Constrained total least squares

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 noise present in both
A
and
b
. In certain problems the noise 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 noise terms in
A
and
b
. If the noise 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 noise by Linear Prediction and others.