CIRCLE FITTING FOR IMPROVED GNSS POSITIONING VIA SMARTPHONES FOR ENGINEERING PURPOSES

With access to the raw data collected by certain Android smartphones, it is possible to perform post-processing of the data. Thus, it is possible to employ certain satellite positioning methods that were previously restricted to geodetic receivers. Thanks to this and other innovations, such as the emergence of smartphones with modern GNSS sensors, a promising scenario is seen when employing these devices in engineering applications. Generally, in certain applications that require high accuracy, centimeter and millimeter order, geodetic receivers are used. However, these devices are expensive when compared to smartphones. In this research, the coordinates of a point were determined via a smartphone with a modern GNSS sensor, whose data were post-processed by the IBGE-PPP service, using the combination GPS+GLONASS and L1 frequency. Thus, using circle adjustment techniques based on least squares, it was possible to obtain horizontal accuracy of approximately 12 cm and 25 cm with a set of about 128-hour and 24-hour sessions respectively. The results obtained in this research suggest that the applied methodology can be used in certain applications in engineering, such as land surveying of rural properties

An Attempt to Analyse Baarda’s Iterative Data Snooping Procedure based on Monte Carlo Simulation

William Sealy Gosset, otherwise known as “Student”, Fisher's disciple, was one of the pioneers in the development of modern statistical method and its application to the design and analysis of experiments. Although there were no computers in his time, he discovered the form of the “t distribution” by a combination of mathematical and empirical work with random numbers. This is now known as an early application of the Monte Carlo simulation. Today with the fast computers and large data storage systems, the probabilities distribution can be estimated using computerized simulation. Here, we use Monte Carlo simulation to investigate the efficiency of the Baarda’s iterative data snooping procedure as test statistic for outlier identification in the Gauss-Markov model. We highlight that the iterative data snooping procedure can identify more observations than real number of outliers simulated. It has a deserved attention in this work. The available probability of over-identification allows enhancing the probability of type III error as well as probably the outlier identifiability. With this approach, considering the analysed network, in general, the significance level of 0.001 was the best scenario to not make mistake of excluding wrong observation. Thus, the data snooping procedure was more realistic when the over-identifications case is considered in the simulation. In the end, we concluded that for GNSS network that the iterative data snooping procedure based on Monte Carlo can locate an outlier in the order of magnitude 4.5σ with high success rate

THE INFLUENCE OF THE DEFLECTION OF THE VERTICAL ON GEODETIC SURVEYS IN BRAZIL

The densification of geodetic surveys using classical positioning techniques such as total stations may be necessary due to the quality of Global Navigation Satellite System (GNSS) positioning in urban canyons. However, the correction of distances and angles due to the deflection of the vertical (DV) is usually neglected in commercial softwares and internal software of total stations. Given that context, this research seeks to estimate the influence of DV on the horizontal geodetic positioning with total station in the Brazilian territory. Secondarily, it seeks to demonstrate the practical application of DV in the densification of geodetic networks. It is important to note that land surveys in Brazil must be connected to a geodetic network; therefore, the neglect of DV may degrade the positional quality of geodetic surveys. Results obtained indicate differences in horizontal geodetic positions of up to 45 ppm. Considering the desired positional quality of the geodetic network, such values demonstrate the importance of a proper correction for the DV

COMO ESTIMAR O PODER DO TESTE MÍNIMO E VALORES LIMITES PARA O INTERVALO DE CONFIANÇA DO DATA SNOOPING.

O Data Snooping (DS) é o método mais bem estabelecido para identificar errosgrosseiros (outliers) em dados geodésicos, com uma determinada probabilidade. O poder do teste do DS é a probabilidade deste identificar corretamente um erro grosseiro, enquanto o intervalo de confiança do DS é a probabilidade deste não rejeitar uma observação não contaminada por erro grosseiro. Na prática, o poder do teste é sempre desconhecido. Desta forma, o objetivo deste trabalho é apresentar uma revisão teórica sobre como determinar o poder do teste mínimo e valores limites para o intervalo de confiança do DS, em um cenário n-dimensional, ou seja, considerando todas as observações envolvidas. Além da revisão teórica, um exemplo numérico envolvendo uma rede de nivelamento geométrico simulada é apresentado. Os resultados obtidos nos experimentos foram concordantes com os valores teóricos previamente calculados, ou seja, a metodologia revista apresentou desempenho satisfatório na prática. O exemplo apresentado também evidencia a  importância da metodologia revista na etapa de planejamento (ou pré-análise) de redes geodésicas

