Abstract:There exist a number of methods for approximating the local geoid surface and studies carried out to determine a local geoid. In this study, performance of geoid by PSO method in modeling local geoid was presented and analyzed. The ellipsoidal heights (h), derived from GPS observations, and known orthometric heights from first-order bench marks were first used to create local geometric geoid model, then the PSO method was used to convert ellipsoidal heights into orthometric heights (H). The resulting values were used to compare between the spirit leveling and GPS methods. The adopted PSO method can improve the fitting of local geometric geoid by quadratic surface fitting method, which agrees with the known orthometric heights within ±1.02cmthe Cartography produced: General Map, Partial Maps, Profile, Cross Sections and others. Keywords: Particle swarm optimization (PSO); Quadratic surface fitting; Ellipsoidal height; Orthometric height. Resumo:Existe uma série de métodos para aproximar a superfície do geoide local bem como vários estudos conduzidos para determinar um geoide local. Neste estudo, apresentou-se e analisou-se o desempenho do geoide pelo método de otimização por exame de partículas (PSO, do inglês Particle Swarm Optimization) na modelagem do geoide local. As altitudes elipsoidais (h), derivada de observações GPS, e altitudes ortométricas de referências de nível de primeira ordem foram usados para criar um modelo do geoide geométrica local, na sequencia usou-se o método PSO para converter altitudes elipsoidais em altitudes ortométricas (H
In this study, test-region global positioning system (GPS) control points exhibiting known first-order orthometric heights were employed to obtain the points of plane coordinates and ellipsoidal heights by using the real-time GPS kinematic measurement method. Plane-fitting, second-order curve-surface fitting, backpropagation (BP) neural networks, and least-squares support vector machine (LS-SVM) calculation methods were employed. The study includes a discussion on data integrity and localization, changing reference-point quantities and distributions to obtain an optimal solution. Furthermore, the LS-SVM was combined with local geoidal-undulation models that were established by researching and analyzing3 kernel functions. The results indicated that the overall precision of the local geometric geoidal-undulation values calculated using the radial basis function (RBF) and third-order polynomial kernel function was optimal and the root mean square error (RMSE) was approximately ± 1.5 cm. These findings demonstrated that the LS-SVM provides a rapid and practical method for determining orthometric heights and should serve as a valuable academic reference regarding local geoid models. RESUMO Este estudo empregou pontos de controle de GPS em regiões-teste com altitudes ortométricas de primeira ordem previamente conhecidas, para a obtenção de pontos de coordenadas planas e altitudes elipsoidais, com a utilização do método cinemático em tempo real (RTK). Este estudo aplicou o ajuste de superfície de primeira ordem, ajuste de superfície de segunda ordem, método da retropropagação para redes neurais e "support vector machine" por mínimos quadrados (LS-SVM). Integridade e localização de dados foram examinados, e a certa quantidade e distribuição de pontos de referência modificados para obtenção da solução ideal. O estudo contou também com o LS-SVM e com o modelo de altitude geoidal local que foi estabelecido usando 3 funções de Kernel para análises e pesquisas. Os resultados indicam que a precisão total dos valores calculados das ondulações geóidais geométricas locais usando a rede neural artificial e o polinômio de terceiraordem da função de Kernel foram ideais com o valor quadrático médio de aproximadamente ± 1.5 cm. O resultado mostrou que o SVM oferece o método rápido e prático para obtenção de altitudes ortométricas e provê a pesquisa acadêmica de referência para modelos geoidais locais. Palavras-chave: Máquina de Vetor Suporte para Mínimos Quadrados; Função de Kernel; Modelo de Geóide Local. INTRODUCTIONThe gravimetric method is the technique most commonly used to precisely determine the local geoid. Recently, a gravimetric geoid model covering Taiwan was generated using gravity survey data, which are relatively difficult and timeconsuming to measure and often yield results that do not fit well with the local terrain. Gravimetric geoid results fit large rather than small areas. Because of the lack of gravity data in mountainous regions of Taiwan, this study was conducted to generate a regional geoid model that ...
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