Recursive estimation for Markov jump linear systems with unknown transition probabilities: A compensation approach

This paper considers the minimum mean square error estimation problem for a class of jump Markov linear systems (JMLSs) with unknown transition probabilities (TPs). Compared with other existing estimators, the underlying real but unknown TPs addressed in our method are allowed to be time-variant. The expectation and covariances of residual error in the traditional interacting multiple-model (IMM) algorithm are computed analytically to show that Kalman filter running under true mode can still perform satisfactorily in the presence of wrong TPs. A compensation operator which heuristically modifies the posterior probabilities by adjusting a compensation parameter automatically is then developed. The proposed method is recursive and reduces to IMM method when the compensation parameter goes to value one. Application results for a simulated system are presented to demonstrate the effectiveness.