Orekit at the U.S. Naval Research Laboratory Evan Ward U.S. Naval Research Laboratory Astrodynamics and Navigation Section, Washington DC November 16, 2017
Outline Introduction Geolocation with Orekit Orekit & an NRL Satellite Orbit Determination Research with Orekit Comparison with Heritage Radius of Convergence Directional Measurement Representation Conclusions & Future Work Questions? U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 2 / 33
Introduction
Introduction NRL The Government should maintain a great research laboratory to develop guns, new explosives, and all the technique of military and naval progression without any vast expense. Thomas Edison, 1915 U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 4 / 33
Introduction Naval Center for Space Technology U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 5 / 33
Geolocation with Orekit
Geolocation Orekit s first use at NRL Sensitivity analysis of geolocation systems Started in 2011 Goal to evaluate non-linear effects of terrain Sensitivity analysis for non-linear error budget Similar to Rugged 1 Sensor Cross Range Up Down Range η r Cross Range Up Down Range Target Results published in 2015 2 1 https://orekit.org/rugged/ 2 Evan Ward. Global sensitivity analysis of terrain effects in geolocation systems. In: IEEE Transactions on Aerospace and Electronic Systems 51.3 (2015), pp. 2039 2046 U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 7 / 33
Geolocation Why Orekit? Astrodynamics library search Requirements Precise and accurate Easy to work with Extensible Thread safe Actively maintained Examined Internal heritage code AGI s STK Some NASA open source code Orekit Orekit met all requirements Thread safety was new to Orekit Contributed patches to improve concurrent performance U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 8 / 33
Geolocation Results Ge l cati n Err r Over Design Space Simulation Airplane with angles-only geolocation sensor Computes intersection with a Digital Elevation Model (DEM) Sensitivity analysis using Analysis of Variance High Dimensional Model Representation (ANOVA-HDMR) A Monte-Carlo method Cr ss Range (m) ST (percent of variance) Linearized ANOVA-HDMR ANOVA-HDMR + DEM 20 10 0 (10 (20 60 40 20 0 20 40 60 Down Range (m) Down Range Sensitivity Over Design Space 100 linearized ANOVA-HDMR ANOVA-HDMR + DEM 80 60 40 20 0 nadir azimuth TSF terrain nadir azimuth down cross altitude error error error range range error error error U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 9 / 33
Orekit & an NRL Satellite
Application of Orekit to an On-Orbit Mission An on orbit satellite A Test And Check Out (TACO) satellite Used for end to end testing of NRL s Blossom Point Tracking Facility Attitude sensors degraded in 2013 Needed new algorithm for attitude estimation and maneuver planning Requirements Low cost Low level of effort Minimal verification requirements Accept ill-conditioned data Moderate accuracy requirements U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 11 / 33
Attitude Determination and Control Orekit and Apache Commons Math based solution Orekit provided Frames Time TLES Attitude propagation Planetary ephemerides Apache Commons Math provided Vector geometry Levenberg-Marquardt Optimizer Concept to spacecraft maneuver in a few weeks Successfully corrected attitude on first try Approaching 4 years of use Still in use today Orekit enabled meeting the requirements U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 12 / 33
Orbit Determination Research with Orekit
Orbit Determination Research State Estimation Application (SEA) Orbit Determination (OD) application using Orekit Written in 2014 Inspired by Luc Maisonobe s addition of tide models Used to evaluate new OD concepts Can be quickly modified Java Extensive OSS libraries Automatic differentiation Used in 3 publications Validation against NRL s Orbit Covariance Estimation & Analysis (OCEAN) application Radius of convergence Directional measurement representation U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 14 / 33
Comparison with Heritage
NRL OCEAN U.S. Naval Research Laboratory High precision OD Fortran-based Extensive heritage Basis of comparison for SEA Orekit at the U.S. Naval Research Laboratory 16 / 33
Comparing SEA and OCEAN Evaluate predictive ability 3 Satellite Laser Ranging (SLR) test case Using STELLA satellite SLR target in Low Earth Orbit (LEO) Use similar configuration for OCEAN and SEA Drag models were biggest difference No drag model supported by both 4 3 Evan M. Ward, John G. Warner, and Luc Maisonobe. Do Open Source Tools Rival Heritage Systems?: A comparison of tide models in OCEAN and Orekit. In: AIAA/AAS Astrodynamics Specialist Conference. 2014 4 STELLA Satellite. Image Credit: CNES U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 17 / 33
Comparison and Results Process Fit to five days of data Predict for 25 days Compare predict to successive five day fits SEA has sufficient accuracy for use in further research U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 18 / 33
Radius of Convergence
