Optimal filtering for a class of linear stochastic systems with sampling

This paper presents a Kalman-type filtering problem for a class of linear continuous-time stochastic systems with state-dependent noise and sampled measurements. The admissible class of filters is represented using dynamic models with finite jumps. Then an H 2 index is defined and computed for the resulting system with jumps. It is proved that the optimal H 2 filter depends on the stabilizing solution of a specific Riccati-type equation. A numerical example illustrates the theoretical developments.