Wavelet shrinkage: High frequency multipath reduction from GPS relative positioning

The wavelet transform is used to reduce the high frequency multipath of pseudorange and carrier phase GPS double differences (DDs). This transform decomposes the DD signal, thus separating the high frequencies due to multipath effects. After the decomposition, the wavelet shrinkage is performed by thresholding to eliminate the high frequency component. Then the signal can be reconstructed without the high frequency component. We show how to choose the best threshold. Although the high frequency multipath is not the main multipath error component, its correction provides improvements of about 30% in pseudorange average residuals and 24% in carrier phases. The results also show that the ambiguity solutions become more reliable after correcting the high frequency multipath.

GPS Satellite Kinematic Relative Positioning: Analyzing and Improving the Functional Mathematical Model Using Wavelets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Using cubic splines to mitigate systematic errors in GPS relative positioning

Systematic errors can have a significant effect on GPS observable. In medium and long baselines the major systematic error source are the ionosphere and troposphere refraction and the GPS satellites orbit errors. But, in short baselines, the multipath is more relevant. These errors degrade the accuracy of the positioning accomplished by GPS. So, this is a critical problem for high precision GPS positioning applications. Recently, a method has been suggested to mitigate these errors: the semiparametric model and the penalised least squares technique. It uses a natural cubic spline to model the errors as a function which varies smoothly in time. The systematic errors functions, ambiguities and station coordinates, are estimated simultaneously. As a result, the ambiguities and the station coordinates are estimated with better reliability and accuracy than the conventional least square method.

Modifying the stochastic model to mitigate GPS systematic errors in relative positioning

The GPS observables are subject to several errors. Among them, the systematic ones have great impact, because they degrade the accuracy of the accomplished positioning. These errors are those related, mainly, to GPS satellites orbits, multipath and atmospheric effects. Lately, a method has been suggested to mitigate these errors: the semiparametric model and the penalised least squares technique (PLS). In this method, the errors are modeled as functions varying smoothly in time. It is like to change the stochastic model, in which the errors functions are incorporated, the results obtained are similar to those in which the functional model is changed. As a result, the ambiguities and the station coordinates are estimated with better reliability and accuracy than the conventional least square method (CLS). In general, the solution requires a shorter data interval, minimizing costs. The method performance was analyzed in two experiments, using data from single frequency receivers. The first one was accomplished with a short baseline, where the main error was the multipath. In the second experiment, a baseline of 102 km was used. In this case, the predominant errors were due to the ionosphere and troposphere refraction. In the first experiment, using 5 minutes of data collection, the largest coordinates discrepancies in relation to the ground truth reached 1.6 cm and 3.3 cm in h coordinate for PLS and the CLS, respectively, in the second one, also using 5 minutes of data, the discrepancies were 27 cm in h for the PLS and 175 cm in h for the CLS. In these tests, it was also possible to verify a considerable improvement in the ambiguities resolution using the PLS in relation to the CLS, with a reduced data collection time interval. © Springer-Verlag Berlin Heidelberg 2007.

Stochastic modelling considering ionospheric scintillation effects on GNSS relative and point positioning

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

GPS receivers for georeferencing of spatial variability of soil attributes

A caracterização da variabilidade espacial dos atributos do solo é indispensável para subsidiar práticas agrícolas de maneira sustentável. A utilização da geoestatística para caracterizar a variabilidade espacial desses atributos, como a resistência mecânica do solo à penetração (RP) e a umidade gravimétrica do solo (UG), é, hoje, prática usual na agricultura de precisão. O resultado da análise geoestatística é dependente da densidade amostral e de outros fatores, como o método de georreferencimento utilizado. Desta forma, o presente trabalho teve como objetivo comparar dois métodos de georreferenciamento para a caracterização da variabilidade espacial da RP e da UG, bem como a correlação espacial dessas variáveis. Foi implantada uma malha amostral de 60 pontos, espaçados em 20 m. Para as medições da RP, utilizou-se de penetrógrafo eletrônico e, para a determinação da UG, utilizou-se de trado holandês (profundidade de 0,0-0,1 m). As amostras foram georreferenciadas, utilizando-se do método de Posicionamento por Ponto Simples (PPS), com de (retirar) receptor GPS de navegação, e Posicionamento Relativo Semicinemático, com receptor GPS geodésico L1. Os resultados indicaram que o georreferenciamento realizado pelo PPS não interferiu na caracterização da variabilidade espacial da RP e da UG, assim como na estrutura espacial da relação dos atributos.

