Abstract
Abstract:In the traditional method of optimal design of displacement monitoring networks a higher precision, times better than the desired accuracy of displacements, is considered for the net points in such a way that the accuracy of the detected displacements meets the desired one. However, in this paper, we develop an alternative method by considering the total number of observations in two epochs without such a simple assumption and we call it two-epoch optimisation. This method is developed based on the Gauss-Helmert adjustment model and the variances of the observations are estimated instead of the weights to optimise the observation plan. This method can deliver the same results as the traditional one, but with less required observations in each epoch
Highlights
The geodetic networks are designed for different purposes, but one of the most important applications of such networks is to monitor deformation of man-made structures or the Earth
Instead of Equation 2, we can write: The least-squares solution of Equation 20 is: where and the VC matrix of the displacement is: the solutions (3) and (21) are identical, where the former equation is derived based on the Gauss-Markov adjustment model, which is a particular case of the Gauss-Helmert adjustment models
Two sets of observations in two frequent epochs are considered together and the network is designed considering all observations in two epochs
Summary
The geodetic networks are designed for different purposes, but one of the most important applications of such networks is to monitor deformation of man-made structures or the Earth. Using the method of Kuang (1996), one can obtain optimal weights and configuration of the network in one step by different optimisation algorithms and OFs. the approach proposed by Kuang (1996), to optimal design of the network, is a combination of FOD and SOD. The approach proposed by Kuang (1996), to optimal design of the network, is a combination of FOD and SOD In this method, the best configuration and observation precisions are determined simultaneously in an optimal way. Amiri-Simkooei (2001a) and Amiri-Simkooei (2001b) considered the analytical approach for FOD, SOD and their combinations in robustness of the network to resist the outliers This optimal design can be carried out using different criteria as an OF. We will discuss both methods of one-epoch and two-epoch optimisation and compare them in theoretical and practical view
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