The paper proposes to identify the parameters of linear dynamic models based on the original implementation of least absolute deviation estimators. It is known that the object estimation procedures synthesized in the sense of the least sum of absolute prediction errors are particularly resistant to occasional outliers and gaps in the analyzed system data series, while the classical least squares procedure unfortunately becomes of little use for reliably identifying systems in the presence of destructive measurement errors. Bearing in mind that the classic task of minimizing the quality functional of absolute deviations encounters fundamental analytical problems, it is proposed to use a dedicated iterative estimator for off-line evaluation of the parameters of the analyzed process. In addition, a simplified recursive version of the absolute deviation estimation procedure was developed, which allows for practical on-line tracking of the evolution of variable parameters of non-stationary systems. Importantly, a novel refinement of the discussed absolute deviation estimators was proposed to effectively overcome some inconvenient numerical effects. We also present an interesting comparison of the improved (by non-linear modification) iterative absolute-deviation estimator with the classical Gauss-Newton gradient algorithm, which leads to constructive conclusions. Finally, using computer simulations, the operation of the developed iterative and recursive estimators minimizing the absolute deviation is illustrated. The work ends with an indication of directions for further research.

中文翻译：

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用于异常值识别的平滑最小绝对偏差估计器


本文提出基于最小绝对偏差估计器的原始实现来识别线性动态模型的参数。众所周知，在绝对预测误差最小和的意义上综合的对象估计过程特别能抵抗所分析的系统数据系列中的偶然异常值和间隙，而不幸的是，经典的最小二乘过程对于可靠地识别系统几乎没有用处。存在破坏性测量误差的情况下。考虑到最小化绝对偏差的质量函数的经典任务会遇到基本的分析问题，因此建议使用专用的迭代估计器来对分析过程的参数进行离线评估。此外，还开发了绝对偏差估计程序的简化递归版本，它允许对非平稳系统的可变参数的演化进行实际的在线跟踪。重要的是，提出了对所讨论的绝对偏差估计器的新颖改进，以有效克服一些不方便的数值效应。我们还对改进的（通过非线性修改）迭代绝对偏差估计器与经典高斯-牛顿梯度算法进行了有趣的比较，从而得出了建设性的结论。最后，使用计算机模拟，说明了所开发的迭代和递归估计器最小化绝对偏差的操作。该工作结束时指出了进一步研究的方向。