Constrained total least squares

Abstract

The Total Least Squares (TLS) method is a generalized least square technique to solve an overdetermined system of equations Ax\simeqb . The TLS solution differs from the usual Least Square (LS) in that it tries to compensate for arbitrary present in both A and b . In certain problems the perturbations of A and b are linear functions of a common noise source vector. In this case we obtain a generalization of the TLS criterion called the Constrained Total Least Squares (CTLS) method by taking into account the linear dependence of the terms in A and b . If the columns of A and b are linearly related then the CTLS solution is obtained in terms of the largest eigenvalue and corresponding eigenvector of a certain matrix. The CTLS technique can be applied to problems like Maximum Likelihood Signal Parameter Estimation, Frequency Estimation of Sinusoids in white or colored by Linear Prediction and others.