TY - GEN

T1 - An adaptive Gaussian sum filtering approach for orbit uncertainty estimation

AU - Giza, Dan

AU - Singla, Puneet

AU - Jah, Moriba

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2010

Y1 - 2010

N2 - An approach for nonlinear filtering when measurements are sparse is discussed which makes use of the Fokker-Planck-Kolmogorov Equation (FPKE). The central idea is to replace the evolution of initial state estimates for a dynamical system with the evolution of a probability density function (pdf) for state variables. The transition pdf corresponding to a dynamical system state vector is approximated by using a finite Gaussian mixture model. The mean and covariance of each Gaussian mixture model component are propagated through the use of an Unscented Kalman Filter (UKF), and the unknown amplitudes are found by minimizing the FPKE error over the entire volume of interest. This leads to a convex quadratic minimization problem guaranteed to have a unique solution. The two-body problem with non-conservative atmospheric drag forces and initial condition uncertainty will be used to show the efficacy of the ideas developed in this paper.

AB - An approach for nonlinear filtering when measurements are sparse is discussed which makes use of the Fokker-Planck-Kolmogorov Equation (FPKE). The central idea is to replace the evolution of initial state estimates for a dynamical system with the evolution of a probability density function (pdf) for state variables. The transition pdf corresponding to a dynamical system state vector is approximated by using a finite Gaussian mixture model. The mean and covariance of each Gaussian mixture model component are propagated through the use of an Unscented Kalman Filter (UKF), and the unknown amplitudes are found by minimizing the FPKE error over the entire volume of interest. This leads to a convex quadratic minimization problem guaranteed to have a unique solution. The two-body problem with non-conservative atmospheric drag forces and initial condition uncertainty will be used to show the efficacy of the ideas developed in this paper.

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M3 - Conference contribution

AN - SCOPUS:80053418735

SN - 9780877035602

T3 - Advances in the Astronautical Sciences

SP - 475

EP - 488

BT - Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences

T2 - AAS/AIAA Space Flight Mechanics Meeting

Y2 - 14 February 2010 through 17 February 2010

ER -