A variable sample size particle filter

This paper investigates the problem of automatically choosing the number of samples for the particle filter (PF) given a certain confidence interval, and a scheme for an adaptive sample size PF (APF) is proposed. It is well known that a conventional PF uses a fixed number of particles which in practice is selected manually by trial-and-error. The automatic selection of sample size for a given task is therefore essential for reducing unnecessary computation and for optimal performance. Based on the assumption that the confidence probability and interval are pre-specified as constants, we show that the sample size is proportional to the variance of the state estimation error. Monte-Carlo simulations are performed to show that the average number of samples of the proposed APF can be significantly reduced compared to the fixed sample size PF.