Carlin, Luca

Hauschild, André

Montenbruck, Oliver

Institute of Transport Research:Publications

Precise Positioning with Broadcast EphemeridesOliver Montenbruck, Luca Carlin, André HauschildITSNT > Toulouse > 24-25 June 20211• Motivation • Broadcast Ephemeris Errors• Models• Applications• Terrestrial• Space• Summary and ConclusionsPrecise Positioning with Broadcast EphemeridesITSNT > Toulouse > 24-25 June 20212GNSS Point PositioningITSNT > Toulouse > 24-25 June 20213Precise Point Positioning(PPP)?Single Point Positioning(SPP)Code ObservationsSingle/Dual-FrequencyBroadcast EphemeridesEpoch-wise position solutionReal-timeMeter-level accuracyCode and Phase  ObservationsDual FrequencyPrecise EphemeridesSequential position solutionOffline / Real-timeCentimeter-level accuracy• Common frequencies (L1/E1/B1, L5,E5a,B2a) and inter-operable signals for GPS, Galileo, BeiDou-3• Dual-frequency GNSS now available for mass market receivers GNSS SignalsITSNT > Toulouse > 24-25 June 20214B1CBeiDouGPS GalileoGLONASSL1 C/AB1IE5aE6B,CL1C L1 C/AE1L2 C/AL5E5bL3B2aB2IB2bL2C B3IAdapted from DOI 10.1109/PLANS46316.2020.9110208PPP with Broadcast Ephemerides?ITSNT > Toulouse > 24-25 June 20215Broadcast EphemeridesReal-timePrecise Point Positioningwith Broadcast Ephemerides(PPP-BCE)Code and Phase  ObservationsDual-Frequency(Multi-Constellation)Sequential position solution(Few) decimeter-level accuracy w/o correction services • Signal-in-Space Ranging Error (SISRE)• Contribution of orbit and clock errors to modelled pseudorange• User Equipment Error (UEE)• Contribution of measurement errors (and uncompensated atmospheric path delays) to observed-minus-modelled pseudorange• Dilution of precision• Ratio of σ(position error) and σ(pseudorange error)• Depends on number and distribution of tracked satellites• Common concept for SPP, partly applicable for (kinematic) PPP• Rule of thumb for assessing impact of ephemeris errors• Largely reduced (negligible) UEE when using carrier phase observationsPositioning ErrorITSNT > Toulouse > 24-25 June 20216𝜎 Δ𝒓 = DOP ⋅ SISRE2 + UEE2Example: GPSITSNT > Toulouse > 24-25 June 20217Cesium clock24 h upload2 h updateSISRE depends on• Clock stability• Upload intervals• Modulation/BiasesBest results for • Galileo • BeiDou-3Note: SISRE(PPP) neglects satellite-specific constant clock biases (no impact on carrier phase based positioning)SISRE of Global Navigation Satellite SystemsITSNT > Toulouse > 24-25 June 20218(DOI 10.1002/navi.416; CC-BY)• (A) Standard PPP ModelPPP-BCE Models (Dual Frequency)ITSNT > Toulouse > 24-25 June 20219𝑝 = 𝒓𝑟 − 𝒓𝑠 + 𝑐 𝑑𝑡𝑟 − 𝑑𝑡𝑠 + 𝑇 + 𝑒𝜑 = 𝒓𝑟 − 𝒓𝑠 + 𝑐 𝑑𝑡𝑟 − 𝑑𝑡𝑠 + 𝑇 + 𝐴 + 𝜖• (B) Modified PPP-BCE Model with SISRE estimation• Pseudorange (𝑝), carrier phase (𝜑), receiver and satellite position (𝒓𝑟, 𝒓𝑠), receiver and satellite clock offsets (𝑑𝑡𝑟 , 𝑑𝑡𝑠), tropospheric delay (𝑇), Ambiguity (𝐴), measurement errors (𝑒, 𝜖), SIS range error (𝑠)• Phase center offsets, patterns, and wind-up ignored for