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

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