Analysis of regional geodetic GNSS networks properties built through the relative method. Complete case

Abstract

In this paper we continue to study the statistical properties of adjusted station coordinates in permanent geodetic networks. Analytical constructing the variance-covariance matrix of the measured vectors redundant set’s coordinates taking into account the covariances between vectors with common stations, is performed. The main attributes of this matrix are shown.Analytical modeling the adjustment of the measured vectors’ redundant set, which has such attributes, is performed. The variance-covariance matrix of the vector network’s adjusted coordinates is obtained and its properties are analyzed. It is shown that at using a simplified method for constructing such network, which neglects correlations between the errors of the measured baselines, the accuracy of its solution is overestimated, but the structure of the covariance matrix does not change. Analytical modeling of the network’s behavior in time is done, taking into account its possible internal dynamics, i.e. temporal changes of the geodetic stations’ relative positions that form it. It is shown that a dynamic vector solution has the same properties as the individual ones which make it, if they use redundant sets of measured vectors of the same type