Hybrid Sampling-Based Particle Filtering With Temporal Constraints

This article presents the state estimation problem of nonlinear dynamic stochastic systems with temporal constraints, depicting the nonlinear interval relationship between states at two successive time instants for the first time. To this end, a hybrid sampling-based particle filter (HSPF) with temporal constraints is proposed by integrating the acceptance–rejection sampling, the repeat sampling, and the sample-to-sample sampling via online optimization, where a decision criterion of improving sampling efficiency is designed to determine whether or not the repeat sampling is activated and a simple sequential quadratic programming (SSQP) is derived to mitigate the computational burden of particle optimizations. Next, compared with filters without introducing temporal constraints, we find that the number of effective particles increases, and the differential entropy of the probability density function as a measure of uncertainty is small, implying that fusing more extra information will help to improve the accuracy of estimates. Finally, two simulation scenarios verify the performance of the proposed filter with temporal constraints.