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

Uthman Olawoye, Cagri Kilic, Jason N Gross

TL;DR

This paper tackles cooperative localization when agents have access only to inter-agent range measurements, a setting challenged by nonlinearities and unknown correlations. It proposes an integrated UT+SCI framework: the Unscented Transform handles nonlinear propagation of uncertainty from range measurements, while Split Covariance Intersection conservatively fuses estimates under unknown cross-correlations. A standard Kalman Filter estimates the reliable agent, and UT propagates its information to the second agent, with SCI ensuring consistency in the fusion. Monte Carlo simulations in a 2D setting show the approach attains robust localization with RMSE in the low-to-mid single digits under moderate noise, and reveal sensitivity primarily to positioning noise and trajectory observability. The work contributes a practical, conservative two-robot ranging-only localization method suitable for GPS-denied or communication-constrained environments, with plans to extend to 3D, additional sensors, and adaptive fusion weighting.

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.

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

TL;DR

This paper tackles cooperative localization when agents have access only to inter-agent range measurements, a setting challenged by nonlinearities and unknown correlations. It proposes an integrated UT+SCI framework: the Unscented Transform handles nonlinear propagation of uncertainty from range measurements, while Split Covariance Intersection conservatively fuses estimates under unknown cross-correlations. A standard Kalman Filter estimates the reliable agent, and UT propagates its information to the second agent, with SCI ensuring consistency in the fusion. Monte Carlo simulations in a 2D setting show the approach attains robust localization with RMSE in the low-to-mid single digits under moderate noise, and reveal sensitivity primarily to positioning noise and trajectory observability. The work contributes a practical, conservative two-robot ranging-only localization method suitable for GPS-denied or communication-constrained environments, with plans to extend to 3D, additional sensors, and adaptive fusion weighting.

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.

Paper Structure

This paper contains 10 sections, 16 equations, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Methodology
  4. Kalman Filter
  5. Unscented Transform
  6. Split Covariance Intersection
  7. Unscented Transform with Split Covariance Intersection
  8. Experimental Design
  9. Results
  10. Conclusion and Future work

Figures (8)

  • Figure 1: Two-Robot Localization Scenario with Inter-Vehicle Range Measurements
  • Figure 2: Architecture of the Proposed method
  • Figure 3: The three distinct paths taken by Robot 2. The red line represents the true position of the robot, and the black line indicates the estimate obtained using the proposed method. The red ellipse is the uncertainty around the estimated position.
  • Figure 4: Effect of Range Variance on RMSE
  • Figure 5: Effect of Positioning solution uncertainty on RMSE
  • ...and 3 more figures