State estimation for Markovian Jump Linear Systems with bounded disturbances

In this paper, we investigate the state estimation problem for a class of Markovian Jump Linear Systems (MJLSs) in the presence of bounded polyhedral disturbances. A set-membership estimation algorithm is first proposed to find the smallest consistent set of all possible states, which is shown to be expressed by a union of multiple polytopes. The posterior probabilities of the system jumping modes are then estimated by introducing the Lebesgue measure, based on which the optimal point estimate is further provided. Moreover, a similarity relationship for polytopes is defined and an approximate method is presented to calculate the Minkowski sum of polytopes, which can help reduce the computational complexity of the overall estimation algorithm.