Limiting performance of optimal linear discrete filters (Q1398400)

A discrete time system is considered where the process noise, the state, and the output are real vectors, possibly, of different dimensions. It is assumed that the measurement vector is corrupted by an additive zero-mean discrete random stationary white noise vector process, and that the process noise is also a zero-mean discrete random stationary white noise vector process. The limiting performance of the optimal linear \(H_2\)-filter for such a discrete-time system in the case when the intensity of the measurement noise tends to zero, is considered. An explicit expression for the performance limits under small measurement white noise is derived. Fundamental limitations are characterized by the system's order, the dimension of the process noise, and the number of the system's transmission zeros. A direct application of the above results occurs in estimating a slowly varying input disturbance and determining the lowest achievable mean-square error in the estimation.