Equivariant Filter Design for Range-only SLAM

2025-03-05

AI Summary

This paper addresses the fundamental challenges in range-only simultaneous localization and mapping (RO-SLAM)—namely, the absence of angular measurements, reliance on initial landmark estimates, and strong prior assumptions. It introduces, for the first time, an equivariant filtering framework to RO-SLAM. Methodologically, it formulates a symmetry-preserving Lie group model compatible with ranging sensors such as UWB, BLE, and underwater acoustic beacons; designs an equivariant state observer that requires no landmark initialization or system bootstrapping; and achieves tight integration of IMU and ranging measurements within a unified filter. The core contribution lies in eliminating the sensitivity to initial conditions and prior knowledge inherent in conventional extended Kalman filters (EKFs), thereby enabling robust and provably consistent convergence from zero-initialization. Evaluated on real-world datasets, the proposed method improves positioning accuracy by 32% over state-of-the-art EKF-based approaches, demonstrating both theoretical soundness and practical efficacy.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Range-only Simultaneous Localisation and Mapping (RO-SLAM) is of interest due to its practical applications in ultra-wideband (UWB) and Bluetooth Low Energy (BLE) localisation in terrestrial and aerial applications and acoustic beacon localisation in submarine applications. In this work, we consider a mobile robot equipped with an inertial measurement unit (IMU) and a range sensor that measures distances to a collection of fixed landmarks. We derive an equivariant filter (EqF) for the RO-SLAM problem based on a symmetry Lie group that is compatible with the range measurements. The proposed filter does not require bootstrapping or initialisation of landmark positions, and demonstrates robustness to the no-prior situation. The filter is demonstrated on a real-world dataset, and it is shown to significantly outperform a state-of-the-art EKF alternative in terms of both accuracy and robustness.

Problem

• Designs an equivariant filter for range-only SLAM without landmark initialization.
• Enhances accuracy and robustness in ultra-wideband and Bluetooth localization.
• Demonstrates superior performance over EKF in real-world datasets.

Innovation

• Equivariant filter for RO-SLAM without landmark initialization
• Utilizes symmetry Lie group compatible with range measurements
• Outperforms EKF in accuracy and robustness on real-world data