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.

翻译：本文提出了一种适用于移动时域估计的自适应鲁棒损失函数框架，通过融合可降低离群点影响的自适应鲁棒损失函数与避免平凡解的正则化项，重点拟合未受污染数据并降低受污染数据的权重。该框架引入调节参数控制损失函数形态，以调整估计器对离群值的鲁棒性。仿真结果表明，自适应过程仅需数次迭代即可完成，而当测量数据无离群点时，传统L₂范数行为仍占主导地位。