Particle Smoother for Nonlinear Systems With One-Step Randomly Delayed Measurements

In this paper, a new particle smoother based on forward filtering backward simulation is developed to solve the nonlinear and non-Gaussian smoothing problem when measurements are randomly delayed by one sampling time. The heart of the proposed particle smoother is computation of delayed posterior filtering density based on stochastic sampling approach, whose particles and corresponding weights are updated in Bayesian estimation framework by considering the one-step randomly delayed measurement model. The superior performance of the proposed particle smoother as compared with existing methods is illustrated in a numerical example concerning univariate non-stationary growth model.