Minimum upper-bound filter of Markovian jump linear systems with generalized unknown disturbances

This paper presents the estimation problem of Markovian jump linear systems (MJLSs) with generalized unknown disturbances (GUDs). There exist multiple uncertainties including Markovian switching parameters and GUDs, along with traditional random noises. Here, the state transition of MJLS is treated as the jump from one vertex to another on a fixed polyhedron whose vertex represents a mode. Since the transition is dependent on stochastic Markovian switching parameter, a more general polytopic system with stochastic weights is considered and the corresponding upper-bound filter (UBF) is derived. Then, the MJLS with GUDs is transformed into a special case of the considered polytopic system by letting the corresponding stochastic weight as the binary value constructed by Markovian switching parameters and hence the recursive UBF is obtained. The parameters in the derived UBF are further optimized in pursuit of the minimum upper bounds of estimation error covariances. The simulation via maneuvering target tracking shows the effectiveness of the proposed filter.