UD分解与偏差补偿结合用于变量带误差模型辨识

本文提出一种基于UD(upper-diagonal)分解与偏差补偿结合的辨识方法,用于变量带误差(errors-in-variables,EIV)模型辨识.考虑单输入单输出(single input and single output,SISO)线性动态系统,当输入和输出含有零均值、方差未知的高斯测量白噪声时,该类系统的模型参数估计是一种典型的EIV模型辨识问题.为了获得这种EIV模型参数的无偏估计,本文先推导出最小二乘模型参数估计偏差量与输入输出噪声方差以及最小二乘损失函数与输入输出噪声方差的关系,然后采用UD分解方法递推获得模型参数估计值,再利用输入输出噪声方差估计值补偿模型参数估计偏差,以此获得模型参数的无偏估计.本文还讨论了算法实现过程中遇到的一些问题及修补方法,并通过仿真例验证了所提辨识方法的有效性.

Combination of UD factorization and bias compensation for errors-in-variables model identification

In this paper, an identification method based on the combination of upper-diagonal (UD) factorization and deviation compensation is proposed for the identification of errors-in-variables (EIV) model. By considering a single input and single output (SISO) linear dynamic system, whose input and output are corrupted by Gaussian white measurement noises with zero means and unknown variances, the model parameter estimation for such system is a typical problem of EIV model identification. In order to obtain an unbiased parameter estimation of the EIV model, the relationships are firstly derived not only between the bias amounts of the least squares model parameter estimates and the variances of input and output noises but also between the least squares loss function and the variances of input and output noises, and then the UD factorization method is adopted to recursively obtain model parameter estimates and the estimated variances of input and output noises are further utilized to compensate for the deviations of the model parameter estimates, thus resulting in the unbiased parameter estimates of the EIV model. In this paper, some issues and compensation schemes encountered in the implementation of our algorithm are also discussed. Finally, the effectiveness of the proposed identification method is verified by a simulation example.