Second and Third Order Ionospheric Effects on GNSS Positioning: A Case Study in Brazil

The Global Positioning System (GPS) transmits signals in two frequencies. It allows the correction of the first order ionospheric effect by using the ionosphere free combination. However, the second and third order ionospheric effects, which combined may cause errors of the order of centimeters in the GPS measurements, still remain. In this paper the second and third order ionospheric effects, which were taken into account in the GPS data processing in the Brazilian region, were investigated. The corrected and not corrected GPS data from these effects were processed in the relative and precise point positioning (PPP) approaches, respectively, using Bernese V5.0 software and the PPP software (GPSPPP) from NRCAN (Natural Resources Canada). The second and third order corrections were applied in the GPS data using an in-house software that is capable of reading a RINEX file and applying the corrections to the GPS observables, creating a corrected RINEX file. For the relative processing case, a Brazilian network with long baselines was processed in a daily solution considering a period of approximately one year. For the PPP case, the processing was accomplished using data collected by the IGS FORT station considering the period from 2001 to 2006 and a seasonal analysis was carried out, showing a semi-annual and an annual variation in the vertical component. In addition, a geographical variation analysis in the PPP for the Brazilian region has confirmed that the equatorial regions are more affected by the second and third order ionospheric effects than other regions.

Quality of TEC Estimated with Mod Ion Using GPS and GLONASS Data

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Higher order ionospheric effects in GNSS positioning in the European region

After removal of the Selective Availability in 2000, the ionosphere became the dominant error source for Global Navigation Satellite Systems (GNSS), especially for the high-accuracy (cm-mm) demanding applications like the Precise Point Positioning (PPP) and Real Time Kinematic (RTK) positioning.The common practice of eliminating the ionospheric error, e. g. by the ionosphere free (IF) observable, which is a linear combination of observables on two frequencies such as GPS L1 and L2, accounts for about 99% of the total ionospheric effect, known as the first order ionospheric effect (Ion1). The remaining 1% residual range errors (RREs) in the IF observable are due to the higher - second and third, order ionospheric effects, Ion2 and Ion3, respectively. Both terms are related with the electron content along the signal path; moreover Ion2 term is associated with the influence of the geomagnetic field on the ionospheric refractive index and Ion3 with the ray bending effect of the ionosphere, which can cause significant deviation in the ray trajectory (due to strong electron density gradients in the ionosphere) such that the error contribution of Ion3 can exceed that of Ion2 (Kim and Tinin, 2007).The higher order error terms do not cancel out in the (first order) ionospherically corrected observable and as such, when not accounted for, they can degrade the accuracy of GNSS positioning, depending on the level of the solar activity and geomagnetic and ionospheric conditions (Hoque and Jakowski, 2007). Simulation results from early 1990s show that Ion2 and Ion3 would contribute to the ionospheric error budget by less than 1% of the Ion1 term at GPS frequencies (Datta-Barua et al., 2008). Although the IF observable may provide sufficient accuracy for most GNSS applications, Ion2 and Ion3 need to be considered for higher accuracy demanding applications especially at times of higher solar activity.This paper investigates the higher order ionospheric effects (Ion2 and Ion3, however excluding the ray bending effects associated with Ion3) in the European region in the GNSS positioning considering the precise point positioning (PPP) method. For this purpose observations from four European stations were considered. These observations were taken in four time intervals corresponding to various geophysical conditions: the active and quiet periods of the solar cycle, 2001 and 2006, respectively, excluding the effects of disturbances in the geomagnetic field (i.e. geomagnetic storms), as well as the years of 2001 and 2003, this time including the impact of geomagnetic disturbances. The program RINEX_HO (Marques et al., 2011) was used to calculate the magnitudes of Ion2 and Ion3 on the range measurements as well as the total electron content (TEC) observed on each receiver-satellite link. The program also corrects the GPS observation files for Ion2 and Ion3; thereafter it is possible to perform PPP with both the original and corrected GPS observation files to analyze the impact of the higher order ionospheric error terms excluding the ray bending effect which may become significant especially at low elevation angles (Ioannides and Strangeways, 2002) on the estimated station coordinates.

Assimilação do IWV-GPS no Brasil: otimização das estimativas do atraso zenital troposférico em tempo real

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

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.

Avaliação de estratégias de detecção e correção de perdas de ciclos na portadora GPS L1

To prevent large errors in the GPS positioning, cycle slips should be detected and corrected. Such procedure is not trivial, mainly for single frequency receivers, but normally it is not noticed by the users. Thus, it will be discussed some practical and more used methods for cycle slips detection and correction using just GPS single-frequency observations. In the detection, the triple (TD) and tetra differences were used. In relation to the correction, in general, each slip is corrected in the preprocessing. Otherwise, other strategies should be adopted during the processing. In this paper, the option was to the second option, and two strategies were tested. In one of them, the elements of the covariance matrix of the involved ambiguities are modified and new ambiguity estimation starts. In the one, a new ambiguity is introduced as additional unknown when a cycle slip is detected. These possibilities are discussed and compared in this paper, as well as the aspects related to the practicity, implementation and viability of each one. Some experiments were carried out using simulated data with cycle slips in different satellites and epochs of the data. This allowed assessing and comparing the results of different occurrence of cycle slip and correction in several conditions.

