Selecting good measurements via ℓ1 relaxation: A convex approach for robust estimation over graphs

Pose graph optimization is an elegant and efficient formulation for robot localization and mapping. Experimental evidence suggests that, in real problems, the set of measurements used to estimate robot poses is prone to contain outliers, due to perceptual aliasing and incorrect data association. While several related works deal with the rejection of outliers during pose estimation, the goal of this paper is to propose a grounded strategy for measurements selection, i.e., the output of our approach is a set of “reliable” measurements, rather than pose estimates. Because the classification in inliers/outliers is not observable in general, we pose the problem as finding the maximal subset of the measurements that is internally coherent. In the linear case, we show that the selection of the maximal coherent set can be (conservatively) relaxed to obtain a linear programming problem with ℓ₁ objective. We show that this approach can be extended to (nonlinear) planar pose graph optimization using similar ideas as our previous work on linear approaches to pose graph optimization. We evaluate our method on standard datasets, and we show that it is robust to a large number of outliers and different outlier generation models, while entailing the advantages of linear programming (fast computation, scalability).