Extensible framework for Rao-Blackwellized Filtering

The Rao-Blackwellized Particle Filter (RBPF) is widely used for high dimensional nonlinear systems, often with a linear Gaussian substructure. However, the RBPF is just a specific method in the class of Rao-Blackwellized Filtering (RBF). This paper analyzes the recursive structure of the RBF from a more general perspective. The research starts from a general system model and studies the interconnected relationships between the two subspaces during the iterations. The results illustrate the working mechanisms of the RBF with an extensible framework for easily building Rao-Blackwellized algorithms with common nonlinear filters. Several examples are given to illustrate how to build new filters using this framework.