An Algorithmic Estimation Scheme for Hybrid Stochastic Systems

In this article we describe a 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 develop is fundamentally distinct from extant methods, such as the so called Interacting Multiple Model algorithm (IMM) in that it is based directly upon the exact hybrid filter dynamics. The enduring and well known obstacle in estimation of jump Markov systems, is managing the geometrically growing history of candidate hypotheses. Our scheme maintains a fixed number of candidate paths in a history, each identified by an optimal subset of estimated mode probabilities. We present here a finite dimensional sub-optimal filter for the information state. Corresponding finite dimensional recursions are also given for the mode probability estimate, the state estimate and is associated state error covariance The memory requirements of our filter are fixed in time. A computer simulation is included to demonstrate performance of the Gaussian-mixture algorithm described.