Modifying Cadzow's algorithm to generate the optimal TLS-solution for the structured EIV-Model of a similarity transformation

In 2005, Felus and Schaffrin discussed the problem of a Structured Errors-in-Variables (EIV) Model in the context of a parameter adjustment fora classical similarity transformation. Their proposal, however, to perform a Total Least-Squares (TLS) adjustment, followed by a Cadzow step to imprint the proper structure, would not always guarantee the identity of this solution with the optimal Structured TLS solution, particularly in view of the residuals. Here, an attempt will be made to modify the Cadzow step in order to generate the optimal solution with the desired structure as it would, for instance, also result from a traditional LS-adjustment within an iteratively linearized Gauss-Helmert Model (GHM). Incidentally, this solution coincides with the (properly) Weighted TLS solution which does not need a Cadzow step.