Attribution and Uncertainty Behavior of Learned Residual Gyro Correction for Gyro-Stellar Estimation

2026-07-27

AI Summary

This work addresses the insufficient quantification of uncertainty and lack of interpretability in deep learning–based gyroscope bias correction by proposing a one-dimensional convolutional neural network that fuses multi-source sensor inputs to jointly predict angular rate residual corrections and quantify two types of uncertainty. Heteroscedastic modeling estimates aleatoric uncertainty, while model ensembles capture epistemic uncertainty. Innovatively, gradient-based attribution analysis is applied for the first time to the joint outputs of correction and uncertainty, revealing their cooperative mechanisms across different rotation axes and under perturbations, with epistemic uncertainty showing heightened sensitivity to distributional shifts. Experiments demonstrate that the two uncertainties are complementary: epistemic uncertainty effectively discriminates between nominal and perturbed conditions, whereas aleatoric uncertainty increases with perturbation intensity yet exhibits inconsistent calibration, providing a reliable basis for system reliability assessment and fault detection.

Abstract

This work investigates uncertainty decomposition and explainability in a deep learning-based framework for gyroscope bias correction. A 1-D Convolutional Neural Network is trained to predict residual angular rate corrections from multi-sensor inputs, including gyroscope and star tracker measurements. The bias corrections are sent to a flight-representative Gyro-Stellar Estimator. The network produces both mean corrections and input-dependent (heteroscedastic) aleatoric uncertainty, while epistemic uncertainty is estimated via an ensemble of independently trained models. The proposed approach is trained under nominal conditions and evaluated in both nominal and structured perturbations that include additive and temporally correlated noise. Gradient-based attribution methods are applied to both the correction and uncertainty outputs, enabling a decomposition of the evidence that drives state updates and uncertainty estimates. By aggregating attribution patterns across rotational axes and regimes, we reveal axis-specific behaviors and characterize how structured perturbations influence the collaboration between aleatoric and epistemic uncertainty. Uncertainty analysis shows that aleatoric uncertainty increases with perturbation intensity, but the distributions overlap and the calibration is not consistent across regimes. On the other hand, epistemic uncertainty gives a clear signal that gets clearer as the distributional shift happens, showing that the models disagree more. These results show that aleatoric and epistemic uncertainty work well together and that epistemic uncertainty is better at distinguishing between nominal and perturbed operating conditions. The results provide insight into the behavior of hybrid learning-based state estimation components and motivate the use of uncertainty for downstream monitoring and fault detection.

Problem

• uncertainty decomposition
• gyro-stellar estimation
• aleatoric uncertainty
• epistemic uncertainty
• explainability

Innovation

• uncertainty decomposition
• heteroscedastic aleatoric uncertainty
• epistemic uncertainty
• gradient-based attribution
• gyro-stellar estimation