Bayesian estimation for jump Markov linear systems with non-homogeneous transition probabilities

This paper considers the state estimation problem for a class of discrete-time non-homogeneous jump Markov linear systems (JMLSs), where the transition probability matrix (TPM) is assumed to be time-variant and takes value in a finite set randomly at each time step. To show the simplicity brought by the finite-valued hypothesis, the optimal recursion for the posterior TPM probability density functions conditioned on that the TPM belongs to a continuous set is firstly derived. Then, we naturally incorporate the proposed TPM estimation into the recursion of system state. Two interacting multiple-model (IMM)-type approximation stages are employed to avoid the exponential computational requirements. The resulting filter reduces to the IMM filter when the number of candidate TPMs is unity. A meaningful example is presented to illustrate the effectiveness of our method.