Analysis of Rank-Based Resampling Based on Particle Diversity in the Rao–Blackwellized Particle Filter for Simultaneous Localization and Mapping

Abstract

In order to solve the simultaneous localization and mapping (SLAM) problem of mobile robots, the Rao–Blackwellized particle filter (RBPF) has been intensively employed. However, it suffers from particle depletion problem, i.e., the number of distinct particles becomes smaller during the SLAM process. As a result, the particles optimistically estimate the SLAM posterior, meaning that particles tend to underestimate their own uncertainty and the filter quickly becomes inconsistent. The main reason of loss of particle diversity is the resampling process of RBPF-SLAM. Standard resampling algorithms for RBPF-SLAM cannot preserve particle diversity due to the behavior of their removing and replicating particles. Thus, we propose rank-based resampling (RBR), which assigns selection probabilities to resample particles based on the rankings of particles. In addition, we provide an extensive analysis on the performance of RBR, including scheduling of resampling. Through the simulation results, we show that the estimation capability of RBPF-SLAM by RBR outperforms that by standard resampling algorithms. More importantly, RBR preserves particle diversity much longer, so it can prevent a certain particle from dominating the particle set and reduce the estimation errors. In addition, through consistency tests, it is shown that RBPF-SLAM by the standard resampling algorithms is optimistically inconsistent, but RBPF-SLAM by RBR is so pessimistically inconsistent that it gives a chance to reduce the estimation errors.