Using Similarity Transformation Technique for Selecting the Optimal Fixed Points for Over Constrained Geodetic Networks (original) (raw)
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Basic Concepts of Optimization and Design of Geodetic Networks
Journal of Surveying Engineering, 2012
This contribution reviews a few basic concepts of optimization and design of a geodetic network. Proper assessment and analysis of networks is an important task in many geodetic-surveying projects. Appropriate quality-control measures should be defined, and an optimal design should be sought. The quality of a geodetic network is characterized by precision, reliability, and cost. The aim is to present a few case studies that have been designed to meet optimal precision and reliability criteria. Though the case studies may be of interest to the geodetic community in their own right, the aim is to gain insight into the general optimization problem of a geodetic network. This is also potentially of interest for educational purposes. The case studies include a zeroth-order design to improve the precision of the network points in a traverse network and a first-order design to meet the high reliability and maximum precision criteria in a geodetic network. It is shown that not only the configuration of the network but also the type of the observations used can affect the design criteria. For example, the case studies presented show that the optimal shape of the trilateration network (intersection with distances) can result in a weak network in the sense of reliability and precision if the observations are replaced by angles rather than distances (triangulation network). In close relation to the optimization problem of a geodetic network, the global positioning system satellite configuration is also optimized for a particular case that provides the minimum value of the geometric dilution of precision.
Design of Geodetic Networks by Using Global Optimization Methods
2019
Jovana Maksimović 1 Tatjana Kuzmić 2 Mehmed Batilović3 Zoran Sušić4 Vladimir Bulatović5 Željko Kanović6 UDK: 528,3 DOI: 10.14415/konferencijaGFS2019.090 Summary: Traditionally, in order to solve geodetic network optimization problems analytical methods such as linear and nonlinear programming or simulation methods are used. However, global optimization techniques such as genetic algorithm (GA) and particle swarm optimization (PSO) algorithm are increasingly used today to solve geodetic network optimization problems. In this paper, an application of these algorithms in second order design optimization of the geodetic network for the dam Liverovići is proposed. Since the subject of the analysis is the geodetic network for monitoring the dam, an optimality criterion is defined based on the sensitivity parameters of the geodetic network.
WEIGHTS AND TRANSFORMATION PARAMETERS IN THE DATUM DEFINITION OF A GEODETIC NETWORK
A geodetic network is a set of physical points that provides parameters which allows us to know the shape and size of the Earth. The estimation of the unknown parameters of the geodetic network based in observations is an inverse problem which can be solved using a principle of optimization in an adjustment model. The datum problem always arises in the adjustment model, when the unknown parameters of the geodetic network are coordinates which cannot be determined from the available observations. Hence, the datum problem must be solved in an arbitrary and reasonable way by introducing additional information not contained in the observations. It can be done by specifying in the adjustment model, the set of all conventions, algorithms and constants necessaries that define and realize the origin, orientation, scale and their time evolution of the Geodetic Reference System (GRS) where the coordinates are expressed, in such a way that these attributes be accessible to the users through occupation, direct or indirect observation. It is developed here, within a Singular Gauss-Markov Model (SGMM) for the adjustment of a two-dimensional trilateration network using a coordinate based formulations, the general form of three linear conditions equations namely minimum constraints to define the datum of the geodetic network based in: a) a known “a priori” Terrestrial Reference Frame TRF (xo,yo), b) a positive definite weight matrix for the unknown parameters, which can be constructed using information about the accuracy of the TRF(xo,yo) and c) three parameters of a plane coordinate Helmert transformation : two translation and one differential rotation.
Control Points Selection based on Maximum External Reliability for Designing Geodetic Networks
2019
Geodetic networks are essential for most geodetic, geodynamics and civil projects, such as monitoring the position and deformation of man-made structures, monitoring the crustal deformation of the Earth, establishing and maintaining a geospatial reference frame, mapping, civil engineering projects and so on. Before the installation of geodetic marks and gathering of survey data, geodetic networks need to be designed according to the pre-established quality criteria. In this study, we present a method for designing geodetic networks based on the concept of reliability. We highlight that the method discards the use of the observation vector of Gauss-Markov model. In fact, the only needs are the geometrical network configuration and the uncertainties of the observations. The aim of the proposed method is to find the optimum configuration of the geodetic control points so that the maximum influence of an outlier on the coordinates of the network is minimum. Here, the concept of Minimal ...
Multi Object Optimization Of Geodetic Network
NCC Geomatics 82 conferences, 2003
networks based on well-specified quantitative considerations and techniques, it suggests planning for the best solution. In particular with respect to terrain difficulties and the choice of methods of measurement, the planning of networks means in practice that one starts with a solution that is feasible under the given circumstances and available material means, and then introduces improvement until the plan in not too expensive and good enough (Alberda-1974). However in the surveying engineering and geodetic science in order to mapping and staking out of civil engineering projects, GIS, earthquake and land slid hazard assessment, monitoring of deformation of civil structure such as dams and towers, aerial photography and in many other applications we need a framework of points that we called geodetic network.
The Adjustment of Some Geodetic Networks Using Microsoft EXCEL
The Solver is an Excel Add-in that is developed to solve mathematical equations and perform optimization solutions for modeled systems as well. In this study, Excel Solver Add-in that is developed by Frontline Systems is used to solve the adjustment problems by using least squares method. As case studies, adjustment of the closed and open traverses, leveling networks and GPS coordinates are selected
Considerations on the Development of Geodetic Network by Classical and GPS Methods
2011
The paper was developed in order to determine solutions for optimizing geodetic networks in conjunction with technology development worldwide, but correlated with the existing situation in our country. Need to address this topic of study derived from a variety of objective, owing to the way they were made, developed and maintained the geodetic networks existing in the country.
Generalized inner constraints for geodetic network densification problems
Journal of Geodesy, 2013
The estimated coordinates from a minimumconstrained (MC) network adjustment are generally influenced by two different error sources, that is the data noise from the available measurements and the so-called datum noise due to random errors in the fiducial coordinates that are used for the datum definition with regard to an external reference frame. Although the latter source does not affect the estimable characteristics of a MC solution, it still contributes a datum-related noise to the estimated positions which reflects the uncertainty of the coordinate system itself for the adjusted network. The aim of this paper is to develop a new type of MCs which minimizes both of the aforementioned effects in the final coordinates of an adjusted network. This particular problem has not been treated in the geodetic literature and the solution which is presented herein offers an elegant unification of the classic inner constraints into a more general framework for the datum choice problem of network optimization theory. Furthermore, the findings of our study provide a useful and rigorous tool for frame densification problems by means of an optimal MC adjustment in geodetic networks.
The international geodetic community lost, in December 2020, one of its eminent contemporary geodesists Professor E.W. Grafarend of the University of Stuttgart, Germany. To pay homage to him, I present to readers this article, it is a translation of one of his publications which appeared in The Canadian Surveyor, Vol. 28, No.5, December 1974, entitled "Optimization of Geodetic Networks".
The Adjustment of Some Geodetic Networks Using Microsoft EXCEL SOLVER
2009
The Solver is an Excel Add-in that is developed to solve mathematical equations and perform optimization solutions for modeled systems as well. In this study, Excel Solver Add-in that is developed by Frontline Systems is used to solve the adjustment problems by using least squares method. As case studies, adjustment of the closed and open traverses, leveling networks and GPS coordinates are selected