On the solution of the Zakai equation for the process diagnostics problem

Fault detection and diagnosis is modelled as the nonlinear filtering problem of a linear systems with jumping parameters. Assuming that faults occur according to a stationary finite state Markov process, the optimal filter is represented in terms of a vector Zakai equation. This equation can be solved explicitly in a manner that reveals both the realization as well as the physical meaning of several suboptimal filtering schemes.