الفهرس 
Some Definitions And ConceptsOnly 14 pages are availabe for public view
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Abstract
Network design is the first step towards establishing a geodetic network. In order to prevent the whole operation from failing, the engineers in charge should know about the result of their work according to the pre-set objectives before any measurement campaign is started. At the design stage of a geodetic network, the fundamental problem that a surveying engineer faces is how to decide on its configuration, i.e., the point location, how to choose the types of geodetic observations, their distribution all over the network. The purpose of network optimal design is in general understood to design an optimum network configuration and an optimum observing plan that will satisfy the pre-set network quality with the minimum effort. Practically, the technique of network optimization serves to help us make decisions on which instruments should be selected from the hundreds of available models of various geodetic instruments and where they should be located in order to estimate the unknown parameters and achieve the desired network quality criteria derived from and determined by purpose of the network. The optimization problems of the design are classified into five design orders, namely: The Zero-order Design ZOD, which means the choice of the optimal reference datum; The First-order Design FOD (the optimal configuration); The Second-order Design SOD (the weight problem); The Combined Design COMD, where both the First-and Second-order Design have to be optimally solved simultaneously; and the Third-order Design problem ThOD (the problem of improvement of an existing design). The present study has four objectives, the first objective is to study the different objective functions which can be classified into two groups, namely: Scalar Risk Function and Criterion Matrices. The Scalar precision criteria are made of global or local scalar precision measures that serves as an overall the precision of a network. A criterion matrix is an artificial variance-covariance matrix possessing an ideal structure, where ”ideal” means that it represents the optimal accuracy situation in the planned network. The criterion matrices could be structured by different ways, for instance, the Taylor–Karman structure, the Chaotic Structure. In this study, an alternative approach was suggested to construct a criterion matrix by modifying the present covariance matrix of coordinates of geodetic netpoints; for special purpose networks such as those met in civil engineering and deformation measurements, the elements of the criterion matrix can be computed from user requirements, such as the shape of error ellipses or the accuracy of derived quantities. The second objective of the current thesis is to make a comparison between the alternative approach and two another approaches; namely Taylor-Karman structure and Scalar Risk function. The first comparison between using the Taylor-Karman structure and the proposed approach to obtain an ideal matrix, the second comparison between using Scalar Risk function and the proposed approach.
The third objective of the current study is the solution of the Second-order Design Problem, in which, the optimal weights of observations are determined, providing that the configuration matrix and the required criteria are given. This leads to the determination of the required variances of the observations, respectively, the choice of the required instruments, repetition numbers of the observations, and the procedures, which satisfy the required variances. The solution methods of the problem are based on the formation of a redundant system of equations in the weights vector, to be solved by the non-linear programming method or the least-squares technique.
The non-linear programming method used the least-squares principle, and a set of approximate values of the weights vector (p), in a similar manner, as the observation equation adjustment process. The solution depends on the equating of the resulting covariance matrix, by the given criterion matrix. This leads to a system of redundant non-linear and inconsistent equations. This method does not produce any elements of the weights to be negative, the resulting weights vector reproduces a covariance matrix, which ensures the required criteria in all parts of a network.