Adaptive state estimation for Markov jump linear system with unknown measurement loss and transition probability matrix

State estimation for the Markov jump linear system (MJLS) is a intractable task when the unpredictable measurement loss exists. Although the conventional methods, such as interacting multiple-model method, are widely used in MJLS, their performance still depends on the known transition probability matrix (TPM). In this article, a novel adaptive state estimation method is proposed for MJLS with unknown measurement loss and TPM based on variational Bayesian inference. Specifically, under system state dynamic and measurement loss are independent, the system state, measurement loss probability and TPM are jointly inferred. In particular, when the stochastic measurement loss occurs, a selective learning mechanism is used to the updating of TPM. The efficiency and superiority of the proposed method is verified by a numerical example and a fermenter process compared with the existing methods.