The paper considers the optimal filtering problem for systems having one or more stochastic parameters as well as an additive stochastic input. A solution is derived by casting the problem into the general form of non-linear stochastic systems with diffusive Markov solutions. The optimal filter is derived assuming linear measurements and additive noise. Simplification of the optimal filter equations is obtained by approximating the second-order error moment of the optimal estimate and defining a sub-optimal filter. Finally a sensitivity of the sub-optimal filter is defined and its formulation is derived. Simulations of systems with stochastic parameters demonstrate the application of both the sub-optimal filter and its sensitivity