A note on Constrained Total Least-Squares estimation

It is shown here how – similarly to the unconstrained case – the Constrained Total Least Squares Estimate (CTLSE) can be generated by solving a certain sequence of eigenvalue problems iteratively. For this, the normal matrix from the constrained (standard) least-squares approach has to be suitably augmented by one row and one column. Further modification of the augmented row and column allows the treatment of “fiducial constraints” for which the RHS vector is affected by random errors, but not the constraining matrix itself.