Constrained maximum likelihood solution of linear equations (Q2734305)

Using the method of total least squares, the authors obtain maximum likelihood solutions to a set of inconsistent linear equations of the form \(Ax\approx y\) in which errors occur not only in the observations \(y\) but also in the modelling matrix \(A\). A difficulty in this approach is that any defined structure shared by \(A\) and \(y\) may not be carried over to the perturbations, and to effect the `carrying over' of such structure the authors introduce a probabilistic framework. Given an a priori perturbation density function, this approach allows the determination of the most probable set of perturbations. Details are given of both Gaussian and non-Gaussian distributions, and the relationship of the constrained maximum likelihood method given here to existing methods is explored.