Real-Time Onboard Navigation of LEO Satellites using GPS

Transcription

1 Real-Time Onboard Navigation of LEO Satellites using GPS O. Montenbruck, DLR/GSOC Slide 1

2 Real-Time Onboard Navigation of LEO Satellites using GPS Navigating in Space Mission needs and how to meet them Real-Time Navigation Systems Concept Models and measurements Filter Design Applications Summary Sample Implementations How good can we get? Slide 2

3 Mission Needs... Timing (~ 1 µs) Synchronization of onboard clock Local Orbital Frame (~ 10 m, ~ 1 cm/s) Conversion of star camera attitude Instrument pointing (nadir or other) Geocoding (1 10 m) Blending of payload data with position information (SAR, optical) Autonomous Instrument and Mission Operations (1 m 100 m) Open-loop altimeter operations Target and ground station acqusition Slide 3

4 Example: Sentinel-3 Open Loop Altimeter Operations (R,T,N) pos rms < (3,6,6) m (R,T,N) vel rms < (2,2,2) cm/s Gate window 60 m Slide 4

5 ... and how to meet them Adequate maturity and availability of spaceborne GPS technology Single-frequency (navigation) Dual-frequency (science, POD) Conservative, bulky, costly! Performance in LEO compatible with Standard Positioning Service No urban canyons, lower ionosphere Few satellites above the poles Typical positioning accuracy of 10 (-20) m Slide 5

6 Really? Limited kinematic positioning accuracy Pseudorange noise 0.1 m 3 m Broadcast ephemeris errors (SISRE m) Ionospheric delays (few m) Other issues Insufficient velocity accuracy (few cm/s) Lacking continuity (gaps, bad PDOP, outliers) Theoretical accuracy potential not fully exploited Conservative design and requirements engineering Slide 6

7 Real-Time Navigation Systems Improved accuracy (0.5-1 m 3D rms) Reduced impact of measurement noise Optional elimination of ionospheric delays in single-frequency processing Partial elimination of broadcast ephemeris errors Reduction of velocity error (long-term averaging) Continuity and predictability Problems Use of dynamical trajectory model Computational complexity (coding, verification) Processor load Slide 7

8 Real-Time Navigation Cookbook Ingredients Dynamical model Numerical integration Measurement model Filtering Montenbruck O., Ramos-Bosch P.; Precision Real-Time Navigation of LEO Satellites using Global Positioning System Measurements ; GPS Solutions 12(3): (2008). DOI /s x Slide 8

9 Reference System Considerations Terrestrial Reference Frame (ITRF, WGS84) Standard for modeling of GPS orbits and observations Baseline for modeling of Earth gravitational acceleration Inertial Reference Frame (ICRF, EME2000) Standard for celestial body ephemerides (Sun, Moon) Common baseline for satellite trajectory propagation Rigorous transformation requires full knowledge of Earth orientation parameters Pole coordinates UT1-TAI time difference Typical user needs accurate ITRF position, but relaxed ICRF accuracy Slide 9

10 Earth-Fixed Formulation ITRF formulation of real-time navigation systems simplifies the filter design reduces the sensitivity to EOP errors but increases the complexity of the equation of motion (law of conservation of trouble) Apparent acceleration Coriolis and centrifugal terms Rotation vector from ICRF-ITRF trafo transformation and its derivative Practical approximation Constant angular velocity Polar motion offset between ITRF z-axis and rotation axis Accuracy ~100 nm/s 2 a Ω CC = = = 2 ω v + ω ω r 2 Ω v + Ω Ω r T [ ω ] = Uɺ U 0 ω Π 0 ω Slide 10

11 Gravitational Accelerations Earth gravity field Spherical harmonics expansion aɺ ɺ GM = r Degree and order 20 to 50 Optional: solid Earth tide (k 2 ) Luni-Solar Perturbations Point mass model n n R Pnm (sinφ)( Cnm cosmλ n + n= 0m= 0 r sinmλ) Cunningham L. E.; On the Computation of the Spherical Harmonic Terms needed during the Numerical Integration of the Orbital Motion of an Artificial Satellite ; Celestial Mechanics 2, (1970). Low-order analytical series of luni-solar coordinates (1 to 5 ) Simplified ICRF-to-ITRF transfomation (precession, Earth rotation) S nm Slide 11

12 Non-Gravitational Accelerations Air Drag No r/t access to solar flux & geomagnetic indices Simple desity model (Harris Priester) Adjustable drag coefficient Solar Radiation Pressure Maneuvers Cannon-ball model Cyclindrical shadow model Adjustable rad. pressure coefficient Empirical Accelerations Adjustable parameters Compensation of force model deficiencies aɺɺ = a aɺɺ = P r e aɺɺ 1 A = C D ρ v v 2 m Sun r C + a t R A m e t s s 3 + a n AU e n 2 Slide 12

