On the performance of Gaussian mixture estimation techniques for dicrete-time jump Markov linear systems

In this article we examine the numerical performance of a new state estimation algorithm for discrete-time Gauss-Markov models, whose parameters are determined at each discrete-time instant by the state of a Markov chain. The scheme we consider is fundamentally distinct from extant methods, such as the so-called Interacting Multiple Model algorithm (IMM) in that it is based directly upon the corresponding exact hybrid filter dynamics. Our new scheme maintains a fixed number of candidate paths in a history, each identified by an optimal subset of estimated mode probabilities. The memory requirements of our filter are fixed in time and can varied by the user to achieve a desired accuracy. Computer simulations are given to demonstrate performance of the Gaussian-mixture algorithm described, against the IMM.