This study introduces an enhanced recursive least-squares algorithm that applies the adaptive accelerated proximal gradient method to identify Auto-Regressive Exogenous models with output outliers. First, the outlier problem was converted into a robust principal component analysis problem. The adaptive accelerated proximal gradient method is then introduced to recover the information matrix, and the recursive least squares algorithm is applied to estimate the model parameters. Furthermore, we demonstrated that the parameter estimation is unbiased and that the parameter estimation error converges to zero under persistent excitation. A series of bench tests consistently highlighted the practicality and effectiveness of the proposed algorithm.

中文翻译：

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具有异常值的自回归外生模型的自适应加速近端梯度算法


本研究引入了一种增强的递归最小二乘算法，该算法应用自适应加速近端梯度法来识别具有输出异常值的自回归外生模型。首先，将异常值问题转化为鲁棒主成分分析问题。然后引入自适应加速近端梯度法来恢复信息矩阵，并应用递归最小二乘算法来估计模型参数。此外，我们证明了参数估计是无偏的，并且在持续激励下参数估计误差收敛到零。一系列的台架测试一致凸显了所提出算法的实用性和有效性。