A novel particle filtering for nonlinear systems with multi-step randomly delayed measurements

For nonlinear discrete-time systems where measurements can be randomly delayed by multiple sampling periods, measurements are dependent conditioned on the state trajectory, and the dependence becomes more complicated with the increase of step of random delay. A particle filtering for this system is developed, which is novel in that the likelihood is computed allowing multi step of delay and dependence of measurements. Multi step of delay is dealt with through utilizing the formula of total probability skillfully, and dependence is dealt with through estimating the filtering probability distribution of random delay. The novel particle filtering is applied to two examples to validate its effectiveness and superiority.