(Georgia Institute of Technology, 2010)
Dellaert, Frank; Carlson, Justin; Ila, Viorela; Ni, Kai; Thorpe, Charles E.
In this paper we propose an efficient preconditioned
conjugate gradients (PCG) approach to solving large-scale
SLAM problems. While direct methods, popular in the
literature, exhibit quadratic convergence and can be quite
efficient for sparse problems, they typically require a lot of
storage as well as efficient elimination orderings to be found. In
contrast, iterative optimization methods only require access to
the gradient and have a small memory footprint, but can suffer
from poor convergence. Our new method, subgraph preconditioning,
is obtained by re-interpreting the method of conjugate
gradients in terms of the graphical model representation of the
SLAM problem. The main idea is to combine the advantages of
direct and iterative methods, by identifying a sub-problem that
can be easily solved using direct methods, and solving for the
remaining part using PCG. The easy sub-problems correspond
to a spanning tree, a planar subgraph, or any other substructure
that can be efficiently solved. As such, our approach provides
new insights into the performance of state of the art iterative
SLAM methods based on re-parameterized stochastic gradient
descent. The efficiency of our new algorithm is illustrated on
large datasets, both simulated and real.