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 elementwise 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 elementwise component with nonequal 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.