Marcelo Tomio Matsuoka

Regional Mapping of the Geoid Using GNSS (GPS) Measurements and an Artificial Neural Network

The determination of the orthometric height from geometric leveling has practical difficulties that, despite a number of scientific and technological advances, passed a century without substantial modifications or advances. Currently, the Global Navigation Satellite System (GNSS) has been used with reasonable success for orthometric height determination. With a sufficient number of benchmarks with known horizontal and vertical coordinates, it is often possible to adjust using the least squares method mathematical expressions that allow interpolation of geoid heights. The objective of this study is to present an alternative method to interpolate geoid heights based on the technique of Artificial Neural Networks (ANNs). The study area is the Brazilian state of Sao Paulo, and for training the ANN the authors have used geoid height information from the EGM08 gravity model with a grid spacing of 10 minutes of arc. The efficiency of the model was tested at 157 points with known geoid heights distributed across the study area. The results were also compared with the Brazilian Geoid Model (MAPGEO2004). Based on those 157 benchmarks it was possible to verify that the model generated by ANNs provided a mean absolute error of 0.24 m in obtaining a geoid height value. Statistical tests have shown that there was no difference between the means from known geoid heights and geoid heights provided by the neural model for a significance level of 5%. It was also found that ANNs provided an improvement of 2.7 times in geoid height estimates when compared with the MAPGEO2004 geoid model.

Planejamento de redes geodésicas resistentes a múltiplos outliers

Ao se planejar o levantamento de uma rede geodesica, deseja-se que as observacoes a serem realizadas e as coordenadas dos pontos a serem estimadas atendam criterios de precisao e confiabilidade pre-estabelecidos de acordo com os objetivos do projeto. Na etapa de pre-analise, antes mesmo da coleta das observacoes, e possivel estimar a precisao e confiabilidade da rede, estipulando uma geometria/configuracao para a mesma e a precisao esperada para as observacoes. O objetivo deste artigo e apresentar o planejamento de uma rede geodesica que atenda criterios de precisao e confiabilidade, considerando a possivel existencia de dois ou mais erros nao detectados nas observacoes, bem como a influencia (simultânea) destes erros sobre os parâmetros (coordenadas ajustadas dos vertices). Alem da revisao teorica, experimentos foram realizados em uma rede GNSS, onde foram estipulados criterios de precisao e confiabilidade considerando a existencia de ate duas observacoes contaminadas por erros (outliers), de maneira simultânea. O planejamento da rede foi feito por meio do metodo da tentativa e erro. Depois do processamento dos dados e do ajustamento da rede, se verificou que os criterios de precisao e confiabilidade que foram estipulados na etapa de pre-analise foram devidamente obtidos.

On evaluation of different methods for quality control of correlated observations

Abstract This paper evaluates, compares, and discusses different methods for quality control in geodetic data analysis in the general scenario of correlated observations and multiple outliers. The investigated methods are the data snooping procedure, the statistical tests for multiple outliers, the recently proposed quasi-accurate detection of outliers method for correlated observations, the Danish method for correlated observations, the robust estimator for correlated observations based on bifactor equivalent weights, and the robust estimator for correlated observations based on a local sensitivity downweighting strategy. To evaluate these methods, outliers between 3σ and 9σ magnitude (positives and/or negatives) are randomly generated and added to some observations (σ being the respective standard deviation of the observation) in two different global navigation satellite system (GNSS) networks that contain correlated observations. For each network, 15 000 scenarios are performed, 5000 with one outlier, 5000 with two outliers, and 5000 with three outliers, using Monte–Carlo simulations. The investigated methods have advantages and limitations, and the discussions and conclusions about the experiments are accurately presented.

