In this contribution, an iterative algorithm for variance-covariance component estimation based on the structured errors-in-variables (EIV) model is proposed. We introduce the variable projection principle and derive alternative formulae for the structured EIV model by applying Lagrange multipliers, which take the form of a least-squares solution and are easy to implement. Then, least-squares variance component estimation (LS-VCE) is applied to estimate different (co)variance components in a structured EIV model. The proposed algorithm includes the estimation of covariance components, which is not considered in other recently proposed approaches. Finally, the estimability of the (co)variance components of the EIV stochastic model is discussed in detail. The efficacy of the proposed algorithm is demonstrated through two applications: multiple linear regression and auto-regression, on simulated datasets or on a real dataset with some assumptions.

为此，提出了一种基于结构化变量误差（EIV）模型的方差-协方差分量估计迭代算法。我们介绍了可变投影原理，并通过应用拉格朗日乘数来得出结构化EIV模型的替代公式，该乘数采用最小二乘解的形式且易于实现。然后，应用最小二乘方差分量估计（LS-VCE）来估计结构化EIV模型中的不同（协）方差分量。所提出的算法包括协方差分量的估计，在其他最近提出的方法中没有考虑。最后，详细讨论了EIV随机模型的（协）方差分量的可估计性。该算法的有效性通过两个应用得到了证明：