Characterizing Marginalization and Incremental Operations on the Bayes Tree

Abstract

Perception systems for autonomy are most useful if they can operate within limited/predictable computing resources. Existing algorithms in robot navigation—e.g. simultaneous localization and mapping—employ concepts from filtering, fixed-lag, or incremental smoothing to find feasible inference solutions. Using factor graphs as a probabilistic modeling language, we emphasize the importance of marginalization operations on the equivalent Bayes (junction) tree. The objective is to elucidate the connection between simple tree-based message passing rules with the aforementioned state estimation approaches, and their frequently overlooked relation to direct marginalization on the Bayes tree. We characterize the inherent marginalization operation as part of the fundamental Chapman-Kolmogorov transit integrals which unifies many state-of-the-art approaches. The belief propagation model is then used to define five major tree inference strategies, with regard to computation recycling and resource constrained operation. A series of illustrative examples and results show the versatility of the method.