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Open Access
December 22, 2013
Abstract
The Global Positioning System (GPS) is increasingly coming into use to establish geodetic networks. In order to meet the established aims of a geodetic network, it has to be optimized, depending on design criteria. Optimization of a GPS network can be carried out by selecting baseline vectors from all of the probable baseline vectors that can be measured in a GPS network. Classically, a GPS network can be optimized using the trial and error method or analytical methods such as linear or nonlinear programming, or in some cases by generalized or iterative generalized inverses. Optimization problems may also be solved by intelligent optimization techniques such as Genetic Algorithms (GAs), Simulated Annealing (SA) and Particle Swarm Optimization (PSO) algorithms. The purpose of the present paper is to show how the PSO can be used to design a GPS network. Then, the efficiency and the applicability of this method are demonstrated with an example of GPS network which has been solved previously using a classical method. Our example shows that the PSO is effective, improving efficiency by 19.2% over the classical method.
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Open Access
December 22, 2013
Abstract
Earth Gravitational Models (EGMs) describe the Earth’s gravity field including the geoid, except for its zero-degree harmonic, which is a scaling parameter that needs a known geometric distance for its calibration. Today this scale can be provided by the absolute geoid height as estimated from satellite altimetry at sea. On the contrary, the above technique cannot be used to determine the geometric parameters of the Mean Earth Ellipsoidal (MEE), as this problem needs global data of both satellite altimetry and gravimetric geoid models, and the standard technique used today leads to a bias for the unknown zero-degree harmonic of the gravimetric geoid height model. Here we present a new method that eliminates this problem and simultaneously determines the potential of the geoid (W0) and the MEE axes. As the resulting equations are non-linear, the linearized observation equations are also presented.
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Open Access
December 22, 2013
Abstract
Array algebra of photogrammetry and geodesy unified multi-linear matrix and tensor operators in an expansion of Gaussian adjustment calculus to general matrix inverses and solutions of inverse problems to find all, or some optimal, parametric solutions that satisfy the available observables. By-products in expanding array and tensor calculus to handle redundant observables resulted in general theories of estimation in mathematical statistics and fast transform technology of signal processing. Their applications in gravity modeling and system automation of multi-ray digital image and terrain matching evolved into fast multi-nonlinear differential and integral array calculus. Work since 1980’s also uncovered closed-form inverse Taylor and least squares Newton-Raphson-Gauss perturbation solutions of nonlinear systems of equations. Fast nonlinear integral matching of array wavelets enabled an expansion of the bundle adjustment to 4-D stereo imaging and range sensing where real-time stereo sequence and waveform phase matching enabled data-to-info conversion and compression on-board advanced sensors. The resulting unified array calculus of spacetime sensing is applicable in virtually any math and engineering science, including recent work in spacetime physics. The paper focuses on geometric spacetime reconstruction from its image projections inspired by unified relativity and string theories. The collinear imaging equations of active object space shutter of special relativity are expanded to 4-D Lorentz transform. However, regular passive imaging and shutter inside the sensor expands the law of special relativity by a quantum geometric explanation of 4-D photogrammetry. The collinear imaging equations provide common sense explanations to the 10 (and 26) dimensional hyperspace concepts of a purely geometric string theory. The 11-D geometric M-theory is interpreted as a bundle adjustment of spacetime images using 2-D or 5-D membrane observables of image, string and waveform matching in the unified array calculus of applied mathematics.
