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Outlier-Robust Nonlinear Moving Horizon Estimation using Adaptive Loss Functions

Nestor Deniz, Guido Sanchez, Fernando Auat Cheein, Leonardo Giovanini

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.

Outlier-Robust Nonlinear Moving Horizon Estimation using Adaptive Loss Functions

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 predominates when the measurements are free of outliers.

Paper Structure

This paper contains 10 sections, 15 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Preliminaries
  4. Adaptive Robust Loss Functions
  5. Outliers-robust $\textrm{MHE}$
  6. Algorithm implementation
  7. Robust stability
  8. Experiments and Results
  9. Performance evaluation
  10. Conclusions and Future Works

Figures (3)

  • Figure B1: Adaptive robust loss functions $\rho(r,\alpha,c)$ and $\varphi(r,\alpha,c)$ for different values of $\alpha$.
  • Figure C1: Normalized estimation error reduction per iteration and mean estimation error reduction under scenario (i) (top) and scenario (ii) (middle).
  • Figure C2: Measured, true, and estimated tractor's $x$ and $y$ coordinates for one trial of the experiments. The bottom panel illustrates the trajectory followed by a tractor pulling a trailer.