Maximum likelihood analysis of the total least squares problem with correlated errors

This paper performs a maximum likelihood analysis of the total least squares problem with Gaussian noise errors and correlated element-wise components in the design matrix. This analysis also includes a derivation of the Fisher information matrix and the error-covariance for the parameter estimates. Furthermore, the error-covariances of the associated coefficient and output estimates are also derived. These error-covariances can yield a much improved covariance approximation than would be achieved using naïve least squares. The results are compared with previously derived results for the uncorrelated element-wise component with non-equal row variance case. Simulation results using three-dimensional bearings-only localization are shown to quantify the theoretical derivations, which show that the derived error-covariances are more consistent than those given by the naïve least squares solution.