UD-based Linear Filtering for Discrete-Time Systems with Multiplicative and Additive Noises

This paper addresses the problem of constructing new linear filtering algorithms for discrete-time linear stochastic systems with multiplicative and additive noises, which are robust to machine roundoff errors. Two algorithms based on UDUT decomposition of covariance and information matrices are proposed. The first of these algorithms is the UD-based covariance filter, and the second one is the UD-based information filter. Both of these filters have an extended array form, and their computational schemes allow for updating all required filter quantities with the use of the numerically stable MWGS orthogonalization procedure. The results of numerical experiments show the robustness of the proposed algorithms against roundoff errors.