Linked, Autonomous, Interplanetary Satellite Orbit Navigation (LiAISON) Presentation by Keric Hill For ASEN 5070 Statistical Orbit Determination Fall 2006 1 Why Do We Need Autonomy? New Lunar Missions: Orbiters Rovers Sample Return Comm Sats Space Stations CEV Observatories L 1 L 2 Planetary images courtesy of http://photojournal.jpl.nasa.gov 2 1
Circular Restricted Three-body Problem y spacecraft z r 1 r2 P 1 Barycenter µ 1-µ P 2 x 3 Lagrange Points y L 4 P 1 P 2 L 3 L 1 L 2 x L 5 4 2
Challenges in Lunar Libration Orbits 5 DSN vs. Autonomy Image courtesy of http://solarsystem.nasa.gov/multimedia/gallery/ 6 3
Types of Autonomy Individual Autonomy Earth limb sensors Sun sensors Star trackers Magnetic field sensors Constellation Autonomy using Satellite-to-Satellite Tracking (SST) SST optical tracking SST crosslink ranging GPS receiver (in LEO) Optical Navigation 7 Satellite-to-Satellite Tracking (SST) SST picture Scalar measurements (range or range-rate) Estimate size, shape of orbits Estimate relative orientation of the orbits. Image courtesy of http://www.centennialofflight.gov/essay/dictionary/tdrss/ 8 4
Satellite-to-Satellite Tracking (SST) Scalar measurements (range or range-rate) Estimate size, shape of orbits Estimate relative orientation of the orbits. Image courtesy of http://www.centennialofflight.gov/essay/dictionary/tdrss/ 9 Two-body Problem SST 10 5
Two-body Problem SST 11 Two-body Problem SST 12 6
Two-Body Symmetry The vector field of accelerations in the x-y plane for the two-body problem. 13 Three-body Symmetry The vector field of accelerations in the x-z plane for the three-body problem. 14 7
Three-body Solutions 15 Strength of the Asymmetry 16 8
Map of the Three-body Asymmetry 17 Three-body Asymmetry and Libration Orbits 18 9
Liaison Navigation Linked, Autonomous, Interplanetary Satellite Orbit Navigation (LiAISON) SST only is used to determine the orbits of multiple spacecraft when at least one is in a locally unique orbit. li-ai-son: Communication for mutual understanding. -Merriam-Webster (www.m-w.com) 19 Orbit Determination Techniques Two spacecraft. Batch processor : Householder transformation. Observation type: SST Range. Gaussian noise 1 σ = 1.0 m. Fit span = 1.5 halo orbit periods (~18 days). Infinite a priori covariance. Observations every ~ 6 minutes. LOS checks. 20 10
LL 1 Family 21 Observability The state vector is observable if all the parameters can be estimated independently using with the available observations. If the H matrix is not full rank, or if the information matrix is singular (not positive definite), then the state vector is unobservable. A priori covariance can make it seem like the state is observable when it is not. The eigenvectors corresponding to the zero eigenvalues of the information matrix show the vector along which the state is unobservable. 22 11
Filter Output Plot of covariance from the Kalman filter showing time to convergence for a LL1B Halo 2 constellation. 23 OD Accuracy Metric 24 12
Position Along the Halo 25 Initial Positions Sat 1 26 13
Spacecraft Separation 27 Out of Plane Component LL 1 Halo 2 constellations 28 14
β con (m) in LL 1 -LL 1 Constellations 29 Halo-Moon 30 15
Other Tests Estimated Range Bias Limited tracking periods SST Doppler Larger interval between observations Constant Force Model Errors Sinusoidal Observation Error Varied Fit Spans Simulation Results 31 Monte Carlo Analysis 32 16
JPL Ephemeris Model JPL s Planetary Ephemerides: DE403 better for the Moon DE405 better for the other planets Solar System Barycenter Coordinates Julian Ephemeris Date Time Scale (TDB) Generating Halo Orbits: Multiple Shooting Method Numerical Precision Problems JED 2,454,069.37575443 (Nov 29, 2006 2100 UTC) R_Moon = 148,376,285.478218 km 33 Two-Satellite Liaison Navigation Simulation Moon Propagation: RK78 with JPL DE405 ephemeris, SRP, LP100K Lunar Gravity (20x20) Orbit Determination: Extended Kalman Filter Observations: Crosslink range with 1 m noise every 60 seconds Halo Orbiter: 4 Δv s per period 5% Δv errors c R error -> 1 x 10-9 m/s 2 position error RSS 80 m Lunar Orbiter: 50x 95 km, polar orbit c R error -> 1 x 10-9 m/s 2 5% Δv errors 1σ gravity field clone position error RSS 7 m Earth The lunar orbiter could hold science instruments and be tracked to estimate the far side gravity field. 34 17
) m ( 1 t a s 1 t a s 200 0 0 Halo Orbiter Position Error from the EKF EKF sat 1 position error with state noise 2.68e-009 m/s 2, RSS = 77.78 m x error 2! stdev x -200 0 5 10 15 20 25 30 Day (RMS = 37.94 m) 64.7% < 1! ) m ( 200 1 t a s z 0 y error 2! stdev y -200 0 5 10 15 20 25 30 Day (RMS = 42.57 m) 52.3% < 1! ) m ( 200 z error 2! stdev -200 0 5 10 15 20 25 30 Day (RMS = 52.90 m) 66.1% < 1! 35 ) m ( 2 t a s 2 t a s 20 0 0 Lunar Orbiter Position Error from the EKF EKF sat 2 position error with state noise 1.34e-008 m/s 2, RSS = 6.87 m x error 2! stdev x -20 0 5 10 15 20 25 30 Day (RMS = 5.70 m) 90.8% < 1! ) m ( 20 y error 2! stdev y -20 0 5 10 15 20 25 30 Day (RMS = 2.40 m) 71.3% < 1! ) m ( 20 2 t a s z 0 z error 2! stdev -20 0 5 10 15 20 25 30 Day (RMS = 2.99 m) 91.0% < 1! 36 18
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