A Spectral Learning Approach to Range-Only SLAM

TL;DR

This paper introduces a spectral learning algorithm for range-only SLAM that is statistically consistent, computationally efficient, and avoids linearization errors common in traditional methods, demonstrating strong practical performance.

Contribution

The paper presents a novel spectral approach to range-only SLAM that guarantees low computational complexity and avoids linearization, with proven theoretical properties and practical effectiveness.

Findings

Spectral SLAM achieves low error comparable to batch optimization.

The method is statistically consistent and free of local optima.

It demonstrates practical efficiency on real-world robotic SLAM tasks.

Abstract

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.