对角双线性模型辨识基础与谱分析

由于能对非线性系统很好的近似，双线性模型在许多工程领域已得到广泛的应用，但其统计基础还很不完善，对于对角双线性模型（DBL（p,q,r)models)利用多元Wiener-Ito随机积分，计算出了输入输出序列的自协方差，互协方差和双互协方差，在此基础上进行了谱分析，得到了该模型的谱密度，互谱密度和双互谱密度，这些结果可以用作该模型的辨识，预报和控制，仿真计算证实了这一点。

Identification theory and spectral analysis of diagonal bilinear models

As a kind of efficient approximation to nonlinear system, bilinear models have a widely applications in many engineer fields. However, Statistical theory of bilinear model is rather limited. By means of multivariate Wiener-Ito stochastic representation, diagonal bilinear model (DBL model) had been discussed. Auto-covariance and cross-covariance and bi-cross-covariance of DBL model are evaluated individually in time domain. Spectral density and cross-spectral density and bi-cross-spectral density are also derived in frequency domain. These results can be used for identification prediction and control of DBL models.