Particle filter for estimating multi-sensor systems using one- or two-step delayed measurements

In this paper, we focus on designing a particle filter for a class of nonlinear discrete-time stochastic systems, where the multi-sensor measurements can be randomly and asynchronously delayed by one- or two- sampling periods. Under the independence assumption of multi-sensor delays, asynchronous delay model is built by using a separate set of Bernoulli random variables to describe the relationship between the ideal measurement and the actual measurement for each sensor. Based on the model, a new weighting scheme for particles is derived with the measurement delay fully considered. By incorporating the weighting scheme into the particle filtering framework, we obtain a new filter for systems with delayed measurements. The performance of the proposed filter is demonstrated by two numerical examples.