The Bayes Tree: Enabling Incremental Reordering and Fluid Relinearization for Online Mapping

Abstract

In this paper we present a novel data structure, the Bayes tree, which exploits the connections between graphical model inference and sparse linear algebra. The proposed data structure provides a new perspective on an entire class of simultaneous localization and mapping (SLAM) algorithms. Similar to a junction tree, a Bayes tree encodes a factored probability density, but unlike the junction tree it is directed and maps more naturally to the square root information matrix of the SLAM problem. This makes it eminently suited to encode the sparse nature of the problem, especially in a smoothing and mapping (SAM) context. The inherent sparsity of SAM has already been exploited in the literature to produce efficient solutions in both batch and online mapping. The graphical model perspective allows us to develop a novel incremental algorithm that seamlessly incorporates reordering and relinearization. This obviates the need for expensive periodic batch operations from previous approaches, which negatively affect the performance and detract from the intended online nature of the algorithm. The new method is evaluated using simulated and real-world datasets in both landmark and pose SLAM settings.