On the equivalence of constrained total least squares and structured total least squares

Several extensions of the total least squares (TLS) method that are able to calculate a structured rank deficient approximation of a data matrix have been developed. The main result of this article is the demonstration of the equivalence of two of these approaches, namely, the constrained total least squares (CTLS) approach and the structured total least squares (STLS) approach. We also present a numerical comparison of both methods.