THE FILTERING PROBLEM FOR CONTINUOUS-TIME LINEAR-SYSTEMS WITH MARKOVIAN SWITCHING COEFFICIENTS

The stochastic model under consideration is a Markovian jump process t heta, with finite state space, feeding the parameters of a linear diff usion process x. The processes y and z observe linearly and separately x and theta in independent white noises. Some properties of the finit e optimal filter for the x and theta processes given the history of me asurements z are investigated. Apart from their theoretical interest, these results have an interesting practical bearing on the general fil tering problem, by providing a natural finite suboptimal solution. Pre liminary experimental results show the effectiveness of our approach t o estimate the state trajectory, even with a relatively low signal-to- noise ratio on the measurement processes.