Good , Bad and Ugly Graphs for SLAM

This paper studies the relation between the graphical structure of simultaneous localization and mapping (SLAM) and the D-criterion. In particular, we define a new connectivity metric for graphs based on the number of spanning trees, and prove that our metric is closely related to the log-determinant of (i) the covariance matrix of the maximum likelihood estimator, and (ii) the Cramér-Rao bound on the highest achievable “accuracy” by unbiased estimators. We also propose an efficient algorithm to compute our metric in large graphs. Our theoretical results are validated using publicly available datasets.

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