Optimal Design For A Three-dimensional Terrestrial Geodetic Network

Abstract

In recent years a number of geodesists have proposed the application of three-dimensional geodesy in the setting up of terrestrial geodetic control networks. The relevant formulations have been presented and actual networks computed to demonstrate the validity of the method. However, one aspect that appears not to have been adequately tackled is the optimal design for such networks. Reported herein is an investigation into the optimal design problem for three-dimensional terrestrial geodetic networks with reference to a specific network. A real network forming a part of the geodetic network of Kenya was adopted for the study. The network is basically a triangulation chain and consists of 36 stations with observational lines ranging from 21 km to 95 km. The effect of type and number of observations on the network were systematically investigated with the aim of eventually arriving at an optimal model of the network. The types of observations considered were vertical angles, horizontal-directions, spatial distances, astronomic ~azimuths, astronomic latitudes, and astronomic longitudes. The study was conducted entirely by computer simulation. From an analysis involving 65 models of the network, an optimal model is offered. The results indicate, among other factors, that with all the possible horizontal directions and vertical angles observed in the network, astronomic positions need to be determined at about one-half of the stations in the network; astronomic azimuths at about one-quarter of the stations; and between one-tenth and one-eighth of the possible spatial distances.