Robust Duncan-Mortensen-Zakai equation for non-stationary stochastic systems

The optimal filtering problem for non-stationary stochastic continuous-time observation models is considered. It is known that the problem solution can be found using both the Duncan-Mortensen-Zakai equation and the robust Duncan-Mortensen-Zakai equation. In this paper the special form of the robust Duncan-Mortensen-Zakai equation, where the drift, diffusion, and potential functions are expressed in the way allowing to apply the particle method, is derived.