Outlier-Robust Nonlinear Moving Horizon Estimation using Adaptive Loss Functions

2026-04-06

AI Summary

This work addresses the significant degradation in state estimation performance caused by measurement outliers in nonlinear moving horizon estimation. To mitigate this issue, an adaptive robust loss function framework is proposed, which incorporates a tunable-shape robust loss combined with a regularization term. This approach preserves the estimator’s ability to fit inliers while automatically down-weighting outliers and dynamically adjusting its robustness. Theoretical analysis and simulation results demonstrate that the method requires only a few iterations to complete the adaptive adjustment process. In the absence of outliers, it recovers the performance of standard L2 estimation, thereby achieving substantially enhanced robustness without compromising estimation accuracy.

Abstract

In this work, we propose an adaptive robust loss function framework for MHE, integrating an adaptive robust loss function to reduce the impact of outliers with a regularization term that avoids naive solutions. The proposed approach prioritizes the fitting of uncontaminated data and downweights the contaminated ones. A tuning parameter is incorporated into the framework to control the shape of the loss function for adjusting the estimator's robustness to outliers. The simulation results demonstrate that adaptation occurs in just a few iterations, whereas the traditional behaviour $\mathrm{L_2}$ predominates when the measurements are free of outliers.

Problem

• outlier-robust
• nonlinear moving horizon estimation
• adaptive loss functions
• state estimation
• robustness

Innovation

• adaptive loss function
• outlier-robust estimation
• moving horizon estimation
• regularization
• nonlinear estimation