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 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

Incremental Sparse GP Regression for Continuous-time Trajectory Estimation & Mapping

Recent work on simultaneous trajectory estimation and mapping (STEAM) for mobile robots has found success by representing the trajectory as a Gaussian process. Gaussian processes can represent a continuous-time trajectory, elegantly handle asynchronous and sparse measurements, and allow the robot to query the trajectory to recover its estimated position at any time of interest. A major drawback of this approach is that STEAM is formulated as a batch estimation problem. In this paper we provide the critical extensions necessary to transform the existing batch algorithm into an extremely efficient incremental algorithm. In particular, we are able to vastly speed up the solution time through efficient variable reordering and incremental sparse updates, which we believe will greatly increase the practicality of Gaussian process methods for robot mapping and localization. Finally, we demonstrate the approach and its advantages on both synthetic and real datasets.Comment: 10 pages, 10 figure