This is some recent work on estimation on manifolds, in collaboration with Luca Carlone.
From Angular Manifolds to the Integer Lattice: Guaranteed Orientation Estimation with Application to Pose Graph Optimization.
IEEE Transactions on Robotics, April 2014.
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Pose optimization is what is used in SLAM to optimize the map after pose-pose and pose-features correspondences have been established. The variables in this problem are poses living on the nodes of a graph, and measurements are relative measurements along the graph edges. The problem is hard because orientations live on a manifold with nontrivial topology, which makes the problem nonlinear, nonconvex, and with multiple minima. Luca and I try to solve the subproblem of orientation estimation. We find a way to convert the problem to an unconstrained optimization problem on integers. This makes it possible to solve the problem globally and return all likely guesses for the orientation.