Squared M split(q) S-transformation of control network deformations

Abstract

Identification of stable potential reference points (PRPs) is the most critical stage of computations in conventional deformation analysis of geodetic control networks. An appropriate matching of two adjusted networks at stable PRPs plays a key role in this task. Unfortunately, the geodetic control networks are free networks suffering from datum defect and can realize infinitely many possible matchings at PRPs. Therefore, accurate estimation of PRP displacements and later efficient identification of stable PRPs is a quite difficult task. This study makes some step forward in this field and presents a new approach to deformation analysis, including the identification of stable PRPs. The idea behind this approach is inspired by the theory of squared Msplit(q) estimation and lies in the non-conventional assumption that estimated displacements of PRPs can be the realizations—not of one but—of many congruence models, which simultaneously realize many different matchings. Displacements of unstable PRPs in such a multi-split congruence model do not have such a negative effect on expected matching at stable PRPs as in the conventional robust S-transformation. Here, these displacements can be realizations of other congruence models and their attention can be absorbed by other, unexpected, matchings. Thanks to this, the robustness of the suggested approach can be relatively high. To establish what the number of congruence models is in a given case, which model is the one expected and whether the chosen model is valid, the statistical hypothesis tests were proposed. The experiments performed on 1D and 2D simulated control networks showed that the presented approach can provide more accurate values of estimated displacements than conventional approaches, and in consequence, more efficient results of stable PRPs identification, especially when there exist more unstable PRPs than stable ones. In light of the above, the correct identification of stable PRPs and, in consequence, the correct final estimation of controlled object point displacements are possible in cases when it has not been possible so far.