Optimal state estimation for finite-field networks with stochastic disturbances

Abstract

This paper investigates the optimal state estimation of finite-field networks (FFNs) with stochastic disturbances. The stochastic disturbances are regarded as independent noise process. The optimal state estimation problem of FFNs in the sense of minimum mean square error (MMSE) is proposed, and a necessary and sufficient condition is proposed to find the optimal state estimator by minimizing the mean square error (MSE). Moreover, the multi-valued Kalman filter is established, including prediction step and update step, based on which, both optimal state estimator and MMSE can be calculated effectively.