Expectation Propagation With Context Adjustment for Smoothing of Jump Markov Linear Systems

A fixed interval smoother for jump Markov linear systems (JMLSs) is proposed in the framework of expectation propagation (EP). The concept of context adjustment is introduced into EP to avoid/alleviate indefinite covariance problem encountered in standard EP implementations in a systematic way. Kullback–Leibler projection problem for factors involving pseudo-Gaussian likelihoods, which are not proper density functions, is solved and the results are used in the backward pass of the proposed smoother. The simulation results on several scenarios where standard EP has numerical problems show that the proposed smoother has a similar or better performance compared to the alternative methods, which keep the same summary statistics in the literature.