Entropy-Based Space Object Data Association Using an Adaptive Gaussian Sum Filter

Abstract

This paper shows an approach to improve the statistical validity of orbital estimates and uncertainties as well as a method of associating measurements with the correct resident space objects and classifying events in near realtime. The approach involves using an adaptive Gaussian mixture solution to the Fokker-Planck-Kolmogorov equation for its applicability to the resident space object tracking problem. The Fokker-Planck-Kolmogorov equation describes the time-evolution of the probability density function for nonlinear stochastic systems with Gaussian inputs, which often results in non-Gaussian outputs. The adaptive Gaussian sum filter provides a computationally efficient and accurate solution for this equation, which captures the non-Gaussian behavior associated with these nonlinear stochastic systems. This adaptive filter is designed to be scalable, relatively efficient for solutions of this type, and thus is able to handle the nonlinear effects which are common in the estimation of resident space object orbital states. The main purpose of this paper is to develop a technique for data association based on entropy theory that is compatible with the adaptive Gaussian sum filter. The adaptive filter and corresponding measurement association methods are evaluated using simulated data in realistic scenarios to determine their performance and feasibility.

Gaussian Sum Filters for Space Surveillance: Theory and Simulations

“…More accurate filters which better approximate model nonlinearities and non-Gaussian PDFs are therefore sought. The Gaussian sum filter is one such example which has been investigated in SSA applications by the authors [2,3] and other researchers [4][5][6][7][8].…”

“…Our philosophy is to not update the weights, which is justified because uncertainty consistency is achieved by working in coordinates adapted to the dynamics (i.e., orbital elements). On the other hand, some researchers [6][7][8] have proposed methods for adapting the weights based on various L 2 optimization criteria, for example, using the FPKE error as feedback. The impact of using one these weight update schemes during propagation is analyzed in this paper.…”

A Gaussian sum filter framework for space surveillance

“…However, there is not complete agreement on how the weights should be updated (if at all) following a prediction. Some researchers [11][12][13] have proposed online methods for adapting the weights based on various L 2 optimization criteria, for example, using the FPKE error as feedback. In another paper, 8 it was found that such weight update schemes do not improve uncertainty consistency when applied to the authors' GSF for the specific two-body problem in space surveillance.…”

“…The Gaussian sum filter is one such example which has been investigated in SSA applications by the authors 6-8 and other researchers. [9][10][11][12][13] The Gaussian sum filter (GSF) is based on a fundamental result of Alspach and Sorenson 9 which states that any PDF can be approximated arbitrarily close (in the L 1 sense) by a weighted sum (mixture) of Gaussian PDFs henceforth called a Gaussian sum. Thus, Gaussian sums provide a mechanism for modeling non-Gaussian densities and for more accurately approximating the solution of the Fokker-Planck-Kolmogorov equation 14 which governs the time evolution of a PDF under a nonlinear stochastic dynamical system.…”

Parallel Computation of Trajectories Using Graphics Processing Units and Interpolated Gravity Models

“…The OD of RSOs can be carried out using many different types of estimation algorithms such as the batch least-squares [13], extended Kalman filter (EKF) [14], second-order Kalman filter [15], unscented Kalman filter [16], divided difference filter [17], Gaussian sum filter (GSF) [18], etc. Particle filtering (PF) [19,20], a Monte Carlo (MC)based method that requires the propagation of a large number of state estimates called particles, is theoretically one of the most accurate and robust, yet computationally intensive, filtering algorithms.…”