一种特殊白化滤波器的广义最小二乘法

 本文提出一种采用特殊白化滤波器的广义最小二乘法,简记为GLS（SF）。这种算法中不需要单独估计白化滤波器的阶次及参数,只需迭代估计模型参数,算法简单,准确度和收敛性也较好。对于输入噪声较小、输出端测量噪声近似白噪声的系统来说,文中证明,用此算法所得模型输出与系统输出观测值之误差平方和最小。文中给出几个实际动态校准中建立动态数学模型的例子。

A GENERALIZED LEAST SQUARE METHOD WITH SPECIAL WHITENING FILTER

A generalized least square method with special whitening filter GLS （SF） is provided in this paper. The parameters of its whitening filter are a part of model parameters, and in consequence the computational method is simplified. The GLS（SF） is superior to the traditional GLS in estimation accuracy because it gets rid of the error due to incorrect choice of the order of the whitening filter. A lot of computational results show that the convergency of GLS（SF） is also better thean that of GLS, therefore GLS （SF） is a GLS method but with simpler algorithm, more accuracy and better convergency. It is proved that the square sum of errors between model output and observed output data is minimum for the system in which the input noise is small and the output measurement noise appximates to white noise. The mathematical model obtained by this method is better than that of the traditional GLS. An example of building up dynamic mathematical model in dynamic calibration is given. The numerical results show that this method is feasible and the modeling effect is quite well.