PROPOSTA PARA A ESTIMATIVA DA ACURÁCIA DE REDES GEODÉSICAS HORIZONTAIS INTEGRANDO ANÁLISE DE ROBUSTEZ E DE COVARIÂNCIA

O objetivo deste trabalho é apresentar uma proposta para o controle de qualidade deredes geodésicas bidimensionais por meio das análises de robustez e de covariância.Na metodologia proposta, a acurácia (exatidão) posicional de cada ponto é estimadapor meio de uma possível tendência posicional (via análise de robustez), além daprópria precisão (incerteza) posicional (via análise de covariância), sendo ainda umamedida independente do datum adotado. Além da apresentação do desenvolvimentoteórico do método, a aplicação do mesmo é demonstrada em um exemplo numérico.Os resultados obtidos indicam que, em geral, quanto maior o afastamento de umvértice desconhecido do(s) ponto(s) de controle da rede, maior é a propagação deerros aleatórios sobre este, e, quanto menos observações redundantes ao redor de umponto, maior é a influência de possíveis erros (não aleatórios) sobre este, quandonão detectados

Analysis of on-line PPP service (GDGPS - APPS) for Dual-frequency Receivers: a study involving data from RBMC stations

O PPP (Posicionamento por Ponto Preciso) é um método de posicionamento por GNSS (Global Navigation Satellite System) que vem sendo amplamente utilizado graças aos serviços on-line de processamento, muitos deles disponibilizados de forma gratuita. O PPP requer fundamentalmente dados GNSS de um único receptor e o emprego de efemérides e correções precisas do relógio dos satélites. Um dos serviços on-line de processamento PPP é o APPS (Automatic Precise Positioning Service), disponibilizado de maneira pós-processada pela NASA e derivado do GDGPS (Global Differential GPS), um sistema de monitoramento GPS (Global Positioning System) em tempo real, com mais de 100 estações de monitoramento contínuo e distribuídas globalmente. Neste artigo, foi avaliado o serviço APPS processando dados GPS correspondentes a um período de 30 dias em duas estações do sul e norte do Brasil (POAL-Porto Alegre/RS, e IMPZ-Imperatriz/MA), pertencentes à rede oficial do referencial SIRGAS. Cada arquivo diário continha 24 horas de observações, com taxa de coleta de 15 segundos, e foram processados tempos de rastreio de 2, 4, 6 e 24 horas para cada arquivo. As coordenadas diárias destas estações, estimadas pelo serviço APPS, foram atualizadas para a época de referência do SIRGAS2000 (2000,4) e comparadas com as coordenadas oficiais das estações. As discrepâncias (para o tempo de rastreio de 24 horas) apresentaram erro médio quadrático inferior a 2 cm para as duas estações, tanto na componente vertical, quanto na resultante horizontal, evidenciando o potencial de uso do serviço PPP/APPS em aplicações de alta acurácia, como, por exemplo, em estudos geodinâmicos. Em relação à melhora da exatidão com o aumento do tempo de rastreio, uma ocupação de 4 horas se mostra a mais vantajosa, segundo o estudo realizado (para ambas as estações, as variâncias dos erros são estatisticamente semelhantes para os tempos de rastreio de 4 e 6 horas). Palavras-chave: GPS, GDGPS, Posicionamento por Ponto Preciso, APPS.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

TEORIA DE CONFIABILIDADE GENERALIZADA PARA MÚLTIPLOS OUTLIERS: APRESENTAÇÃO, DISCUSSÃO E COMPARAÇÃO COM A TEORIA CONVENCIONAL

Após o ajustamento de observações pelo método dos mínimos quadrados (MMQ) ter sido realizado, é possível a detecção e a identificação de erros não aleatórios nas observações, por meio de testes estatísticos. A teoria da confiabilidade faz uso de medidas adequadas para quantificar o menor erro detectável em uma observação, e a sua influência sobre os parâmetros ajustados, quando não detectado. A teoria de confiabilidade convencional foi desenvolvida para os procedimentos de teste convencionais, como o data snooping, que pressupõem que apenas uma observação está contaminada por erros grosseiros por vez. Recentemente  foram desenvolvidas medidas de confiabilidade generalizadas, relativas a testes estatísticos que pressupõem a existência, simultânea, de múltiplas observações com erros (outliers). O objetivo deste trabalho é apresentar, aplicar e discutir a teoria de confiabilidade generalizada para múltiplos  outliers. Além da formulação teórica, este artigo também apresenta experimentos realizados em uma rede GPS (Global Positioning System), onde erros propositais foram inseridos em algumas observações e medidas de confiabilidade e testes estatísticos foram calculados utilizando a abordagem para múltiplos  outliers. Comparações com a teoria de confiabilidade convencional também são realizadas. Por fim, apresentam-se as discussões e conclusões obtidas com estes experimentos.

