Optimal H2 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 H2 index is defined and computed for the resulting system with jumps. It is proved that the optimal H2 filter depends on the stabilizing solution of a specific Riccati-type equation. A numerical example illustrates the theoretical developments.