基于变步长分块滤波器的Volterra级数简化辨识方法

Simplified Volterra Series Identification Method Based on Variable Step Size Block Least Mean Square Filter

针对Volterra级数辨识中的维数灾难问题,提出了一种基于变步长分块最小均方滤波器的Volterra级数简化辨识方法.该方法利用影响指数的概念,在保证一定辨识精度的前提下,对每个Volterra核根据其对辨识的贡献大小进行筛选,再用筛选出的有效核作为对原系统的近似,从而达到降低辨识中核向量维数的目的.同时,该方法将块滤波器的块平均绝对误差与滤波器的步长因子相关联,使得块滤波器的步长因子随着数据块的平均绝对误差而动态调整,改善了辨识的收敛性能.将该方法应用于某型直升机电动舵机的Volterra级数模型的辨识,结果表明,在保证一定精度的前提下,可以将核的数量降低50%以上.

Volterra series identification often surfers from the so called dimension disaster, since the scale of Volterra kernels increases exponentially with increasing system's order or degree. In order to solve this problem, a simplified identification method based on block least mean square (BLMS) filter was proposed, in which the concept of the effective index was applied to select Volterra kernels according to their contributions to Volterra series identification, and then the affective kernels were used to approximate the original Volterra system, so that the dimension of Volterra kernels was reduced. Meanwhile, in order to improve the convergence properties of the identification, the step size of BLMS was made to associate with the absolute mean error of each data blocks. The method has been used to identify the Volterra series model of electric rudders of certain type helicopter and the result indicates that the number of kernels can be reduced more than 50% while keeping relatively high identification accuracy.