Fault detection in a class of stochastic hybrid systems

We consider the problem of fault detection for a stochastic hybrid system described by a state-space model with the following properties: the state equation evolves continuously in time according to a linear stochastic differential equation; noisy measurements of the continuous state are made available at discrete deterministic times, by a static linear equation; the parameters of both the state evolution and the measurement equation depend on a discrete state described as a continuous-time Markov chain. This model is particularly suitable for those applications where the frequency of measurements is comparable to the "rate of change" of the Markov chain, and allows the discrete state to switch in between measurements. We solve the problem of estimating both the continuous and the discrete state, given the measurements up to a certain time, in an on-line manner. We also provide the results of significant numerical simulations.