Optimal Filtering for Non-parametric Observation Models: Applications to Localization and SLAM

In this work we address the problem of optimal Bayesian filtering for dynamic systems with observation models that cannot be approximated properly as any parameterized distribution. In the context of mobile robots this problem arises in localization and simultaneous localization and mapping (SLAM) with occupancy grid maps. The lack of a parameterized observation model for these maps forces a sample-based representation, commonly through Monte Carlo methods for sequential filtering, also called particle filters. Our work is grounded on the demonstrated existence of an optimal proposal distribution for particle filters. However, this optimal distribution is not directly applicable to systems with non-parametric models. By integrating ideas from previous works on adaptive sample size, auxiliary particle filters, and rejection sampling, we derive a new particle filter algorithm that enables the usage of the optimal proposal to estimate the true posterior density of a non-parametric dynamic system. This new filter is better suited, both theoretically and in practice, than previous approximate methods for indoor and outdoor localization and SLAM, as confirmed by experiments with real robots.