Supervisory Measurement-Guided Noise Covariance Estimation

2025-10-28

AI Summary

Inaccurate calibration of sensor noise covariances severely degrades the robustness of state estimation in multi-sensor fusion. Method: This paper proposes a novel bi-level collaborative optimization framework. It innovatively decomposes the Bayesian joint likelihood into a chain structure, decoupling the nested dependency between odometry and supervisory measurements to enable parallel optimization of trajectory estimation (lower level) and noise covariance adaptation (upper level). The lower level employs an augmented-state invariant extended Kalman filter; the upper level leverages a derivative filter to efficiently compute analytical gradients for iterative covariance refinement. Results: Extensive experiments on both synthetic and real-world datasets demonstrate significant improvements in covariance estimation accuracy and convergence speed, while maintaining favorable computational scalability. The method provides a robust, efficient, and adaptive solution for heterogeneous sensor fusion, particularly under uncertain or time-varying noise statistics.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Reliable state estimation hinges on accurate specification of sensor noise covariances, which weigh heterogeneous measurements. In practice, these covariances are difficult to identify due to environmental variability, front-end preprocessing, and other reasons. We address this by formulating noise covariance estimation as a bilevel optimization that, from a Bayesian perspective, factorizes the joint likelihood of so-called odometry and supervisory measurements, thereby balancing information utilization with computational efficiency. The factorization converts the nested Bayesian dependency into a chain structure, enabling efficient parallel computation: at the lower level, an invariant extended Kalman filter with state augmentation estimates trajectories, while a derivative filter computes analytical gradients in parallel for upper-level gradient updates. The upper level refines the covariance to guide the lower-level estimation. Experiments on synthetic and real-world datasets show that our method achieves higher efficiency over existing baselines.

Problem

• Estimating sensor noise covariances for reliable state estimation
• Addressing covariance identification challenges from environmental variability
• Formulating covariance estimation as bilevel optimization for computational efficiency

Innovation

• Bilevel optimization for noise covariance estimation
• Factorization enabling parallel computation of gradients
• Invariant extended Kalman filter with state augmentation