NONLINEAR GAUSSIAN MIXTURE SMOOTHING FOR ORBIT DETERMINATION

The forward filtering solution to the Bayesian estimation problem provides the best possible solution for a probability density function given all past and current data. The backward smoothing solution, by contrast, makes use of all data over a fixed interval, through a fixed data lag, or beyond a fixed point in order to determine an improved solution for the probability density function. Achieving a better understanding of the probabilistic description of the state in orbit determination is key to providing reliable situational awareness. This paper investigates a method of combining forward filtering and backward smoothing solutions for non-Gaussian distributions in the orbit determination problem. A simulation of a low-Earth orbit tracking scenario is considered, where a forward filter/backward smoother is applied to assess and compare the performance of filtering and smoothing recursions in a nonlinear, non-Gaussian orbit determination problem.