A Spectral Learning Approach to Range-Only SLAM
This work addresses the challenge of efficient and accurate SLAM for robotics, offering a method that is theoretically consistent and computationally efficient, though it appears incremental as it builds on existing spectral frameworks.
The paper tackles the problem of simultaneous localization and mapping (SLAM) using range-only data by introducing a spectral learning algorithm that avoids linearization errors common in methods like EKF and EIF. It demonstrates that the algorithm achieves low computational costs and competitive tracking performance, with nearly as good results as batch optimization at far lower cost in real-world robotic tests.
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 identification 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 offers guaranteed low computational requirements and good tracking performance. Compared with popular extended Kalman filter (EKF) or extended information filter (EIF) approaches, and many MHT ones, our approach does not need to linearize a transition or measurement model; such linearizations can cause severe errors in EKFs and EIFs, and to a lesser extent MHT, particularly for the highly non-Gaussian posteriors encountered in range-only SLAM. 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.