Information theoretic space object data association methods using an adaptive Gaussian sum filter

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 space objects. The approach involves using an adaptive Gaussian mixture solution to the Fokker-Planck-Kolmogorov equation for its applicability to the space object tracking problem. The Fokker-Planck-Kolmogorov equation describes the timeevolution 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 information theoretic approaches that are 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.