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Forward–backward particle smoother for non-linear systems with one-step random measurement delay

Forward–backward particle smoother for non-linear systems with one-step random measurement delay

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This study is concerned with the state smoothing problem for a class of non-linear discrete-time stochastic systems with one-step random measurement delay (ORMD). The main contribution is that the forward–backward particle smoothing scheme is successfully extended to the systems with ORMD. First, the particle filter, specially designed to deal with ORMD, is implemented to obtain the filtering distribution and the joint distribution of state history. Then, by marginalising the joint distribution, the one-step fixed-lag smoothing distribution can be obtained. Finally, based on the forward–backward smoothing scheme, the particle approximation of the fixed-interval smoothing distribution can be obtained by re-weighting the particles which have been used in the foregoing one-step fixed-lag smoothing distribution. Simulation results demonstrate the effectiveness of the proposed smoother.

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