Handling Particle Filter Sample Impoverishment for Orbit Determination

Abstract

The paper aims at discussing techniques for managing one implementation issue that often arises in the application of particle filters: sample impoverishment. Dealing with such problem can significantly improve the performance of particle filters, and can make the difference between success and failure. Sample impoverishment occurs because of the reduction in the number of truly distinct sample values. Eventually, all of the particles will collapse to the same va1ue, and the problem is intensified when modelling errors occur. A simple solution can be to increase the number of particles, which can quickly lead to unreasonable computational demands and often only delays the inevitable sample impoverishment. There are more intelligent ways of dealing with this problem, such as roughening and prior editing, procedures to be discussed herein. The nonlinear particle filter is based on the bootstrap filter for implementing recursive Bayesian filters. The application consists of determining the orbit of an artificial satellite using real data from the GPS receivers. The nonlinear problem of orbit determination consists essentially of estimating values that completely specify the body trajectory in the space, processing a set of observations, like space GPS receivers on-board the satellite. From this set is possible to obtain nonlinear measurements (pseudo-ranges) that can be processed to estimate the orbital state. The standard differential equations describing the orbital motion and the GPS measurements equations are adapted for the nonlinear particle filter, so that the bootstrap algorithm is also used for estimating the orbital state. The evaluation will be done through convergence speed and computational implementation complexity, comparing the bootstrap algorithm results obtained for each technique that deals with sample impoverishment. Based on the analysis of such criteria, the advantages and drawbacks of the implementations will be presented.