The problem of adaptive estimation of constant parameters in the linear regressor model is studied without the hypothesis that regressor is persistently excited. First, the initial vector estimation problem is transformed to a series of the scalar ones using the method of dynamic regressor extension and mixing. Second, several adaptive estimation algorithms are proposed for the scalar scenario. In such a case, if the regressor is nullified asymptotically or in finite time, then the problem of estimation is also posed on a finite interval of time. Robustness of the proposed algorithms with respect to measurement noise and exogenous disturbances is analyzed. The efficiency of the designed estimators is demonstrated in numeric experiments for academic examples.

中文翻译：

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无激励持续性有限时间鲁棒参数估计

研究了线性回归模型中常数参数的自适应估计问题，不假设回归器是持续激发的。首先，使用动态回归量扩展和混合的方法将初始向量估计问题转化为一系列标量问题。其次，针对标量场景提出了几种自适应估计算法。在这种情况下，如果回归量渐近或在有限时间内无效，那么估计问题也出现在有限时间间隔上。分析了所提出算法在测量噪声和外源干扰方面的稳健性。设计的估计器的效率在学术例子的数值实验中得到了证明。