State estimation for discrete-time linear systems with multiplicative and correlated additive noises

In this paper, the state estimation problem for discrete-time linear systems with multiplicative noises and correlated additive noises is considered where the multiplicative noises are continuous random matrices of proper dimensions and occur both in the state and measurement models. Using two typical equalities of the optimal linear mean-square estimate and some results obtained in this paper, an optimal recursive algorithm is proposed in the sense of linear minimum mean-square error. Computer simulations are carried out to demonstrate the performance of the proposed algorithm.