Supervisory Measurement-Guided Noise Covariance Estimation
Haoying LI, Yifan Peng, Xinghan Li, Junfeng Wu
AI summary
Problem
Accurate sensor noise covariance specification is vital for reliable robotic state estimation but remains difficult to determine due to environmental changes and preprocessing artifacts. Existing calibration methods often fail to balance full information utilization with computational tractability.
Approach
The method factorizes the joint likelihood into odometry and supervisory losses, casting covariance estimation as a bilevel optimization problem. This structure enables a State Filter and a Derivative Filter to run in parallel, efficiently computing trajectories and analytical gradients for covariance updates.
Key results
- Likelihood factorization into odometry and supervisory losses for bilevel optimization
- Parallel State and Derivative Filters for efficient trajectory and gradient computation
- Closed-form analytical gradients for both loss components
- Demonstrated accuracy and superior computational efficiency on synthetic and real-world datasets
Why it matters
Enables robust, scalable sensor calibration for robotic SLAM and navigation systems without requiring ground-truth trajectory data.
Abstract
Reliable state estimation hinges on accurate speci- fication of sensor noise covariances, which weigh heterogeneous measurements. In practice, these covariances are difficult to identify due to environmental variability, front-end prepro- cessing, 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 than existing baselines.