New Gaussian mixture state estimation schemes for discrete time hybrid Gauss-Markov systems

In this article we compute state and mode estimation algorithms for discrete-time Gauss-Markov models whose parameter-sets switch according to a known Markov law. Our algorithms are distinct from extant methods, such as the so called interacting multiple model algorithm (IMM) and sequential Monte Carlo methods, in that they are based on exact hybrid filter dynamics. The fundamental difficulty in estimation of jump Markov systems, is managing the geometrically growing history of candidate hypotheses. In our scheme, we address this issue by proposing an extension of an idea due to Viterbi. Our scheme maintains a fixed number of candidate paths in a history, each identified by an optimal subset of estimated mode probabilities. We compute a finite dimensional sub-optimal filter, which estimates the hidden state process and the mode probability. A computer simulation is provided.