Adaptive upper-bound linear mean square error filter of Markovian jump linear systems with generalized unknown disturbances

This paper presents a novel estimation problem of Markovian jump linear systems (MJLSs) with generalized unknown disturbances (GUDs) in measurements. In these systems, there exist multiple uncertainties such as Markovian switching parameters, the GUD and system noises. Here, the multi-mode complexity in original system is transformed into the randomness of parameters in new system by geometric augmentation. Then, an upper-bound linear mean square error filter (UBLF) is proposed and its existence condition is given. Meanwhile, the minimum upper-bound covariances are derived so that the minimum UBLF (MUBLF) and the corresponding optimal parameters are obtained. The numerical example shows the effectiveness of the proposed filter.