Potencialidades do serviço on-line de Posicionamento por Ponto Preciso (CSRS-PPP) em aplicações geodésicas

O metodo de Posicionamento por Ponto Preciso (PPP) com a utilizacao de GPS ( Global Positioning System ) vem se popularizando nos ultimos anos, principalmente, com o surgimento de servicos gratuitos e de processamento on-line , tais como, o Natural Resource Canada (NRCan), denominado Canadian Spatial Reference System – Precise Point Positioning (CSRS-PPP). Neste metodo, o posicionamento utiliza dados de somente um receptor e, fundamentalmente, requer apenas o uso de efemerides e correcoes dos relogios dos satelites precisos. Neste artigo, avaliou-se seu desempenho mediante a utilizacao de um longo periodo de dados (1.596 dias), obtidos na estacao POAL da Rede Brasileira de Monitoramento ContInuo (RBMC), localizada em Porto Alegre, RS, Brasil. A analise das series temporais das coordenadas diarias estimadas pelo CSRS-PPP mostraram discrepâncias de poucos centimetros, quando comparadas com os valores oficiais adotados para a estacao POAL. Palavras-chave: GPS, Posicionamento por Ponto Preciso (PPP), servicos on-line de PPP, CSRS-PPP.

O GPS: unindo ciência e tecnologia em aulas de física

Neste artigo, os conceitos fisicos envolvendo a tecnologia usada no Sistema de Posicionamento Global (GPS) sao analisados do ponto de vista historico e didatico. As conexoes existentes entre o funcionamento do GPS e as descobertas recentes da fisica, como a mecânica quântica e a teoria da relatividade, assim como os erros inerentes ao sistema, sao descritos e exemplificados numericamente. Ao final, uma tarefa pratica visando o melhor entendimento e familiarizacao com o sistema e sugerida. A partir da realizacao da atividade com alunos de graduacao em fisica, algumas observacoes sao feitas com o objetivo de orientar a execucao da mesma.

Análise do serviço on-line de PPP (GDGPS - APPS) para Receptores de Dupla Frequência: um estudo envolvendo dados de estações da RBMC

The PPP (Precise Point Positioning) is a positioning method by GNSS (Global Navigation Satellite System) that has gained great popularity, due to on-line services for processing, most of them available for free. The PPP requires GNSS data from a unique receiver and the use of precise ephemeris and corrections. One of these freely available on-line PPP processing services is the APPS (Automatic Precise Positioning Service), a post-processed mode from NASA, and derivated from GDGPS (Global Differential GPS), which is a real-time GPS monitoring system with more than 100 globally distributed stations. This paper is focused on the evaluation of the APPS processing service to GPS data corresponding to a period of 30 days from the Brazilian stations POAL and IMPZ, respectively located in the South and North of Brazil, which belong to the official network of SIRGAS reference system. Each daily file contains 24 hours of observations with collection rate of 15 seconds, and it was processed time tracking of 2, 4, 6 and 24 hours. The daily coordinates of these stations, estimated by the PPP, have been updated to the SIRGAS2000 reference’s epoch (2000,4), and compared with the official station coordinates. The discrepancies to a time tracking of 24 hours showed root mean square error less than 2 cm, both in planimetry and altimetry, which attests the potential use of PPP/APPS in high-accuracy applications, as geodynamic studies. It also shows an improve of accuracy of few millimeters when the time tracking increases to four hours, and minor or statically similar error variances when the time was six hours. Key words: GPS, GDGPS, Precise Point Positioning, APPS.

Análise da ionosfera usando dados de receptores GPS durante um período de alta atividade solar e comparação com dados de Digissondas

The use of GPS (Global Positioning System) in studies of the Earths atmosphere has increased significantly in recent years. In this paper, the behavior of Earths upper atmosphere, called the ionosphere has been studied over a period of high solar activity (year 2001) using data from dual-frequency GPS receivers located in the Brazilian region, belonging to RBMC (Brazilian Network of Continuous Monitoring). Using the GPS data the ionospheric TEC (Total Electron Content) was calculated. Additionally, data of critical frequency of F2 layer were included in the study, derived from Digisondes located in Sao Luis/MA (3oS; 44oW) and Cachoeira Paulista/SP (22oS; 45oW), Brazil, for comparison purposes. In general, the results showed higher values of TEC during the equinoxes and lower during the winter months. Regarding the daily variation, the lowest TEC values were observed at around 4-6 HL and higher values occurred in the afternoon, with values slightly higher in Sao Luis. The second peak of the equatorial anomaly was observed at Cachoeira Paulista during the equinoxes and summer months. In most case, the comparison between critical frequency and TEC showed high linear correlation, especially in Sao Luis.