13 Numerical Integration Real-time navigation systems Frequent measurement updates y h h Short propagation intervals (0.001 to 0.01 revs) Limited resources Use low order Runge-Kutta methods 2h t 0 t 1 t 2 t RK4 with Richardson Extrapolation Combines two RK4 steps of size h with one step of size H=2h Gives 5 th order at 6 function calls per h Hermite interpolation 5 th order polynomial for y(t)=(r,v) from y 0, y 1, y 2, y 0, y 1, y 2 Gill E., Montenbruck O., Kayal H.; The BIRD Satellite Mission as a Milestone Towards GPS-based Autonomous Navigation ; Navigation - Journal of the Institute of Navigation 48/2, (2001). Montenbruck O., Gill E.; State Interpolation for On-board Navigation Systems ; Aerospace Science and Technology 5, (2001). DOI /S (01) ). Slide 13

14 Measurement Model Ionosphere-free measurements Dual-frequency pseudorange (P 12 ) Dual-frequency pseudorange and carrier phase (P 12 & L 12 ) GRAPHIC (GRoup and PHase Ionospheric Calibration) (C/A+L 1 ) Average of code and carrier phase measurement Biased measurement Noise reduced by 50% Requires only C/A code tracking (better signal-to-noise ratio) Broadcast ephemerides Signal-In-Space-Range-Error ~ m ICD-GPS-200 models for GPS position, velocity, clock Slide 14

15 Filter State Vector and Process Noise Model State Vector Parameter Dim Process Noise Y r v CR = C D aemp cδt B Position Velocity Radiation pressure coeff. Drag coefficient Empirical accelerations Clock Offset Biases N CH Maneuver-free arcs: none Maneuvers: white noise None None Expon. Correlated Random Vars. White noise (White noise) Slide 15

16 Update Scheme Time Update Trajectory Integration Time Update Data Screening State Reconfiguration Data Screening Measurement Update State Reconfiguration Trajectory Integration Measurement Update Interpolation High-Rate Processing Low-Rate Processing Slide 16

17 Phoenix-XNS Extension of DLR s Phoenix GPS receiver 32-bit ARMTDMI MHz 12 Channels L1 tracking Real-time Kalman filtering of GPS raw measurements Ionosphere-free C1+L1 combination Code noise ~ 0.4 m, carrier phase <1 mm Complements Phoenix standard software for GPS tracking and navigation C++ software extension 40x40 gravity model 30s filter update rate First in-flight demonstration on PROBA-2 Montenbruck O., Markgraf M., Santandrea S., Naudet J., Gantois K., Vuilleumier P.; Autonomous and Precise Navigation of the PROBA-2 Spacecraft ; AIAA ; AIAA Astrodynamics Specialist Conference, Aug. 2008, Honolulu, Hawaii (2008). Slide 17

18 Phoenix-XNS Signal Simulator Test (PROBA-2) Slide 18

19 RTNav Software DLR analysis and development tool for trade-off and design studies Offline implementation of real-time navigation filter RINEX observation interface SP3 or RINEX ephemeris interface Gravity model interface User configurable processing parameters Close match with XNS design Add on s Same core models and filtering scheme Simple RK4 integrator (no need for interpolation) Attitude and antenna offset modeling Data editing Maneuver handling Slide 19

20 RTNav with Broadcast Ephemerides (GRAS) 55 cm 3D rms Slide 20

21 GRAS Preformance Study Data Type Radial [m] Along [m] Cross [m] 3D rms 2F CP (& PR) ± ± ± m 2F PR ± ± ± m 1F PR & CP ± ± ± m Broadcast ephemerides, 70x70 gravity field Ephemeris Radial [m] Along [m] Cross [m] 3D rms Broadcast ± ± ± m IGU predicted ± ± ± m JPL R/T ± ± ± m Dual Frequency Carrier Phase, 70 x 70 gravity field Slide 21

22 Outlook Galileo Targeted SISRE 0.8 m Improved clocks (H-Maser) Needs to demonstrate competetivness TDRSS Augmentation Satellite System (TASS) Real-time transmission of precise GPS orbit and clock information via geostationary satellite Enables real-time navigation at the 10 cm level Future users Radio-occultation missions? SAR imaging? Are we too good? Slide 22

23 Summary Dynamical filtering of GPS measurements offers improved Accuracy Robustness Predictability Reference algorithms defined Compatible with low power microprocessors Real-time capability demonstrated (Phoenix) Proper accuracy (0.5 m 3D rms) demonstrated Next steps Broadcast ephemerides sufficient for current applications Even single-frequency GPS can provide excellent performance Implementation in Sentinel-3 GPS receiver (RUAG) XNS flight demonstration on PROBA-2 Slide 23