Fig. 1:The main idea in this paper is to combine the advantages of direct and iterative methods: we identify a subgraph that can easily be solved using direct methods, and use that as a preconditioner in conjugate gradients. This is illustrated above with a map of Beijing, where the subgraph is a spanning tree (in black), and the remaining loop-closing constraints are shown in red.Abstract-In this paper we propose an efficient preconditioned conjugate gradients (PCG) approach to solving largescale 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 and 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.

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