Constructing maximum likelihood estimates for statistically uncertain linear systems

We consider the parameters estimation problem for a statistically uncertain linear model, i.e., a model whose observations contain both random perturbations with known distributions and uncertain perturbations for which we only know the domain of their possible values. To solve this problem, we use an approach related to the maximum likelihood method for statistically uncertain systems. We show that as the variances of random perturbations tend to zero, maximum likelihood estimates converge to the information set of the system without random perturbations.