Quadratic estimation problem in discrete-time stochastic systems with random parameter matrices

This paper addresses the least‐squares quadratic filtering problem in discrete‐time stochastic systems with random parameter matrices in both the state and measurement equations. Defining a suitable augmented system, this problem is reduced to the least‐squares linear filtering problem of the augmented state based on the augmented observations. Under the assumption that the moments, up to the fourth‐order one, of the original state and measurement vectors are known, a recursive algorithm for the optimal linear filter of the augmented state is designed, from which the optimal quadratic filter of the original state is obtained. As a particular case, the proposed results are applied to multi‐sensor systems with state‐dependent multiplicative noise and fading measurements and, finally, a numerical simulation example illustrates the performance of the proposed quadratic filter in comparison with the linear one and also with other filters in the existing literature.