(Georgia Institute of Technology, 2012-02)
Kaess, Michael; Johannsson, Hordur; Roberts, Richard; Ila, Viorela; Leonard, John; Dellaert, Frank
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.
(Georgia Institute of Technology, 2011)
Kaess, Michael; Johannsson, Hordur; Roberts, Richard; Ila, Viorela; Leonard, John; Dellaert, Frank
We present iSAM2, a fully incremental, graphbased
version of incremental smoothing and mapping (iSAM).
iSAM2 is based on a novel graphical model-based interpretation
of incremental sparse matrix factorization methods, afforded by
the recently introduced Bayes tree data structure. The original
iSAM algorithm incrementally maintains the square root
information matrix by applying matrix factorization updates.
We analyze the matrix updates as simple editing operations
on the Bayes tree and the conditional densities represented by
its cliques. Based on that insight, we present a new method
to incrementally change the variable ordering which has a
large effect on efficiency. The efficiency and accuracy of the
new method is based on fluid relinearization, the concept of
selectively relinearizing variables as needed. This allows us
to obtain a fully incremental algorithm without any need for
periodic batch steps. We analyze the properties of the resulting
algorithm in detail, and show on various real and simulated
datasets that the iSAM2 algorithm compares favorably with
other recent mapping algorithms in both quality and efficiency.