In this article we introduce a multivariate structural linear error-in-variables model which is suitable for longitudinal data. We construct estimators of the regression parameters, which correspond to the modified least squares estimators used in the univariate case. We show that these estimators are consistent. We prove a central limit theorem, which is completely data-based, under the assumption that the vector of latent variables belongs to the generalized domain of attraction of the normal law. Our results can be viewed as an extension of the results of  to include the longitudinal case.
"Estimation for a longitudinal linear model with measurement errors." Electron. J. Statist. 4 486 - 524, 2010. https://doi.org/10.1214/09-EJS503