Adjustment of an Integrated Geodetic Network Composed of GNSS Vectors and Classical Terrestrial Linear Pseudo-Observations

Abstract

The paper proposes a new method for adjusting classical terrestrial observations (total station) together with satellite (GNSS-Global Navigation Satellite Systems) vectors. All the observations are adjusted in a single common three-dimensional system of reference. The proposed method does not require the observations to be projected onto an ellipsoid or converted between reference systems. The adjustment process follows the transformation of a classical geodetic network (distances and horizontal and vertical angles) into a spatial linear (distance) network. This step facilitates easy integration with GNSS vectors when results are numerically processed. The paper offers detailed formulas for calculating pseudo-observations (spatial distances) from input terrestrial observations (horizontal and vertical angles, horizontal distances, height of instrument and height of target). The next stage was to set observation equations and transform them into a linear form (functional adjustment model of geodetic observations). A method was provided as well for determining the mean errors of the pseudo-observations, necessary to assess the accuracy of the values following the adjustment (point coordinates). The proposed algorithm was verified in practice whereby an integrated network made up of a GNSS vector network and a classical linear-angular network was adjusted.