The filtering problem for continuous-time linear systems with Markovian switching coefficients

The stochastic model under consideration is a Markovian jump process θ, with finite state space, feeding the parameters of a linear diffusion process x. The processes y and z observe linearly and separately x and θ in independent white noises. Some properties of the finite optimal filter for the x and θ 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.