Rao-Blackwellised particle filtering and smoothing for jump Markov non-linear systems with mode observation

This study is concerned with the problem of filtering and fixed-lag smoothing for jump Markov non-linear systems when the mode information can be extracted from an image sensor. Based on the idea of Rao-Blackwellisation, the authors present a general theoretical framework to derive the recursive estimates by employing the particle filtering method. A suboptimal image-enhanced Rao-Blackwellised particle filter is proposed, in which the mode state is estimated by using random sampling and the continuous state as well as the relevant likelihood function are approximated as Gaussian distributions. The one-step fixed-lag smoothing result is also obtained for such systems with lagged mode observations. Performance comparison of the proposed algorithms with the existing methods is provided through a manoeuvring target tracking simulation study.