Topics in Total Least-Squares Adjustment within the Errors-In-Variables Model: Singular Cofactor Matrices and Prior Information

Abstract

This dissertation is about total least-squares (TLS) adjustments within the errorsin-variables (EIV) model.In particular, it deals with symmetric positive-(semi)definite cofactor matrices that are otherwise quite arbitrary, including the case of crosscorrelation between cofactor matrices for the observation vector and the coefficient matrix and also the case of singular cofactor matrices.The former case has been addressed already in a recent dissertation by Fang [2011], whereas the latter case has not been treated until very recently in a presentation by Schaffrin et al. [2012b], which was developed in conjunction with this dissertation.The second primary contribution of this work is the introduction of prior information on the parameters to the EIV model, thereby resulting in an errors-in-variables with random effects model (EIV-REM ) [Snow and Schaffrin, 2012].The (total) least-squares predictor within this model is herein called weighted total least-squares collocation (WTLSC), which was introduced just a few years ago by Schaffrin [2009] as TLSC for the case of independent and identically distributed (iid) data.Here the restriction of iid data is removed.The EIV models treated in this work are presented in detail, and thorough derivations are given for various TLS estimators and predictors within these models.Algorithms for their use are also presented.In order to demonstrate the usefulness of the presented algorithms, basic geodetic problems in 2-D line-fitting and 2-D similarity Publications