Optimal Selection of the Adjustment Principles for Structured Weighted Total Least Squares Model

Objectives:  In the structured EIV model encountered in spatial coordinate transformation, part of the random observations (or their negative values) in the coefficient matrix appear repeatedly in different positions. Whether the repetitions of the random errors should be taken into account and how to deal with the repetitions in the adjustment principle, no consensus has been reached up to now.   Methods:  A generalized structured EIV model is proposed and a synthetic weight is introduced to describe different adjustment principles and the algorithm is derived. Then the generalized EIV model is transformed to the Gauss-Helmert model through linear approximation. The solution and its approximate variance are derived.   Results:  It is verified that the repetitions should not be taken into consideration in the adjustment principle from the aspects of model analysis and numerical simulation.   Conclusions:  The optimal adjustment principle is confirmed and the approximate formula to calculate the accuracy is proved to be feasible and effective.