Radius of Convergence Examine sensitivity to errors in initial conditions 5 Using SLR satellite LAGEOS-1 SLR provides high precision measurements Initial condition moved progressively further from truth Used SEA and Hipparchus optimizers At what point is the OD algorithm unable to find a solution? Evaluate several algorithms Iteration Method Matrix Decomposition Explicit Normal Equations Levenberg- QR No Marquardt Gauss-Newton Cholesky Yes Gauss-Newton LU Yes Gauss-Newton QR No Gauss-Newton SVD No 5 John G. Warner et al. Comparing Radius of Convergence in Solving the Nonlinear Least Squares Problem for Precision Orbit Determination of Geodetic Satellites. In: AIAA/AAS Astrodynamics Specialist Conference. 2016, p. 5339 U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 20 / 33
Radius of Convergence Results Levenberg-Marquardt 30.0 RMS at Convergence (meters) Method Radius of Convergence Distance (km) 25.0 Iterations Levenberg-Marquardt 175.1 Gauss-Newton Cholesky 9.353 Gauss-Newton LU 9.353 Gauss-Newton QR 9.353 Gauss-Newton SVD 9.353 RMS (m), Iterations 20.0 15.0 10.0 5.0 0.0 0 20 40 60 80 100 120 140 160 180 200 Initial Condition Offset (km) Levenberg-Marquardt uses trust region for larger radius of convergence U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 21 / 33
Directional Measurement Representation
Motivation Angles only orbit determination6 Ground station measures direction to satellite Does the coordinate system matter? Using Weighted Least Squared Assumes residuals are Normally distributed OD textbooks recommend spherical coordinates OCEAN weights azimuth by cosine of elevation 6 Evan M. Ward and Greg Carbott. On Directional Measurement Representation in Orbit Determination. In: AIAA/AAS Astrodynamics Specialist Conference. 2016. DOI: 10.2514/6.2016-5369 U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 23 / 33
Three Angular Representations Cost Functions Spherical Coordinates C s = (α c α o ) 2 + (ε c ε o ) 2 Weighted Spherical Coordinates C w = ((α c α o )cosε o ) 2 + (ε c ε o ) 2 Elevation (deg) Cost Function Distortion Near The Pole +85 +85 C w C s C u u o +80 +80 Unit Vector sinθ = u c u o C u = θ 2-25 -20-15 -10-5 0 +5 +10 +15 +20 +25 Azimuth (deg) Representation determines shape of probability distribution U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 24 / 33
Comparison Analytic C w, C u equivalent for small α, ε Distortion increases with α, ε C w, C s equivalent for small ε o Distortion increases with ε o All three equivalent with all above assumptions Hypotheses Unit vector quicker to converge Measured using number of iterations Unit vector attains more accurate solution Measured using RSS ephemeris difference U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 25 / 33
Observation Simulation Noise Symmetric about true direction Independent of true direction Normal with σ = 0.1-90 Representative Error Distribution Near The Pole +89.6 +89.8 +89.8 +89.6 +90 Satellites 500km circular LEO GEO Ground station near sub-satellite point Several initial conditions Control size of residuals -45 +45 U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 26 / 33 +89.4 +89.2 0 +89.4 +89.2
Results Speed 25 LEO Convergence Speed 25 GEO Convergence Speed 20 20 Iterations 15 10 Iterations 15 10 5 5 0 200 300 400 500 600 700 800 900 Error in Initial Condition (km) 0 0 20 40 60 80 100 120 140 160 Error in Initial Condition (km) Spherical Coordinates Weighted Spherical Coordinates Unit Vector U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 27 / 33
Results Accuracy 10 3 Method Accuracy GEO Ground Station View of Orbits 0 Average Ephemeris Difference RSS (km) 10 2 10 1 10 0 270 315 225 45 89.8 89.9 90 135 10-1 Weighted Spherical Coordinates LEO Unit Vector GEO Spherical Coordinates Truth Weighted Spherical Coordinates 180 Spherical Coordinates Unit Vector Unit vector method best for high elevation angles U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 28 / 33
Why? Distortion Small θ does not imply small (α c α o ) Shortest path is not a straight line Clipping Positive probability placed on non-physical solutions Both effects prevent averaging Unit vector method has neither effect U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 29 / 33
Conclusions & Future Work
Final Thoughts on Orekit Great tool for research Highly reconfigurable Quick development High fidelity Welcoming Community Responds quickly Patient with new users Opportunity to improve documentation Documentation is good for experts in astrodynamics and computer science Received feedback from several new users Documentation is unclear / confusing Can t find the answer Perhaps more high level overviews and tutorials U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 31 / 33
Orekit Future Work Interoperability with other analysis tools Parser & Writer for STK.e and Cesium CZML files Add covariance to EphemerisFile interface Better frame to name mapping One Line Element Sets (OLES) Internal Interoperability Instantiatable FramesFactory, TimeScaleFactory Compare EOP series Frame from/to PVCoordinatesProvider, AttitudeProvider Analytic Propagator from a PVCoordinatesProvider Event detection for planets, etc. U.S. Naval Research Laboratory Orekit at the U.S. Naval Research Laboratory 32 / 33
Questions?