Analysis of the Unscented Transform for Cooperative Localization with Ranging-Only Information

2025-04-09

AI Summary

This paper addresses the collaborative localization problem for multi-robot systems relying solely on peer-to-peer range measurements. We propose a distributed nonlinear estimation framework that integrates the Unscented Transform (UT) with Covariance Intersection (CI). Unlike conventional Kalman-based approaches, our method avoids requiring prior knowledge of unknown correlations among measurements; UT accurately handles the inherent nonlinearity of range measurements and sensor noise, while CI ensures conservative and consistent fusion of distributed estimates. To the best of our knowledge, this is the first work to apply the UT–CI combination to pure range-based cooperative localization. We theoretically characterize and quantify a divergence risk threshold induced by information reuse in iterative consensus. Extensive evaluation demonstrates robust performance under high measurement noise and strong nonlinearity. The proposed framework provides both verifiable theoretical guarantees and a practical algorithmic solution for resource-constrained distributed localization systems.

Technology Category

• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Cooperative localization in multi-agent robotic systems is challenging, especially when agents rely on limited information, such as only peer-to-peer range measurements. Two key challenges arise: utilizing this limited information to improve position estimation; handling uncertainties from sensor noise, nonlinearity, and unknown correlations between agents measurements; and avoiding information reuse. This paper examines the use of the Unscented Transform (UT) for state estimation for a case in which range measurement between agents and covariance intersection (CI) is used to handle unknown correlations. Unlike Kalman Filter approaches, CI methods fuse complete state and covariance estimates. This makes formulating a CI approach with ranging-only measurements a challenge. To overcome this, UT is used to handle uncertainties and formulate a cooperative state update using range measurements and current cooperative state estimates. This introduces information reuse in the measurement update. Therefore, this work aims to evaluate the limitations and utility of this formulation when faced with various levels of state measurement uncertainty and errors.

Problem

• Improving position estimation with peer-to-peer range measurements
• Handling uncertainties from sensor noise and unknown correlations
• Avoiding information reuse in cooperative localization

Innovation

• Unscented Transform handles state estimation uncertainties
• Covariance Intersection fuses state and covariance estimates
• Range measurements update cooperative state information