Application of ionospheric corrections in the equatorial region for L1 GPS users

In the absence of the selective availability, which was turned off on May 1, 2000, the ionosphere can be the largest source of error in GPS positioning and navigation. Its effects on GPS observable cause a code delays and phase advances. The magnitude of this error is affected by the local time of the day, season, solar cycle, geographical location of the receiver and Earth's magnetic field. As it is well known, the ionosphere is the main drawback for high accuracy positioning, when using single frequency receivers, either for point positioning or relative positioning of medium and long baselines. The ionosphere effects were investigated in the determination of point positioning and relative positioning using single frequency data. A model represented by a Fourier series type was implemented and the parameters were estimated from data collected at the active stations of RBMC (Brazilian Network for Continuous Monitoring of GPS satellites). The data input were the pseudorange observables filtered by the carrier phase. Quality control was implemented in order to analyse the adjustment and to validate the significance of the estimated parameters. Experiments were carried out in the equatorial region, using data collected from dual frequency receivers. In order to validate the model, the estimated values were compared with ground truth. For point and relative positioning of baselines of approximately 100 km, the values of the discrepancies indicated an error reduction better than 80% and 50% respectively, compared to the processing without the ionospheric model. These results give an indication that more research has to be done in order to provide support to the L1 GPS users in the Equatorial region.

Análise do modelo troposférico empregado na geração de uma estação de referência virtual utilizando o posicionamento por ponto preciso

In the past few years the interest is accomplishing a high accuracy positioning increasing. One of the methods that has been applied by the scientific community is the network based on positioning. By using multiple reference station data, it is possible to obtain centimetric positioning in a larger coverage area, in addition to gain in reliability, availability and integrity of the service. Besides, using this concept, it is possible to model the atmospheric effects (troposphere refraction and ionosphere effect). Another important question concerning this topic is related to the transmission of the network corrections to the users. There are some possibilities for this fact and an efficient one is the Virtual Reference Station (VRS) concept. In the VRS concept, a reference station is generated near to the rover receiver (user). This provides a short baseline and the user has the possibility of using a single frequency receiver to accomplish the relative positioning. In order to test this kind of positioning method, a software has been developed at São Paulo State University. In this paper, the methodology applied to generate the VRS data is described and the VRS quality is analyzed by using the Precise Point Positioning (PPP) method.

Efeitos de segunda e terceira ordem da ionosfera no posicionamento GNSS no Brasil

O Sistema de Posicionamento Global (GPS) transmite seus sinais em duas freqüências, o que permite eliminar matematicamente os efeitos de primeira ordem da ionosfera através da combinação linear ionosphere free. Porém, restam os efeitos de segunda e terceira ordem, os quais podem provocar erros da ordem de centímetros nas medidas GPS. Esses efeitos, geralmente, são negligenciados no processamento dos dados GPS. Os efeitos ionosféricos de primeira, segunda e terceira ordem são diretamente proporcionais ao TEC presente na ionosfera, porém, no caso dos efeitos de segunda e terceira ordem, comparecem também o campo magnético da Terra e a máxima densidade de elétrons, respectivamente. Nesse artigo, os efeitos de segunda e terceira ordem da ionosfera são investigados, sendo que foram levados em consideração no processamento de dados GPS na região brasileira para fins de posicionamento. Serão apresentados os modelos matemáticos associados a esses efeitos, as transformações envolvendo o campo magnético da Terra e a utilização do TEC advindo dos Mapas Globais da Ionosfera ou calculados a partir das observações GPS de pseudodistância. O processamento dos dados GPS foi realizado considerando o método relativo estático e cinemático e o posicionamento por ponto preciso (PPP). Os efeitos de segunda e terceira ordem foram analisados considerando períodos de alta e baixa atividade ionosférica. Os resultados mostraram que a não consideração desses efeitos no posicionamento por ponto preciso e no posicionamento relativo para linhas de base longas pode introduzir variações da ordem de poucos milímetros nas coordenadas das estações, além de variações diurnas em altitude da ordem de centímetros.

Período de mínima atividade solar: melhora no desempenho do posicionamento relativo

In the relative positioning, even considering that part of the errors due to ionosphere is canceled with the double-difference observations, strong ionospheric effects can occur in maximum solar activity period. However, in minimum solar activity period, the ionospheric effects decrease significantly and therefore an improvement of the relative positioning performance takes place. In this paper we aim at showing that improvement for the scientific and GPS community users. So, have been experiments by using GPS data of two stations of the Brazilian Network for Continuous Monitoring of GPS, forming a baseline of 430 km. The processing were use accomplished with interval of two hours, and only L1 carrier data have been used. The analysis of the obtained results has been carried out from the discrepancies between the "true" coordinates and corresponding ones obtained in the processing. In maximum solar activity period the discrepancy value reached 25 m. on the other hand, in minimum solar activity period, the discrepancy value reached 5,5 m. It is important to emphasize that the majority of the discrepancy values didn't exceed 0,50 m, and in some cases only reached 0,10 m. This shows the increase of application possibilities of the relative positioning using single-frequency GPS receivers in minimum solar activity period.

