# Optimal Design in Geodetic GNSS-based Networks

Sammanfattning: An optimal design of a geodetic network helps the surveying engineers maximise the efficiency of the network. A number of pre-defined quality requirements, i.e. precision, reliability, and cost, of the network are fulfilled by performing an optimisation procedure. Today, this is almost always accomplished by implementing analytical solutions, where the human intervention in the process cycle is limited to defining the requirements. Nevertheless, a trial and error method can be beneficial to some applications. In order to analytically solve an optimisation problem, it can be classified to different orders, where an optimal datum, configuration, and optimal observation weights can be sought such that the precision, reliability and cost criteria are satisfied.In this thesis, which is a compilation of six peer-reviewed papers, we optimised and redesigned a number of GNSS-based monitoring networks in Sweden by developing new methodologies. In addition, optimal design and efficiency of total station establishment with RTK-GNSS is investigated in this research.Sensitivity of a network in detecting displacements is of importance for monitoring purposes. In the first paper, a precision criterion was defined to enable a GNSS-based monitoring network to detect 5 mm displacements at each network point. Developing an optimisation model by considering this precision criterion, reliability and cost yielded a decrease of 17% in the number of observed single baselines implying a reliable and precise network at lower cost. The second paper concerned a case, where the precision of observations could be improved in forthcoming measurements. Thus a new precision criterion was developed to consider this assumption. A significant change was seen in the optimised design of the network for subsequent measurements. As yet, the weight of single baselines was subject to optimisation, while in the third paper, the effect of mathematical correlations between GNSS baselines was considered in the optimisation. Hence, the sessions of observations, including more than two receivers, were optimised. Four out of ten sessions with three simultaneous operating receivers were eliminated in a monitoring network with designed displacement detection of 5 mm. The sixth paper was the last one dealing with optimisation of GNSS networks. The area of interest was divided into a number of three-dimensional elements and the precision of deformation parameters was used in developing a precision criterion. This criterion enabled the network to detect displacements of 3 mm at each point.A total station can be set up in the field by different methods, e.g. free station or setup over a known point. A real-time updated free station method uses RTK-GNSS to determine the coordinates and orientation of a total station. The efficiency of this method in height determination was investigated in the fourth paper. The research produced promising results suggesting using the method as an alternative to traditional levelling under some conditions. Moreover, an optimal location for the total station in free station establishment was studied in the fifth paper. It was numerically shown that the height component has no significant effect on the optimal localisation.

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