF positions & metadata (SOPAC) Real-Time Data, Various Servers Generate Satellite Clocks Generate Fractional-Cycle Biases CRTN Server Operational Generate California-Based Troposphere and Ionosphere Model RTCM3 75 stations used as reference stations which are located >200 km away from western US coast PPP client with accelerometers RTK User Other Users

4. Typical performance: fixed solutions for 25 days

5. Brawley swarm on Aug 26 2012 • PBO and SCIGN real-time GPS stations in the vicinity of Brawley Swarm of August 26, 2012, operated at 1 Hz during event • WLA (Wildlife Liquefaction Array) is accelerometer run by Jamie Steidl (UCSB), continuously at 200 Hz, ~ 5 km from P506 • 4 events (GPS time) • 19:20:15 (M4.6) • 19:31:35 (M5.4) • 20:58:05 (M5.5) • 23:33:25 (M4.6) • Collocation of GPS/Accelerometers • P506/WLA (8km) • P494/WES (35km)

6. Example: GPS waveforms in real time for Event 3 M5.5

7. Tightly-coupled GPS/Accelerometers based on PPP-AR • Introduce raw accelerometer measurements into GPS data processing • Loosely-coupled GPS/Accelerometers GPS measurements Tightlycoupled Displacementsandvelocities Accelerometer measurements GPS measurements GPS-derived displacements GPSprocess Looselycoupled Displacementsandvelocities Accelerometer measurements

8. Improvement of ambiguity resolution performance

9. Brawley Seismic Swarm: Comparison of seismogeodetic and broadband seismometer velocity waveforms P494/WES (80 m apart), 35 km from hypocenter Mw 4.6 Mw 5.4 Mw 5.5 Mw 4.6

10. Solutions in dual-frequency PPP for fast convergence • Partial solution: rapid re-convergences/Cycle-slip repair • Unsatisfactory solution: precise ionosphere products, e.g. dense augmentation network, ionosphere tomography, etc.

11. Triple-frequency PPP • Enable rapid ambiguity resolution for triple-frequency PPP • Triple-frequency means various combinations of frequencies for long wave-length observable • Resolve ambiguities for long-wavelength observable • Using the resolved long-wavelength observable to constrain the ambiguity resolution of short-wavelength observable

12. A method for triple-frequency PPP • Basic carrier-phase equation: • Step 1: resolve extra-wide-lane ambiguity with a wavelength of 5.8m • Step 2: resolve wide-lane ambiguity with a wavelength of 3.4m, but the noise is amplified by 100 times. • Wide-lane ambiguity resolution can still be very efficient • Step 3: with ambiguity-fixed ionosphere-free (AFIF) wide-lane carrier-phase, resolve narrow-lane ambiguity (0.1m wavelength) AFIF observations

13. Data simulation • GSS8000 hardware simulator by Spirent • Septentrio receiver • Troposphere delay: RTCA06 • Ionosphere delay: Klobuchar • Receiver antenna level pattern is applied • Elevation-dependent attenuation • Use default satellite orbit and satellite clocks • Land mobile multipath effect • Rural environment • <15°, reflected signals only • <40°, allow reflected signals

14. How AFIF carrier-phase outperform pseudorange? • Position accuracy with ionosphere-free pseudorange (Dural-frequency PPP) • Position accuracy from ambiguity-fixed ionosphere-free carrier-phase (triple-frequency PPP)

15. How AFIF carrier-phase outperform pseudorange?

16. Success rate & correctness rate of ambiguity fixing

17. Multipath effects Interrupt every 30 s Interrupt every 30 s Interrupt every 120 s Interrupt every 120 s

18. Question 1: optimum combination? • Do we have to use ionosphere-free combinations or not? • How residual ionospheric delays affect hardware bias estimation? • What if the residual ionospheric delays are small enough? • What are the optimum combinations? • Which combinations are used depends on not only PPP users, but also satellite clock providers • How to define satellite clock products in future for multi-frequency and multi-constellation GNSS? • What if we have 4, 5 … frequencies? • Do we have to look for the optimum again and again?

19. Question 2: A general way to PPP? • Do we have to manually look for the optimum combinations? • We can use raw observation equations • LAMBDA method • Multi-frequencies: the problem is how b_1, b_2 … B_1, B_2 …affect the clock, ionosphere parameters? • Can multi-frequency clocks be used for dual-frequency data processing?

20. Summary and conclusions • Dual-frequency PPP-ambiguity resolution improves positioning accuracy, but not convergence speed to ambiguity-fixed solutions. • Triple-frequency PPP can speed up convergences to ambiguity-fixed solutions from a few tens of minutes to a few minutes. • Potential of multi-frequency PPP has not been exploited, especially in how to design a general way to do multi-frequency PPP. • Satellite clock product may need to be re-defined to accommodate the future multi-frequency signals.