simplicitymodelledestimatedestimated, process noise𝑝 = 𝒓𝑟 − 𝒓𝑠 + 𝑐 𝑑𝑡𝑟 − 𝑑𝑡𝑠 + 𝑇 + 𝑠 + 𝑒𝜑 = 𝒓𝑟 − 𝒓𝑠 + 𝑐 𝑑𝑡𝑟 − 𝑑𝑡𝑠 + 𝑇 + 𝑠 + 𝐴 + 𝜖• (C) Simplified PPP-BCE Model, SISRE lumped into ambiguity 𝑝 = 𝒓𝑟 − 𝒓𝑠 + 𝑐 𝑑𝑡𝑟 − 𝑑𝑡𝑠 + 𝑇 + 𝑒𝜑 = 𝒓𝑟 − 𝒓𝑠 + 𝑐 𝑑𝑡𝑟 − 𝑑𝑡𝑠 + 𝑇 + 𝐴 + 𝜖• 11 globally distributed stations (various rcvs and antennas)• 31 days (Dec 2019)• Kinematic processing• Kalman filter (forward-only)• 24-h arcs, first hour excluded• Clear benefit of SISRE handling • Simplified method gives similar  performance at notably reduced complexity• 0.20-0.40 m 3D rms accuracy with Galileo or GPS+GalileoTest with IGS Permanent StationsITSNT > Toulouse > 24-25 June 202110A B C(DOI 10.1007/s10291-021-01111-4; CC-BY) • 1 h boat ride on Lake Ammer(11 Sep. 2019)• AsteRx3 rcv, Zephyr 3 antenna• RTK reference solution• 0.1 RMS horizontal, 0.3 m up for GPS+Galileo• 15 min convergenceBoat TestITSNT > Toulouse > 24-25 June 202111A B C precise• Dynamical Model• Predict satellite motion (and uncertainty) under known external forces • Observations• Pseudorange and carrier phase• One or multiple GNSSs• Kalman filter• Time update (state and covariance prediction)• Measurement update (correct state with observations)• Applications• Constellation/formation control• Onboard science data processing (radio occultation, images, SAR)Flying High: Real-Time Orbit DeterminationITSNT > Toulouse > 24-25 June 202112• Extended Kalman filter in forward-only mode• Position & velocity • Drag, SRP, empirical accelerations • 1 clock offset per constellation• 1 float ambiguity per tracked satellite• Earth gravity, luni-solar perturbations, empirical accelerations • Multi-constellation, dual-frequency code and phase observations• GNSS orbit, clock & EOP data from broadcast ephemerides (RINEX)• Line-of-sight SISRE errors lumped into float ambiguityPlayback Real-time Navigation FilterITSNT > Toulouse > 24-25 June 202113© ESAStudy:- True GPS observations for Swarm-C satellite- Simulated GPS, Galileo, BeiDou observationsResults (Multi-GNSS, simulated)ITSNT > Toulouse > 24-25 June 202114G GPSE GalileoC BeiDou(DOI 10.1002/navi.416; CC-BY)• Carrier-phase positioning with broadcast ephemeris (“PPP-BCE”) works!• (Few) decimeter accuracy achievable• Applicable to terrestrial and low-Earth orbit navigation• Best prospects for new GNSSs (Galileo, BeiDou-3)• Particularly attractive for dual- (or even triple-)constellation L1/L5 use Summary and Conclusions ITSNT > Toulouse > 24-25 June 202115Further ReadingCarlin L., Hauschild A., Montenbruck O., Precise Point Positioning with GPS and Galileo Broadcast Ephemerides; GPS Sol 25(2):77 (2021) DOI 10.1007/s10291-021-01111-4Hauschild A., Montenbruck O.; Precise On-Board Navigation of LEO Satellites with GNSS Broadcast Ephemerides; Navigation 68(29):419-432 (2021) DOI 10.1002/navi.416

Precise Positioning with Broadcast Ephemerides

https://elib.dlr.de/143055/1/ITSNT_21_PPPBCE.pdf

Precise Positioning with Broadcast Ephemerides

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