Abstract
We consider the identification problem for a linear system when the variances of the system and/or the observation noises take on two unknown values. It is assumed that the system and observation noises can be represented in terms of Bernoulli sequences and two random variables with specified but unknown variances. We propose an algorithm to simultaneously estimate the unknown variances and the switching parameters by applying the EM (expectation-maximization) algorithm, avoiding non-linear optimizations that arise in the Maximum Likelihood (ML) and the Maximum A Posteriori (MAP) estimations. Several numerical examples are given to illustrate the effectiveness of the present algorithm.
