State estimation of discrete‐time systems with arbitrarily correlated noises

SUMMARY In this paper, the state estimation problem for discrete‐time systems is considered where the noises affecting such systems do not require any constraint condition for the correlation and distribution, that is, the noises can be arbitrarily correlated and arbitrarily distributed random vector. For this, two filtering algorithms based on the criterion of linear minimum mean‐square error are proposed. The first algorithm is an optimal algorithm that can exactly compute the linear minimum mean‐square error estimate of system states. The second algorithm is a suboptimal algorithm that is proposed to reduce the computation and storage load of the proposed optimal algorithm. Computer simulations are carried out to evaluate the performance of the proposed algorithms.