iSAM2: Incremental smoothing and mapping using the Bayes tree

TLDR

A Bayes tree encodes a factored probability density like a clique tree but is directed and aligns naturally with the square‑root information matrix used in SLAM. The paper introduces the Bayes tree data structure to deepen understanding of graphical‑model inference and sparse matrix factorization, and outlines three key insights. The Bayes tree serves as the foundation for iSAM2, a novel incremental nonlinear optimization algorithm that performs variable re‑ordering and fluid relinearization to eliminate periodic batch steps. The Bayes tree clarifies matrix‑factorization relationships, maps updates to tree edits, and iSAM2 achieves superior quality and efficiency compared to recent mapping algorithms on real and simulated datasets.

Abstract

We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root information matrix of the simultaneous localization and mapping (SLAM) problem. In this paper, we highlight three insights provided by our new data structure. First, the Bayes tree provides a better understanding of the matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a matrix factorization translate to a simple editing of the Bayes tree and its conditional densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for sparse nonlinear incremental optimization, named iSAM2, which achieves improvements in efficiency through incremental variable re-ordering and fluid relinearization, eliminating the need for periodic batch steps. We analyze various properties of iSAM2 in detail, and show on a range of real and simulated datasets that our algorithm compares favorably with other recent mapping algorithms in both quality and efficiency.