Estimativa de alturas geoidais para o estado de São Paulo baseada em redes neurais artificiais

The information of height provided by the GNSS (Global Navigation Satellite System) is purely geometrical, and in most engineering papers, the height must be referenced to the geoid. Provided we have a sufficient number of Bench Marks (BMs) with known horizontal and vertical coordinates, it is nearly always possible to adjust mathematical expressions that allow for the interpolation of geoidal heights. The aim of this paper is to evaluate the efficiency of Artificial Neural Network (ANN) in the process of predicting geoidal heights, having the State of Sao Paulo as the area of study. The information used is based on a set of 157 BMs, evenly distributed all across the State. The horizontal coordinates (latitude and longitude) and the vertical coordinates (geometrical, orthometrical and geoidal heights) of these BMs are known. From the 157 BMs, 115 were used for the training of RNA and 42 in the process of simulation to assess the efficiency of the model proposed. Efficiency is based in determining the discrepancies (error) between known geoidal heights and those which were obtained by the neural model. As a contribution to this research, we have compared the values simulated with the Earth Gravitational Model 2008 (EGM2008) and with the MAPGEO2004 as well. In terms of results, the RNA produced a mean absolute error of 0.19 m ± 0.14 m and a strong correlation (R2 = 0.9871) with the values taken as true. Statistically, the tests showed that there was no difference between known geoidal heights and those which were provided by the neural model for a level of significance of 5%. When we compare these results with the EGM2008 and MAPGEO2004, the RNA has an error reduction of 0.07 and 0.44 m, respectively.

A new relationship between the quality criteria for geodetic networks

The goal of this paper is to present a new relationship between the quality criteria for geodetic networks. The quality criteria described here are fourfold: positional uncertainty of network points, considering both bias and precision (at a given confidence level); the maximum allowable number of undetected outliers; the level of reliability and its homogeneity for the observations; and the minimum power of the data snooping test procedure for multiple alternative hypotheses. The highlights consist of the use of advanced concepts, such as reliability measures for multiple outliers and the power of the test for multiple alternative hypotheses (instead of the single outlier and/or the single alternative hypothesis case); and a sequential computational procedure, wherein the quality criteria are mathematically related, instead of being treated as separate criteria. Its practical application is demonstrated numerically in the design of a real horizontal network. A satisfactory performance was achieved by means of simulations. Furthermore, Monte Carlo experiments were conducted to verify the power of the test and the positional uncertainty following the approach proposed. Results provide empirical evidence that the quality criteria present realistic outputs.

PROPOSTA DE MÉTODO DE REDE GNSS POR PPP E ANÁLISE DE CONFIABILIDADE

Embora o metodo de posicionamento GNSS tradicionalmente utilizado em redes geodesicas seja o relativo. O nivel de acuracia obtido com o metodo de Posicionamento por Ponto Preciso (PPP) abre uma nova perspectiva. No PPP sao utilizados dados de apenas um receptor GNSS e e fundamental o uso de efemerides e correcoes dos relogios dos satelites, ambas com alta precisao. Neste artigo e apresentada uma metodologia de desenvolvimento de rede utilizando dados GNSS processados pelo metodo de PPP e a verificacao da sua potencialidade em aplicacoes geodesicas. Os dados utilizados sao de estacoes GNSS pertencentes a RBMC/IBGE. O servico de processamento de PPP utilizado e o fornecido pelo IBGE. A partir dos resultados foram feitas analises para verificar a aplicabilidade da metodologia descrita em rede com dados GNSS de 24, 6 e 4 horas de rastreio. Apos o ajustamento, os testes global e data snooping foram aplicados e tambem foi analisada a confiabilidade da rede com o objetivo de avaliar o metodo proposto, alem de verificar a influencia do tempo de rastreio nos resultados.