This paper considers the recursive state estimation problem for a class of Markov jump linear systems(JMLSs)with unknown transition probabilities(TPs).Compared with other existing recursive estimators,the underlying real but unknown TPs to be addressed in our method are allowed to be time-variant.The expectation and covariances of residual error calculated in the interacting multiple model(IMM)algorithm are computed to demonstrate that Kalman filter running under true systems can still perform satisfactorily in the presence of wrong TPs and the various mode probabilities reflect the influences of uncertain TPs.A compensation operator which heuristically modifies the posterior probabilities by adjusting a compensation parameter is then developed.A moving target tracking example of the proposed method is presented to demonstrate the effectiveness.