How far is SLAM from a linear least squares problem?

Abstract

Most people believe SLAM is a complex nonlinear estimation/optimization problem. However, recent research shows that some simple iterative methods based on linearization can sometimes provide surprisingly good solutions to SLAM without being trapped into a local minimum. This demonstrates that hidden structure exists in the SLAM problem that is yet to be understood. In this paper, we first analyze how far SLAM is from a convex optimization problem. Then we show that by properly choosing the state vector, SLAM problem can be formulated as a nonlinear least squares problem with many quadratic terms in the objective function, thus it is clearer how far SLAM is from a linear least squares problem. Furthermore, we explain that how the map joining approaches reduce the nonlinearity/nonconvexity of the SLAM problem.