Eine in der Geoda¨sie bekannte Regel besagt, dass die Genauigkeit zu transformierender Neupunkte im Schwerpunkt der Anschlusspunkte am höchsten ist. Weniger bekannt ist, unter welchen Voraussetzungen dies generell gilt. Allgemein unbekannt ist bisher, auf welche Koordinatentransformationen man diese Regel ausdehnen kann. Wir zeigen dies auf und untersuchen einen Fall, in dem diese Regel nicht gilt. Es stellt sich heraus, dass der am genauesten transformierbare Neupunkt theoretisch sogar außerhalb der konvexen Hülle der Anschlusspunkte liegen kann. / A rule well-known in Geodesy states that the accuracy of points to be transformed is best in the centre of gravity of the control points. Less well- known is, under which conditions this rule gen- erally applies. The exact set of coordinate transforms, to which we can extend the validity of this rule, is widelyunknown. We demonstrate this and investigate a case, in which this rule does not apply. It turns out that the most accurately transformable point be even be located outside the convex hull of the control points.

Recent advances in space geodetic techniques such as Very Long Baseline Interferometry, Global Navigation Satellite Services, Satellite Laser Ranging and advanced numerical weather prediction model simulations, provide huge tropospheric data sets with improved spatial temporal resolution. These data sets exhibit unique fluctuations that have a spatial-temporal structure which are thought to mimic the complex behaviour of the atmosphere. As a result, the analysis of non-stationary structure in the tropospheric parameters derived from geodetic and numerical model simulations could be used to probe the extent of universality in the dynamics of the atmosphere, with applications in space geodesy. In order to identify the physical causes of variability of tropospheric parameters, parametric and nonparametric data analyses strategies which are investigated and reported in this thesis, are used to inform on the geophysical signals embedded in the data structure. In the first task of this research work, it is shown that the fluctuations of atmospheric water vapour over southern Africa are non-linear and non-stationary. Secondly, the tropospheric data sets are transformed to stationarity and the stochastic behaviour of water vapour fluctuations are assessed by use of an automatic algorithm that estimates the model parameters. By using a data adaptive modelling algorithm, an autoregressive-movingaverage model was found to sufficiently characterise the derived stationary water vapour fluctuations. Furthermore, the non-linear and non-stationary properties of tropospheric delay due to water vapour were investigated by use of robust and tractable non-linear approaches such as detrended fluctuation analysis, independent component analysis, wavelet transform and empirical mode decomposition. The use of non-linear approaches to data analysis is objective and tractable because they allow data to speak for themselves during analysis and also because of the non-linear components embedded in the atmosphere system. In the thesis, we establish that the non-linear and non-stationary properties in the tropospheric data sets (i.e., tropospheric delay due to water vapour and delay gradients) could be triggered from strongly non-linear stochastic processes that have a local signature (e.g. local immediate topography, weather and associated systems) and/or exogenous. In addition, we explore and report on the presence of scaling properties (and therefore memory) in tropospheric parameters. This self-similar behaviour exhibit spatial-temporal dependence and could be associated with geophysical processes that drive atmosphere dynamics. Satellite Laser Ranging data are very sensitive to atmospheric conditions, which causes a delay of the laser pulse, hence an apparent range increase. A test for non-linearity is applied within specialised software for these data; it is found that the range residuals (i.e., the observed minus computed residuals) are improved when possible non-linearity of the locally measured meteorological parameters as applied to a range delay model are considered. / Thesis (PhD)--University of Pretoria, 2011. / Geography, Geoinformatics and Meteorology / PhD / Unrestricted

This thesis is engaged in geodetic works related to the increase of the capacity of the road II/497 and the modification of the intersection with the road I/55 in the town of Uherské Hradiště. The work is mostly focused on the field of the engineering geodesy. It resolves the issues from the alignment during the construction to the focus of the construction itself. Individual survey procedures are analyzed in the context of the prescribed deviations specified in the project documentation or ČSN. Geodetic documentation for the selected measurements is worked out.

