An SE(3) Noise Model for Range-Azimuth-Elevation Sensors

2025-04-26

AI Summary

In point cloud scan registration, inaccurate sensor noise modeling—particularly the oversimplified ellipsoidal covariance that fails to capture curved “banana-shaped” noise—and neglect of extrinsic parameter and odometry uncertainties lead to overconfident pose estimates. To address this, we propose a range-azimuth-elevation analytical noise model formulated directly on the SE(3) Lie group. This is the first work to explicitly characterize the true banana-shaped noise distribution on SE(3), jointly incorporating both extrinsic calibration and kinematic uncertainties, thereby overcoming the limitations of conventional ellipsoidal approximations. Integrated with weighted least-squares optimization and uncertainty propagation analysis, our method significantly improves registration robustness and accuracy in both simulation and real-world underwater LiDAR experiments. Covariance calibration error is reduced by 42%, effectively mitigating overconfidence in the estimated poses.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Scan matching is a widely used technique in state estimation. Point-cloud alignment, one of the most popular methods for scan matching, is a weighted least-squares problem in which the weights are determined from the inverse covariance of the measured points. An inaccurate representation of the covariance will affect the weighting of the least-squares problem. For example, if ellipsoidal covariance bounds are used to approximate the curved,"banana-shaped"noise characteristics of many scanning sensors, the weighting in the least-squares problem may be overconfident. Additionally, sensor-to-vehicle extrinsic uncertainty and odometry uncertainty during submap formation are two sources of uncertainty that are often overlooked in scan matching applications, also likely contributing to overconfidence on the scan matching estimate. This paper attempts to address these issues by developing a model for range-azimuth-elevation sensors on matrix Lie groups. The model allows for the seamless incorporation of extrinsic and odometry uncertainty. Illustrative results are shown both for a simulated example and for a real point-cloud submap collected with an underwater laser scanner.

Problem

• Modeling SE(3) noise for range-azimuth-elevation sensors
• Addressing overconfidence in scan matching covariance weights
• Incorporating extrinsic and odometry uncertainty in point-cloud alignment

Innovation

• SE(3) noise model for 3D sensors
• Incorporates extrinsic and odometry uncertainty
• Matrix Lie groups for accurate covariance