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

Tadeusz Gargula

doi:10.3390/app11104352

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.

Highlights

Integrated measurement methods are usually employed for various surveying engineering jobs, such as monitoring land surface displacements or structure deformation [1,2,3,4,5,6,7]
Survey results are usually processed by a simultaneous adjustment of classical observations and GNSS vectors in a common mathematical space [5]
It is necessary to pre-process the observations in both cases. This process can include the projection of GNSS vectors onto an ellipsoid, projection of classical observations onto the surface of an ellipsoid, or transformation of GNSS vectors (∆X, ∆Y, ∆Z) onto a horizontal plane [10,11,12,13]

Summary

Introduction

Integrated measurement methods are usually employed for various surveying engineering jobs, such as monitoring land surface displacements or structure deformation [1,2,3,4,5,6,7]. Survey results are usually processed by a simultaneous adjustment of classical observations (angles and distances) and GNSS vectors in a common mathematical space [5]. Integrated networks may be adjusted on the GRS’80 (Geodetic Reference System ‘80) reference ellipsoid surface or a horizontal projection plane in a local system. It is necessary to pre-process the observations in both cases This process can include the projection of GNSS vectors onto an ellipsoid (calculating the length of a geodetic line and its original azimuth), projection of classical observations (horizontal distances) onto the surface of an ellipsoid (calculating the projection corrections), or transformation of GNSS vectors (∆X, ∆Y, ∆Z) onto a horizontal plane [10,11,12,13]. One cannot avoid errors resulting from the transforming of the original observations into pseudo-observations on a common plane of reference (such as projection errors or errors of the geoid model)

Methods

Results

Conclusion