  In this paper, we prove strong consistency of an estimator by the truncated
singular value decomposition for a multivariate errors-in-variables linear
regression model with collinearity. This result is an extension of Gleser's
proof of the strong consistency of total least squares solutions to the case
with modern rank constraints. While the usual discussion of consistency in the
absence of solution uniqueness deals with the minimal norm solution, the
contribution of this study is to develop a theory that shows the strong
consistency of a set of solutions. The proof is based on properties of
orthogonal projections, specifically properties of the Rayleigh-Ritz procedure
for computing eigenvalues. This makes it suitable for targeting problems where
some row vectors of the matrices do not contain noise. Therefore, this paper
gives a proof for the regression model with the above condition on the row
vectors, resulting in a natural generalization of the strong consistency for
the standard TLS estimator.
