Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model AX=B

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On the equivalence between total least squares and maximum likelihood PCA (2005, background): “Some of the variables are allowed to be exactly known (observable) [5,21].”
Consistency of the structured total least squares estimator in a multivariate errors-in-variables model (2005, methodology): “Here d(ns + ds − (d + 1)/2) equals the dimension of s as a manifold, see ( Kukush and Van Huffel, 2004, Section 6.2 ).”
Overview of total least-squares methods (2007, methodology): “Consistency of the weighted total least squares estimator is proven and a n iterative procedure for its computation is proposed in [32].”