Weights and Transformation Parameters in the Datum Definition of a Geodetic Network

Abstract

A geodetic network is a set of physical points that provides parameters which allows us to know the shape and size of the Earth. The estimation of the unknown parameters of the geodetic network based in observations is an inverse problem which can be solved using a principle of optimization in an adjustment model.
The datum problem always arises in the adjustment model, when the unknown parameters of the geodetic network are coordinates which cannot be determined from the available observations.
Hence, the datum problem must be solved in an arbitrary and reasonable way by introducing additional information not contained in the observations.
It can be done by specifying in the adjustment model, the set of all conventions, algorithms and constants necessaries that define and realize the origin, orientation, scale and their time evolution of the Geodetic Reference System (GRS) where the coordinates are expressed, in such a way that these attributes be accessible to the users through occupation, direct or indirect observation.
It is developed here, within a Singular Gauss-Markov Model (SGMM) for the adjustment of a two-dimensional trilateration network using a coordinate based formulations, the general form of three linear conditions equations namely minimum constraints to define the datum of the geodetic network based in: a) a known “a priori” Terrestrial Reference Frame TRF (xo,yo), b) a positive definite weight matrix for the unknown parameters, which can be constructed using information about the accuracy of the TRF(xo,yo) and c) three parameters of a plane coordinate Helmert transformation : two translation and one differential rotation.