Global Optimization of Redescending Robust Estimators

[EN] Robust estimation has proved to be a valuable alternative to the least squares estimator for the cases where the dataset is contaminated with outliers. Many robust estimators have been designed to be minimally affected by the outlying observations and produce a good fit for the majority of the data. Among them, the redescending estimators have demonstrated the best estimation capabilities. It is little known, however, that the success of a robust estimation method depends not only on the robust estimator used but also on the way the estimator is computed. In the present paper, we show that for complicated cases, the predominant method of computing the robust estimator by means of an iteratively reweighted least squares scheme may result in a local optimum of significantly lower quality than the global optimum attainable by means of a global optimization method. Further, the sequential use of the proposed global robust estimation proves to successfully solve the problem of M-split estimation, that is, the determination of parameters of different functional models implicit in the data.Baselga Moreno, S.; Klein, I.; Sampaio Suraci, S.; Castro De Oliveira, L.; Tomio Matsuoka, M.; Francisco Rofatto, V. (2021). Global Optimization of Redescending Robust Estimators. Mathematical Problems in Engineering. 2021:1-13. https://doi.org/10.1155/2021/9929892S113202

An attempt to analyse Iterative Data Snooping and L1-norm based on Monte Carlo simulation in the context of leveling networks

[EN] The goal of this paper is to evaluate the outlier identification performance of iterative Data Snooping (IDS) and L-1-norm in levelling networks by considering the redundancy of the network, number and size of the outliers. For this purpose, several Monte-Carlo experiments were conducted into three different levelling networks configurations. In addition, a new way to compare the results of IDS based on Least Squares (LS) residuals and robust estimators such as the L-1-norm has also been developed and presented. From the perspective of analysis only according to the success rate, it is shown that L-1-norm performs better than IDS for the case of networks with low redundancy ((r) over bar < 0.5), especially for cases where more than one outlier is present in the dataset. In the relationship between false positive rate and outlier identification success rate, however, IDS performs better than L-1-norm, independently of the levelling network configuration, number and size of outliers.Klein, I.; Suraci, SS.; De Oliveira, LC.; Rofatto, VF.; Matsuoka, MT.; Baselga Moreno, S. (2022). An attempt to analyse Iterative Data Snooping and L1-norm based on Monte Carlo simulation in the context of leveling networks. Survey Review. 54(382):70-78. https://doi.org/10.1080/00396265.2021.187833870785438

Performance comparison of least squares, iterative and global L1 Norm minimization and exhaustive search methods for outlier detection in leveling networks

[EN] Different approaches have been proposed to determine the possible outliers existing in a dataset. The most widely used consists in the application of the data snooping test over the least squares adjustment results. This strategy is very likely to succeed for the case of zero or one outliers but, contrary to what is often assumed, the same is not valid for the multiple outlier case, even in its iterative application scheme. Robust estimation, computed by iteratively reweighted least squares or a global optimization method, is other alternative approach which often produces good results in the presence of outliers, as is the case of exhaustive search methods that explore elimination of every possible set of observations. General statements, having universal validity, about the best way to compute a geodetic network with multiple outliers are impossible to be given due to the many different factors involved (type of network, number and size of possible errors, available computational force, etc.). However, we see in this paper that some conclusions can be drawn for the case of a leveling network, which has a certain geometrical simplicity compared with planimetric or three-dimensional networks though a usually high number of unknowns and relatively low redundancy. Among other results, we experience the occasional failure in the iterative application of the data snooping test, the relatively successful results obtained by both methods computing the robust estimator, which perform equivalently in this case, and the successful application of the exhaustive search method, for different cases that become increasingly intractable as the number of outliers approaches half the number of degrees of freedom of the network.Baselga Moreno, S.; Klein, I.; Suraci, SS.; Castro De Oliveira, L.; Matsuoka, MT.; Rofatto, VF. (2020). Performance comparison of least squares, iterative and global L1 Norm minimization and exhaustive search methods for outlier detection in leveling networks. Acta Geodynamica et Geomaterialia. 17(4):425-438. https://doi.org/10.13168/AGG.2020.003142543817