Um dos principais problemas no monitoramento das estruturas de uma barragem por meio de instrumentação geodésica se refere à confirmação da estabilidade dos pontos da rede geodésica de referência. Os eventuais deslocamentos detectados nas estruturas podem ser resultados de análises e interpretações equivocadas, já que os pontos de referência podem ser considerados estáveis sem indicação dessa condição. Considerando o objetivo deste trabalho, de verificar a estabilidade dos pilares da rede geodésica da Usina Hidrelétrica de ITAIPU por meio da tecnologia GPS, foi proposta uma metodologia que compreendesse o planejamento e a coleta dos dados, realizada em quatro épocas (campanhas) distintas, seguidos do seu processamento e ajustamento. No processamento dos dados verificou-se a melhor estratégia usando a fase da portadora L1, devido às linhas de base curtas (até 5km). Já no ajustamento, constatou-se a importância da detecção de erros grosseiros nas observações das linhas de base e também do controle de qualidade. Os resultados da aplicação desta metodologia foram as coordenadas ajustadas dos pilares da rede com as suas respectivas precisões para cada época. Estas coordenadas e suas matrizes variância-covariância foram então comparadas entre combinação de campanhas com a aplicação do teste de congruência global, para a verificação final da significância estatística das diferenças encontradas. Os resultados demonstraram que as investigações da estabilidade dos pilares da rede geodésica em estudo, dependem diretamente da qualidade das observações e do ajustamento, bem como da configuração da rede geodésica. / One of the main problems in dams structures monitoring by geodetic instruments is the confirmation of the stability of reference points in geodetic networks. The detection of displacements on the structures can bring results of wrong analysis just because the reference points assumed as stable points may be not. Considering the objective of this work which is to verify the stability of the pillars in ITAIPU Power Plant geodetic network by GPS, a methodology was proposed including the planning and field surveys of four campaigns in different epochs, followed by data processing and baseline adjustment. According to the results of data processing it was verified that the better strategy is process the carrier phase L1 because the baselines are short (up to 5km). Regarding the adjustment, it was confirmed the significance of observations blunders detection and quality control. The results of methodology application were the adjusted coordinates of each geodetic network pillar and the respective accuracy for each campaign. Those coordinates with its variance-covariance matrices were compared between the campaigns by means of global congruency test verifying if statistically significant differences would be found. The results demonstrated that the pillars stability of studied geodetic network is directly dependent of the observations and adjustment quality, and also of the geodetic network layout.

O cálculo da área de poligonais geodésicas é um desafio matemático instigante. Como calcular a área de uma poligonal sobre o elipsóide, se seus lados não possuem parametrização conhecida? Alguns trabalhos já foram desenvolvidos no intuito de solucionar este problema, empregando, em sua maioria, sistemas projetivos equivalentes ou aproximações sobre esferas autálicas. Tais métodos aproximam a superfície de referência elipsoidal por outras de mais fácil tratamento matemático, porém apresentam limitação de emprego, pois uma única superfície não poderia ser empregada para todo o planeta, sem comprometer os cálculos realizados sobre ela. No Código de Processo Civil, Livro IV, Título I, Capítulo VIII, Seção III artigo 971 diz, em seu parágrafo único, que não havendo impugnação, o juiz determinará a divisão geodésica do imóvel. Além deste, existe ainda a Lei 10.267/2001, que regula a obrigatoriedade, para efetivação de registro, dos vértices definidores dos limites dos imóveis rurais terem suas coordenadas georreferenciadas ao Sistema Geodésico Brasileiro (SGB), sendo que áreas de imóveis menores que quatro módulos fiscais terão garantida isenção de custos financeiros.Este trabalho visa fornecer uma metodologia de cálculo de áreas para poligonais geodésicas, ou loxodrômicas, diretamente sobre o elipsóide, bem como fornecer um programa que execute as rotinas elaboradas nesta dissertação. Como a maioria dos levantamentos geodésicos é realizada usando rastreadores GPS, a carga dos dados é pautada em coordenadas (X, Y, Z), empregando o Sistema Geodésico WGS-84, fornecendo a área geodésica sem a necessidade de um produto tipo SIG. Para alcançar o objetivo deste trabalho, foi desenvolvida parametrização diferente da abordagem clássica da Geodésia geométrica, para transformar as coordenadas (X, Y, Z) em geodésicas. / The area calculation of geodetic polygonal is a compelling mathematical challenge. How could one calculate the area of a polygon over the ellipsoid, if the sides do not have known parameterization? Some works have already been developed in order to solve this problem, employing mostly equivalent projective systems or authalic spheres approaches. Such methods near the ellipsoidal reference surface by other of easier mathematical treatment, but have limited employment, for a single surface cannot be used for the entire planet, without compromising the calculations over it. In the Code of Civil Procedure, Book IV, Title I, Chapter VIII, Section III, Article 971 says, in its sole paragraph, that "if there is no objection, the judge shall determine the division of the geodesic property. Besides this, there is the Law 10.267/2001, which regulates the requirement for effective registration, that the vertices defining the boundaries of the farms should have their geo-referenced coordinates to Brazilian Geodetic System (BGS), and areas of buildings less than four modules have guaranteed tax-free financial costs. This paper aims to provide a methodology of area calculation for traverses delimited by geodetic lines, or rhumb lines, directly on the ellipsoid, and provide a program that executes routines developed on this work. Since most geodetic surveys are developed using GPS equipment, the data input is based on (X, Y, Z) coordinates, using WGS-84 datum, providing the geodetic area without needing a GIS product. In order to achieve the paper objective, it was developed a different parameterization from the classical geometric Geodesy approach, to transform (X, Y, Z) coordinates into geodetic ones.

