Total least-squares collocation: the general case

For many situations in geodesy and allied disciplines, data are collected that not only enter the usual observation vector y , but also the coefficient matrix A after linearization. Such models fall into the category of errors-in-variables (EIV) models and may be treated by total least-squares (TLS) adjustment. However, if stochastic prior information is available for the unknown parameters of the model that follows certain quantifiable “expectations,” these normally non-random parameters will turn into “random effects,” in which case the standard estimation procedure needs to be replaced by one that resembles collocation, but is here obviously based on the TLS principle. While early work by Schaffrin on this topic admitted only iid (independent and identically distributed) data from the side of the EIV Model, eventually the authors presented models for TLS collocation with a more arbitrary cofactor matrix Q 1 of full rank, which will be extended herein to admit an even larger class of singular covariance matrices. Use of the developed formulas will be demonstrated by a 3D similarity transformation in the context of a geodetic network.