A Multifidelity Approach to Robust Orbit Determination

This paper presents an algorithm for the preprocessing of observation data aimed at improving the robustness of orbit determination tools. Two objectives are fulfilled: obtain a refined solution to the initial orbit determination problem and detect possible outliers in the processed measurements. The uncertainty on the initial estimate is propagated forward in time and progressively reduced by exploiting sensor data available in said propagation window. Differential algebra techniques and a novel automatic domain splitting algorithm for second-order Taylor expansions are used to efficiently propagate uncertainties over time. A multifidelity approach is employed to minimize the computational effort while retaining the accuracy of the propagated estimate. At each observation epoch, a polynomial map is obtained by projecting the propagated states onto the observable space. Domains that do no overlap with the actual measurement are pruned thus reducing the uncertainty to be further propagated. Measurement outliers are also detected in this step. The refined estimate and retained observations are then used to improve the robustness of batch orbit determination tools. The effectiveness of the algorithm is demonstrated for a geostationary transfer orbit object using synthetic and real observation data from the TAROT network.

[1]  R. Armellin,et al.  Robust Initial Orbit Determination for Surveillance Doppler-Only Radars , 2023, IEEE Transactions on Aerospace and Electronic Systems.

[2]  R. Armellin,et al.  Perturbed Initial Orbit Determination , 2023, ArXiv.

[3]  R. Armellin,et al.  A low-order automatic domain splitting approach for nonlinear uncertainty mapping , 2023, ArXiv.

[4]  E. Delande,et al.  Multifidelity Orbit Uncertainty Propagation using Taylor Polynomials , 2022, AIAA SCITECH 2022 Forum.

[5]  K. Alfriend,et al.  Least Sum of Absolute Residuals Orbit Determination , 2021, Journal of Guidance, Control, and Dynamics.

[6]  W. Folkner,et al.  The JPL Planetary and Lunar Ephemerides DE440 and DE441 , 2021 .

[7]  Roberto Armellin,et al.  Probabilistic data association: the orbit set , 2020, Celestial Mechanics and Dynamical Astronomy.

[8]  Renato Zanetti,et al.  Recursive Polynomial Minimum Mean-Square Error Estimation with Applications to Orbit Determination , 2020, Journal of Guidance, Control, and Dynamics.

[9]  Ryan M. Weisman,et al.  Multi-fidelity orbit uncertainty propagation , 2019, Acta Astronautica.

[10]  David J. Gondelach,et al.  Multiple Revolution Perturbed Lambert Problem Solvers , 2018, Journal of Guidance, Control, and Dynamics.

[11]  Christopher N. D’Souza,et al.  Navigation Filter Best Practices , 2018 .

[12]  Juan Carlos Dolado Pérez,et al.  TAROT: a network for space surveillance and tracking operations , 2017 .

[13]  Ya-Zhong Luo,et al.  A review of uncertainty propagation in orbital mechanics , 2017 .

[14]  Steven Gehly,et al.  Lp-Norm Batch Estimation As Applied To Orbit Determination , 2016 .

[15]  Puneet Singla,et al.  Conjugate Unscented Transformation-Based Approach for Accurate Conjunction Analysis , 2015 .

[16]  M. Berz,et al.  Propagation of large uncertainty sets in orbital dynamics by automatic domain splitting , 2015 .

[17]  D. Izzo.  Revisiting Lambert’s problem , 2014, 1403.2705.

[18]  Carolo Friederico Gauss.  Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium , 2014 .

[19]  A. Doostan,et al.  Nonlinear Propagation of Orbit Uncertainty Using Non-Intrusive Polynomial Chaos , 2013 .

[20]  Michèle Lavagna,et al.  Nonlinear Mapping of Uncertainties in Celestial Mechanics , 2013 .

[21]  N. Delsate,et al.  Symplectic integration of space debris motion considering several Earth's shadowing models , 2012, 1201.5274.

[22]  Aubrey B. Poore,et al.  Gaussian Sum Filters for Space Surveillance: Theory and Simulations , 2011 .

[23]  R. Park,et al.  Nonlinear Mapping of Gaussian Statistics: Theory and Applications to Spacecraft Trajectory Design , 2006 .

[24]  T. S. Kelso,et al.  Revisiting Spacetrack Report #3 , 2006 .

[25]  R. Branham.  Laplacian Orbit Determination and Differential Corrections , 2005 .

[26]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[27]  B. Tapley,et al.  Statistical Orbit Determination , 2004 .

[28]  Will Featherstone,et al.  A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions , 2002 .

[29]  R. Koenker,et al.  The Gaussian hare and the Laplacian tortoise: computability of squared-error versus absolute-error estimators , 1997 .

[30]  R. Battin.  An introduction to the mathematics and methods of astrodynamics , 1987 .

[31]  Subhash C. NarulaI,et al.  The Minimum Sum of Absolute Errors Regression: A State of the Art Survey , 1982 .

[32]  Jorge J. Moré,et al.  User Guide for Minpack-1 , 1980 .

[33]  Wolfgang Priester,et al.  TIME-DEPENDENT STRUCTURE OF THE UPPER ATMOSPHERE , 1962 .

[34]  Vladimir,et al.  [American Institute of Aeronautics and Astronautics 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference) - Miami, Florida ()] 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference) - High-Accuracy Viscous Analysis of Unsteady Flexible Airfoil Response to , 2009 .

[35]  J. Junkins,et al.  How Nonlinear is It? A Tutorial on Nonlinearity of Orbit and Attitude Dynamics , 2003 .

[36]  P. W. Hawkes,et al.  Modern map methods in particle beam physics , 1999 .

[37]  Daryl E. Carlson,et al.  A simple approximation of the sampling distribution of least absolute residuals regression estimates , 1977 .