Die Verknüpfung von geodätischen Raumtechniken wie GNSS, DORIS, SLR oder VLBI zur Ableitung eines geodätischen Referenzrahmens wie dem ITRF gelingt erst durch sogenannte Kolokationsstationen. Die geometrischen Beziehungen zwischen den betriebenen Raumtechniken sind dabei aus präzisen lokalen Vermessungen abzuleiten. Es wird ein Konzept zur automatisierten Bestimmung des IVS-Referenzpunktes am TWIN Radioteleskop Wettzell vorgestellt. Erste Untersuchungsergebnisse werden präsentiert.

This diploma thesis focuses on introduction of nowadays quite common technology - GNSS (global navigation satelite systems). In its part, it revises and completes a courseware geodetic field Lipno, which has been established for the needs of geodetic operations courses for students of University of South Bohemia in České Budějovice, landscape management.

O cálculo da área de poligonais geodésicas é um desafio matemático instigante. Como calcular a área de uma poligonal sobre o elipsóide, se seus lados não possuem parametrização conhecida? Alguns trabalhos já foram desenvolvidos no intuito de solucionar este problema, empregando, em sua maioria, sistemas projetivos equivalentes ou aproximações sobre esferas autálicas. Tais métodos aproximam a superfície de referência elipsoidal por outras de mais fácil tratamento matemático, porém apresentam limitação de emprego, pois uma única superfície não poderia ser empregada para todo o planeta, sem comprometer os cálculos realizados sobre ela. No Código de Processo Civil, Livro IV, Título I, Capítulo VIII, Seção III artigo 971 diz, em seu parágrafo único, que não havendo impugnação, o juiz determinará a divisão geodésica do imóvel. Além deste, existe ainda a Lei 10.267/2001, que regula a obrigatoriedade, para efetivação de registro, dos vértices definidores dos limites dos imóveis rurais terem suas coordenadas georreferenciadas ao Sistema Geodésico Brasileiro (SGB), sendo que áreas de imóveis menores que quatro módulos fiscais terão garantida isenção de custos financeiros.Este trabalho visa fornecer uma metodologia de cálculo de áreas para poligonais geodésicas, ou loxodrômicas, diretamente sobre o elipsóide, bem como fornecer um programa que execute as rotinas elaboradas nesta dissertação. Como a maioria dos levantamentos geodésicos é realizada usando rastreadores GPS, a carga dos dados é pautada em coordenadas (X, Y, Z), empregando o Sistema Geodésico WGS-84, fornecendo a área geodésica sem a necessidade de um produto tipo SIG. Para alcançar o objetivo deste trabalho, foi desenvolvida parametrização diferente da abordagem clássica da Geodésia geométrica, para transformar as coordenadas (X, Y, Z) em geodésicas. / The area calculation of geodetic polygonal is a compelling mathematical challenge. How could one calculate the area of a polygon over the ellipsoid, if the sides do not have known parameterization? Some works have already been developed in order to solve this problem, employing mostly equivalent projective systems or authalic spheres approaches. Such methods near the ellipsoidal reference surface by other of easier mathematical treatment, but have limited employment, for a single surface cannot be used for the entire planet, without compromising the calculations over it. In the Code of Civil Procedure, Book IV, Title I, Chapter VIII, Section III, Article 971 says, in its sole paragraph, that "if there is no objection, the judge shall determine the division of the geodesic property. Besides this, there is the Law 10.267/2001, which regulates the requirement for effective registration, that the vertices defining the boundaries of the farms should have their geo-referenced coordinates to Brazilian Geodetic System (BGS), and areas of buildings less than four modules have guaranteed tax-free financial costs. This paper aims to provide a methodology of area calculation for traverses delimited by geodetic lines, or rhumb lines, directly on the ellipsoid, and provide a program that executes routines developed on this work. Since most geodetic surveys are developed using GPS equipment, the data input is based on (X, Y, Z) coordinates, using WGS-84 datum, providing the geodetic area without needing a GIS product. In order to achieve the paper objective, it was developed a different parameterization from the classical geometric Geodesy approach, to transform (X, Y, Z) coordinates into geodetic ones.

