The Case of the Homogeneous Errors-In-Variables Model - Schaffrin B.; Snow K. (Journal of Geodetic Science)
Recently, it has been claimed that the HomogeneousErrors-In-Variables (HEIV) Model, where the lefthandside (LHS) vector is allowed to be multiplied withan unknown scale factor, would represent a generalizationof the regular EIV-Model for which a number of efficientalgorithms already exist. Unfortunately, due to theforced rank deficiency in the case of the HEIV-Model, anadditional constraint needs to be introduced to guaranteeuniqueness of the TLS solution (“datum constraint”).If this constraint is linear, a simple manipulation will reducethe HEIV-Model with one constraint to the regularEIV-Model. But also in the case of a non-linear datum constraint,by introducing parameter ratios as unknowns, anEIV-Model may result that can be treated by standard TLSadjustment, followed by a solution of the datum constraintfor the additional LHS scale parameter. This approach willbe applied to an example where the datum constraint ischosen to be quadratic.