Multirate output functional filter design and control

The Kalman filter is a recursive estimator for a linear dynamic system with uncorrelated white process and measurement noises. In this paper, we consider the problem of unbiased minimum-variance functional estimation for linear discrete-time stochastic systems. The proposed method is based on multirate sampling of plant output. The necessary and sufficient conditions for the existence of the functional filter are given and the stability of the filter is discussed. A numerical example is considered to demonstrate the procedure and efficacy of the approach.