Cramér–Rao Bounds and Optimal Design Metrics for Pose-Graph SLAM

Two-dimensional (2-D)/3-D pose-graph simultaneous localization and mapping (SLAM) is a problem of estimating set poses based on noisy measurements relative rotations translations. This article focuses the relation between graphical structure SLAM Fisher information matrix (FIM), Cramér-Rao lower bounds (CRLB), its optimal design metrics (T-optimality D-optimality). As main contribution, assumption isotropic Langevin noise for rotation block-isotropic Gaussian translation, FIM CRLB are derived shown to be closely related graph structure, in particular, weighted Laplacian matrix. We also prove that total node degree number spanning trees, as two connectivity metrics, are, respectively, trace determinant FIM. The discussions show that, compared with D-optimality metric, T-optimality metric more easily computed but less effective. present upper which can efficiently almost independent estimation results. results verified several well-known datasets, such Intel, KITTI, sphere, so on.