Online estimation of transition probabilities for nonlinear discrete time systems

Since the Markov transition probability matrix (MTPM) in the interactive multiple model (IMM) based on the unscented Kalman filter (UKF) is a constant value, the IMMUKF algorithm can´t exactly describe the transition probability of each model and produce lots of error in the result. Taking account of this situation, in this paper, a novel method which combines the posterior Cramer-Rao lower bound (PCRLB) with the likelihood ratio is proposed to improve tracking accuracy. PCRLB is calculated by mean and covariance of the estimated online state. The residual covariance that can be used to calculate the likelihood function of each model is updated by substituting PCRLB for the filtering error covariance matrix of UKF. Real-time estimation of MTPM can be obtained according to updated likelihood function and likelihood ratio, and then applied in IMMUKF. An adaptive MTPM IMMUKF algorithm can be obtained. Finally, to verify the correctness and validity, the proposed method is applied to a missile trajectory tracking. The root-mean-square (RMS) error is used as a performance evaluation index. The simulation results show that the proposed algorithm outperforms the IMMUKF algorithm and achieves a RMS tracking performance which is quite close to the PCRLB.