(Georgia Institute of Technology, 2006-08)
Krauthausen, Peter; Kipp, Alexander; Dellaert, Frank
The computational complexity of SLAM is dominated
by the cost of factorizing a matrix derived from the measurements
into a square root form, which has cubic complexity
in the worst case. However, the matrices associated with the full
SLAM problem are typically very sparse, as opposed to the dense
problems one obtains in a filtering context. Hence much faster,
sparse factorization algorithms can be used. Furthermore, the
cost can be further reduced by choosing a good order in which
to eliminate variables during the factorization process, leading
to more or less fill-in. In particular, in this paper we investigate
how a nested dissection ordering method can provably improve
the performance of the full SLAM algorithm. We show that the
computational complexity for the factorization of a large class of
measurement matrices occurring in the SLAM problem can be
tightly bound under reasonable assumptions.