基于正交基函数的广义FIR模型辨识方法

为了解决高阶脉冲响应模型带来的分析和计算上的困难，利用系统的部分已知信息构造正交基函数，并将其引入到传统脉冲响应建模中，提出了一种广义脉冲响应模型辨识方法。该方法通过正交基函数对输入数据进行滤波，使得滤波后的数据蕴涵着系统的部分动态特性，但也使滤波后的数据不再满足时移特性，因而无法直接使用梯度算法对模型参数进行辨识。结合递推最小二乘原理，给出了模型参数的计算公式。最后给出了仿真算例，结果表明，给出的方法具有优良的性能，完全能够满足系统建模要求。

Generalized FIR model identification method based on orthonormal basis functions

To solve the problem of analysis and computation during using a finite impulse response (FIR) model with high orders, orthonormal basis functions are constructed by utilizing partial system information and then introduced into traditional FIR modeling. A generalized FIR modeling method is proposed. This method pre-filters input data by the orthonormal basis functions in order to get some dynamic characteristics. Unfortu-nately, the gradient algorithm could not be directly used in parameter identification because the pre-filtered data do not have time shift characteristic anymore. Combined with the principle of reeursive least mean squares, the parameter calculation formulas are presented. Lastly a numerical example is studied. The results shows that the generalized FIR modeling method has good performances and can fully satisfy the requirement of system identifi-cation.