Maximum Likelihood Estimation in Random Linear Models: Generalizations and Performance Analysis

We consider the problem of estimating an unknown deterministic parameter vector in a linear model with a Gaussian model matrix. The matrix has a known mean and independent rows of equal covariance matrix. Our problem formulation also allows for some known columns within this model matrix. We derive the maximum likelihood (ML) estimator associated with this problem and show that it can be found using a simple line-search over a unimodal function which can be efficiently evaluated. We then analyze its asymptotic performance using the Cramer Rao bound. Finally, we discuss the similarity between the ML, total least squares (TLS), and regularized TLS estimators