Outlier-Robust Nonlinear Moving Horizon Estimation using Adaptive Loss Functions

TL;DR

This paper introduces an adaptive robust loss function framework for nonlinear moving horizon estimation that effectively reduces outlier impact by dynamically adjusting the loss function shape.

Contribution

It presents a novel adaptive loss function approach with a tuning parameter, enhancing robustness in MHE against measurement outliers.

Findings

Rapid adaptation within a few iterations to changing data conditions.

Outperforms traditional L2 loss in contaminated measurement scenarios.

Effectively prioritizes uncontaminated data fitting while downweighting outliers.

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.