Particle filter with one-step randomly delayed measurements and unknown latency probability

In this paper, a new particle filter is proposed to solve the nonlinear and non-Gaussian filtering problem when measurements are randomly delayed by one sampling time and the latency probability of the delay is unknown. In the proposed method, particles and their weights are updated in Bayesian filtering framework by considering the randomly delayed measurement model, and the latency probability is identified by maximum likelihood criterion. The superior performance of the proposed particle filter as compared with existing methods and the effectiveness of the proposed identification method of latency probability are both illustrated in two numerical examples concerning univariate non-stationary growth model and bearing only tracking.