The errors-in-variables model in which the unobserved true values satisfy multiple linear restrictions is considered. Under the assumptions that the unobservable true values are normally distributed and that an estimator of the covariance matrix of the measurement error is available, the maximum likelihood estimators are derived. The limiting properties of the estimators are obtained for a wide range of assumptions, including the assumption of fixed true values.
"Estimation for the Multivariate Errors-in-Variables Model with Estimated Error Covariance Matrix." Ann. Statist. 12 (2) 497 - 509, June, 1984. https://doi.org/10.1214/aos/1176346502