Constrained total least squares

Abstract

The Total Least Squares (TLS) method is a generalized least square technique to solve an overdetermined system of equationsAx\simeqb. The TLS solution differs from the usual Least Square (LS) in that it tries to compensate for arbitrary noise present in bothAandb. In certain problems the noise perturbations ofAandbare 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 noise terms inAandb. If the noise columns ofAandbare 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 noise by Linear Prediction and others.