基于全局最小二乘的维纳误差变量系统建模算法(英文)

Total Least-Squares Algorithm for Wiener Errors-in-Variables System Modeling

讨论了一类非线性维纳误差变量系统的建模问题,该系统的输入和输出端均存在不可测的高斯白噪声。在重构误差变量模型的基础上,提出了一类基于全局最小二乘的两阶段辨识方法,引入奇异值分解取得系统的辨识解,并证明了非线性误差变量系统在持续激励情况下,当数据采样次数趋近无穷大时,所提出的全局最小二乘算法的辨识解即为非线性模型参数的极大似然解。仿真结果体现了采用该全局最小二乘两阶段算法解决非线性系统建模问题的有效性。

The modeling problem of Wiener errors-in-variables systems was investigated where measurements of the system input and output were corrupted by the additive white Gauss noise. After the provided reformulation of the errors-in-variables system, a two-stage algorithm was developed to estimate the unknown parameters with the first stage employing the total least-squares algorithm, followed by a singular value decomposition in the second stage. The asymptotic maximum likelihood estimation property under the PE condition was strictly proven that with data length tends to infinite, and the proposed total least-squares solution provided an asymptotic maximum likelihood estimate for the nonlinear system parameter vector. The simulation result shows the effectiveness of the proposed algorithm in solving the nonlinear system modeling problem.