Analyzing Gaussian proposal distributions for mapping with Rao-Blackwellized particle filters

Particle filters are a frequently used filtering technique in the robotics community. They have been successfully applied to problems such as localization, mapping, or tracking. The particle filter framework allows the designer to freely choose the proposal distribution which is used to obtain the next generation of particles in estimating dynamical processes. This choice greatly influences the performance of the filter. Many approaches have achieved good performance through informed proposals which explicitly take into account the current observation. A popular approach is to approximate the desired proposal distribution by a Gaussian. This paper presents a statistical analysis of the quality of such Gaussian approximations. We also propose a way to obtain the optimal proposal in a non-parametric way and then identify the error introduced by the Gaussian approximation. Furthermore, we present an alternative sampling strategy that better deals with situations in which the target distribution is multi-modal. Experimental results indicate that our alternative sampling strategy leads to accurate maps more frequently that the Gaussian approach while requiring only minimal additional computational overhead.