Aujstamento de redes GPS em conformidade com as exigências da Lei 10.267/2001

In Brazil, there have been several GPS applications and with the introduction of the Law 10.267/2001 that among other dispositions, deals with georeferencing of the rural parcels. However, most commercial softwares of processing and adjustment of GPS data don't let users to evaluate their results in a reliable way. For example, the constraints are normally used as absolute, which provides results with very optimists precisions. The adoption of additional analyses and the implementation of softwares can reduce these kinds of problems. Thus, a software for adjustment of GPS networks was developed, aiming at assisting the requirements of the Law 10.267/2001 in a reliable way. In this context, in this work it is analyzed the adjustments of GPS networks, by using absolute and relative constraints. In the latter, the adjustments were accomplished considering and not considering the correlations among the coordinate positions.

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)

Artificial satellites orbits in 2:1 resonance: GPS constellation

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

Orbit determination using GPS including perturbations due to geopotential coefficients of high degree and order and solar radiation pressure

The main target here is to determine the orbit of an artificial satellite, using signals of the GPS constellation and least squares algorithms implemented through sequential Givens rotations as a method of estimation, with the aim of improving the performance of the orbit estimation process and, at the same time, minimizing the computational procedure cost. Geopotential perturbations up to high order and direct solar radiation pressure were taken into account. It was also considered the position of the GPS antenna on the satellite body that, lately, consists of the influence of the satellite attitude motion in the orbit determination process. An application has been done, using real data from the Topex/Poseidon satellite, whose ephemeris is available at Internet. The best accuracy obtained in position was smaller than 5 meters for short period (2 hours) and smaller than 28 meters for long period (24 hours) orbit determination. In both cases, the perturbations mentioned before were taken into consideration and the analysis occurred without selective availability on the signals measurements.

GPS Satellites Orbits: Resonance

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Efeitos de tempestades magnéticas em sinais de gps, em Natal, Brasil

Satellites signals present disturbances (scintillations), due to presence of irregularities in the ionospheric plasma. In the present work, we dedicate to the study of the attenuation of these scintillations that is, an improvement in the signal, during the main magnetic storm phase during the period of October 2006 to February 2007. Using amplitude of scintillation 1.5GHz (L1) data of the net of satellites GPS, in the ionospheric station of Natal (5.84o S, 35.20o O, -20o dip) and geomagnetic indices, during the minimum solar cycle (referred to as cycle 23), demonstrating its anti-correlation between magnetic activity (Kp) and index of scintillation () (Bonelli2005 method, that works for solar maximum, Bonelli(2005)). These results show that these storms correspond to category I of Aarons (1991). The magnetic storms can generate irregularities when the electric feld of penetration eastward on the pre-reversal hour intensificating that and can too generate irregularities on midnight and sunlight period. The limitation of the method applied here is that it is not considering some storms that had also occurred during equinox and summer in the Brazilian region. For this reason, we will use additional data of the stations of São João de Cariri (Imager and Photometer) and of the station at Fortaleza (Digissonde data), as aid to analyze these storms. The storms that had been left out by the applied method, fit in the other two categories of Aarons, with one only exception (storm of January, 02). We show that in the day of the main phase of the magnetic storm, and with presence of bubbles (according to data of the Imager and Photometer), the speed of vertical drift ~E ~B (hF=t) is below 20m/s, that is the threshold found for Anderson al., (2004) (>20m/s as condition favorable to the formation of irregularities and increase in the scintillation index). This reduction of the speed is due to solar minimum

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

Cada vez mais é crescente o uso do GPS (Global Positioning System ) em estudos da atmosfera terrestre. Neste artigo, a atmosfera superior da Terra, denominada ionosfera, foi estudada durante um período de alta atividade solar (ano de 2001) usando dados de receptores GPS de dupla freqüência localizados na região brasileira, pertencentes à RBMC (Rede Brasileira de Monitoramento Contínuo). A partir dos dados GPS foram calculados os valores de TEC (Total Electron Content - Conteúdo Total de Elétrons) da ionosfera. Adicionalmente foram incluídos no estudo dados de freqüência crítica da camada F2 advinda de Digissondas localizadas em São Luís/MA (3ºS; 44ºW) e Cachoeira Paulista/SP (22ºS; 45ºW), para fins de comparação. de uma forma geral, os resultados mostraram maiores valores de TEC durante os meses próximos aos equinócios e menores durante os meses de inverno. Quanto à variação diária do TEC, os menores valores foram verificados por volta das 4-6 HL (Hora Local) e os maiores durante o período da tarde, com valores um pouco maiores para São Luís. O segundo pico da anomalia equatorial foi verificado em Cachoeira Paulista nos meses próximos aos equinócios e verão. Na maioria dos meses, uma alta correlação linear foi verificada quando realizada a comparação entre os valores de freqüência crítica da camada F2 e os de TEC, principalmente para São Luís.

Avaliação de perfis atmosféricos de rádio ocultação GPS do satélite CHAMP sobre a América do Sul

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