A Spectral Learning Approach to Range-Only SLAM

We present a novel spectral learning algorithm for simultaneous localization and mapping (SLAM) from range data with known correspondences. This algorithm is an instance of a general spectral system identifi- cation framework, from which it inherits several desirable properties, including statistical consistency and no local optima. Compared with popular batch optimization or multiple-hypothesis tracking (MHT) methods for range-only SLAM, our spectral approach o↵ers guaranteed low computational requirements and good tracking performance. Compared with MHT and with popular extended Kalman filter (EKF) or extended information filter (EIF) approaches, our approach does not need to linearize a transition or measurement model. We provide a theoretical analysis of our method, including finite-sample error bounds. Finally, we demonstrate on a real-world robotic SLAM problem that our algorithm is not only theoretically justified, but works well in practice: in a comparison of multiple methods, the lowest errors come from a combination of our algorithm with batch optimization, but our method alone produces nearly as good a result at far lower computational cost.