一种含有异常值数据的鲁棒辨识算法

A Robust Identification Algorithm for ARX Model of Linear System with Abnormalities Present

在回归问题中，当存在坏数据或异常值时，Ｈｕｂｅｒ方法是一种有效的稳健估计方法。将Ｈｕｂｅｒ的极小极大方法推广到ＡＲＸ模型的参数鲁棒辨识，并得到了系统参数的不确定性区间的估计，最后给出了仿真算例。

Abnormalities in linear system often make identification results bad if not unusable. The MinMax approach of Huber could give good identification results for a relatively simple linear system. We succeeded in extending Huber′s approach to the relatively complex ARX model of linear system. Our extension of Huber′s MinMax approach to ARX model was accomplished with a recursive algorithm. The mathematical derivation involved eqs. (1) through (10). The recursive algorithm required the use of some of these equations, particularly eq. (8). In addition to the equations, the algorithm also required proper handling of the initial values of parameters as explained by us when deriving these equations. Numerical simulation was done and the simulation results in the first two rows of Table 1 show that results computed by the algorithm are close to real values. Eq.(12), though not directly related to our algorithm, is a very important relationship which we obtained. With it, we can compute the uncertainty interval of each parameter, which is useful in design of robust controller.