High precision GPS network with precise ephemerides and earth body tide model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Avaliação do nível de multicaminho no posicionamento relativo GPS e sua atenuação através da análise de multiresolução

The multipath effect affects the differential and relative positioning, even that one involving short baselines. So it is necessary to detect this effect, check the caused error level, and mainly, its removal. This paper aims at analysing and comparing some useful components in the detection of this effect. These components are the Signal to Noise Ratio (SNR), the values of MP1 and MP2 obtained from the TEQC software that indicates the multipath level in the carriers L1 and L2, the multipath repeatability in consecutive days and the elevation angle and the azimuth of the satellites. For this purpose, an experiment is carried out, comparing such components in the presence and the absence of reflector objects that cause the multipath. Not only there is clear multipath repeatability in the residuals, but it also appears in the measures SNR, MP1 and MP2, reaching up 99% of correlation. For reduction, at least, of the high frequency multipath effect, the Multi-Resolution Analysis using wavelets is applied in the double differences (DD) measures. Some statistical tests were accomplished, which indicate results improvement, and mainly, larger reliability in the solution of the ambiguities, reaching up 49% of improvement concerning the Ratio test without applying the proposed method.

Conseqüências de uma tempestade geomagnética no posicionamento relativo com receptores GPS de simples freqüência

The error associated with the ionosphere depends on Total Electron Content (TEC) of the ionosphere. The geomagnetic field exerts strong influence in the TEC variation, because it controls the movement of the electrons. After solar events the magnetic lines of force can be compressed, characterizing the geomagnetic storm. The aim of this paper is to present to geodesic community the effects of a geomagnetic storm in the relative positioning. The processing of the data was accomplished with an interval of two hours, with a 430 km baseline. The analyze of the obtained results have been carried out from the discrepancies between the true coordinates and corresponding ones obtained in the processing of the baseline. The used data in this paper include the period of 30/03/2001 up to 02/04/2001. In March 31 a strong geomagnetic storm happened. One day after, that it corresponds to main phase of the storm, the values of the discrepancies decreased significantly. For instance, in 01:00-03:00 UT period, the value of the planimetric discrepancy reached 20 m in the storm day. However, in the main phase of the storm, the planimetric discrepancy decreased to 0.1 m.

Geração de VRS a partir de modelos atmosféricos: Conceito, implementação e resultados

Nowadays, with the implantation of GNSS (Global Navigation Satellite System) reference station networks, several positioning techniques have been developed and/or improved. Using such kind of network data it is possible to model the GNSS distance dependent errors and to compute correction terms for the network region. Several methods have been developed to formulate the corrections terms from network stations data. A method that has been received a great attention is the Virtual Reference Station (VRS). The idea is that the VRS data resemble as much as possible a real receiver data placed in the same local. Therefore, the user has the possibility of using the VRS as if it were a real reference station in your proximities, and to accomplish the relative positioning with a single frequency receiver. In this paper it is described a different methodology applied to implement the VRS concept, using atmospheric models developed by Brazilian researchers. Besides, experiments for evaluating the quality of generated VRS are presented, showing the efficiency of the proposed method.

Towards forecasting and mitigating ionospheric scintillation effects on GNSS

The effect of the ionosphere on the signals of Global Navigation Satellite Systems (GNSS), such as the Global Positionig System (GPS) and the proposed European Galileo, is dependent on the ionospheric electron density, given by its Total Electron Content (TEC). Ionospheric time-varying density irregularities may cause scintillations, which are fluctuations in phase and amplitude of the signals. Scintillations occur more often at equatorial and high latitudes. They can degrade navigation and positioning accuracy and may cause loss of signal tracking, disrupting safety-critical applications, such as marine navigation and civil aviation. This paper addresses the results of initial research carried out on two fronts that are relevant to GNSS users if they are to counter ionospheric scintillations, i.e. forecasting and mitigating their effects. On the forecasting front, the dynamics of scintillation occurrence were analysed during the severe ionospheric storm that took place on the evening of 30 October 2003, using data from a network of GPS Ionospheric Scintillation and TEC Monitor (GISTM) receivers set up in Northern Europe. Previous results [1] indicated that GPS scintillations in that region can originate from ionospheric plasma structures from the American sector. In this paper we describe experiments that enabled confirmation of those findings. On the mitigation front we used the variance of the output error of the GPS receiver DLL (Delay Locked Loop) to modify the least squares stochastic model applied by an ordinary receiver to compute position. This error was modelled according to [2], as a function of the S4 amplitude scintillation index measured by the GISTM receivers. An improvement of up to 21% in relative positioning accuracy was achieved with this technnique.