Um dos principais problemas no monitoramento das estruturas de uma barragem por meio de instrumentação geodésica se refere à confirmação da estabilidade dos pontos da rede geodésica de referência. Os eventuais deslocamentos detectados nas estruturas podem ser resultados de análises e interpretações equivocadas, já que os pontos de referência podem ser considerados estáveis sem indicação dessa condição. Considerando o objetivo deste trabalho, de verificar a estabilidade dos pilares da rede geodésica da Usina Hidrelétrica de ITAIPU por meio da tecnologia GPS, foi proposta uma metodologia que compreendesse o planejamento e a coleta dos dados, realizada em quatro épocas (campanhas) distintas, seguidos do seu processamento e ajustamento. No processamento dos dados verificou-se a melhor estratégia usando a fase da portadora L1, devido às linhas de base curtas (até 5km). Já no ajustamento, constatou-se a importância da detecção de erros grosseiros nas observações das linhas de base e também do controle de qualidade. Os resultados da aplicação desta metodologia foram as coordenadas ajustadas dos pilares da rede com as suas respectivas precisões para cada época. Estas coordenadas e suas matrizes variância-covariância foram então comparadas entre combinação de campanhas com a aplicação do teste de congruência global, para a verificação final da significância estatística das diferenças encontradas. Os resultados demonstraram que as investigações da estabilidade dos pilares da rede geodésica em estudo, dependem diretamente da qualidade das observações e do ajustamento, bem como da configuração da rede geodésica. / One of the main problems in dams structures monitoring by geodetic instruments is the confirmation of the stability of reference points in geodetic networks. The detection of displacements on the structures can bring results of wrong analysis just because the reference points assumed as stable points may be not. Considering the objective of this work which is to verify the stability of the pillars in ITAIPU Power Plant geodetic network by GPS, a methodology was proposed including the planning and field surveys of four campaigns in different epochs, followed by data processing and baseline adjustment. According to the results of data processing it was verified that the better strategy is process the carrier phase L1 because the baselines are short (up to 5km). Regarding the adjustment, it was confirmed the significance of observations blunders detection and quality control. The results of methodology application were the adjusted coordinates of each geodetic network pillar and the respective accuracy for each campaign. Those coordinates with its variance-covariance matrices were compared between the campaigns by means of global congruency test verifying if statistically significant differences would be found. The results demonstrated that the pillars stability of studied geodetic network is directly dependent of the observations and adjustment quality, and also of the geodetic network layout.

This contribution describes an automatic and robust method, which can be applied to all classical geodetic computation problems. Starting from given input quantities (e.g. coordinates of known points, observations) computation opportunities for all other relevant quantities are found. For redundant input quantities there exists a multitude of different computation opportunities from different minimal subsets of input quantities, which are all found automatically, and their results are computed and compared. If the computation is non-unique, but only a finite number of solutions exist, then all solutions are found and computed. By comparison of the different computation results we may detect outliers in the input quantities and produce a robust final result. The method does not work stochastically, such that no stochastic model of the observations is required. The description of the algorithm is illustrated for a practical case. It is implemented on a webserver and is available for free via internet. / Der Beitrag beschreibt ein automatisches und robustes Verfahren, welches auf alle klassischen geodätischen Berechnungsprobleme angewendet werden kann. Ausgehend von vorgelegten Eingabegrößen (z.B. Koordinaten bekannter Punkte, Beobachtungen) werden Berechnungsmöglichkeiten für alle anderen relevanten Größen gefunden. Bei redundanten Eingabegrößen existiert eine Vielzahl von verschiedenen Berechnungsmöglichkeiten aus verschiedenen minimalen Untermengen von Eingabegrößen, die alle automatisch gefunden und deren Ergebnisse berechnet und verglichen werden. Wenn die Berechnung nicht eindeutig ist, aber nur eine endliche Anzahl von Lösungen existiert, dann werden alle Lösungen gefunden und berechnet. Durch den Vergleich verschiedener Berechnungsergebnisse können Ausreißer in den Eingabegrößen aufgedeckt werden und ein robustes Endergebnis wird erhalten. Das Verfahren arbeitet nicht stochastisch, so dass kein stochastisches Modell der Beobachtungen erforderlich ist. Die Beschreibung des Algorithmus wird an einem praktischen Fall illustriert. Er ist auf einem Webserver installiert und über das Internet frei verfügbar.