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.

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.

Integration of a regional GPS network within ITRF using precise point positioning

GPS precise point positioning (PPP) can provide high precision 3-D coordinates. Combined pseudorange and carrier phase observables, precise ephemeris and satellite clock corrections, together with data from dual frequency receivers, are the key factors for providing such levels of precision (few centimeters). In general, results obtained from PPP are referenced to an arbitrary reference frame, realized from a previous free network adjustment, in which satellite state vectors, station coordinates and other biases are estimated together. In order to obtain consistent results, the coordinates have to be transformed to the relevant reference frame and the appropriate daily transformation parameters must be available. Furthermore, the coordinates have to be mapped to a chosen reference epoch. If a velocity field is not available, an appropriated model, such as NNR-NUVEL-IA, has to be used. The quality of the results provided by this approach was evaluated using data from the Brazilian Network for Continuous Monitoring of the Global Positioning System (RBMC), which was processed using GIPSY-OASIS 11 software. The results obtained were compared to SIRGAS 1995.4 and ITRF2000, and reached precision better than 2cm. A description of the fundamentals of the PPP approach and its application in the integration of regional GPS networks with ITRF is the main purpose of this paper.

Atmospheric Models Applied to DGPS and RTK Network in Brazil: Preliminary Results

Several positioning techniques have been developed to explore the GPS capability to provide precise coordinates in real time. However, a significant problem to all techniques is the ionosphere effect and the troposphere refraction. Recent researches in Brazil, at São Paulo State University (UNESP), have been trying to tackle these problems. In relation to the ionosphere effects it has been developed a model named Mod_Ion. Concerning tropospheric refraction, a model of Numerical Weather Prediction(NWP) has been used to compute the zenithal tropospheric delay (ZTD). These two models have been integrated with two positioning methods: DGPS (Differential GPS) and network RTK (Real Time Kinematic). These two positioning techniques are being investigated at São Paulo State University (UNESP), Brazil. The in-house DGPS software was already finalized and has provided very good results. The network RTK software is still under development. Therefore, only preliminary results from this method using the VRS (Virtual Reference Station) concept are presented.

Análise de séries temporais de coordenadas estimadas com GPS: uma proposta metodológica para detecção, remoção e recuperação de efeitos sazonais

GPS active networks are more and more used in geodetic surveying and scientific experiments, as water vapor monitoring in the atmosphere and lithosphere plate movement. Among the methods of GPS positioning, Precise Point Positioning (PPP) has provided very good results. A characteristic of PPP is related to the modeling and/or estimation of the errors involved in this method. The accuracy obtained for the coordinates can reach few millimeters. Seasonal effects can affect such accuracy if they are not consistent treated during the data processing. Coordinates time series analyses have been realized using Fourier or Harmonics spectral analyses, wavelets, least squares estimation among others. An approach is presented in this paper aiming to investigate the seasonal effects included in the stations coordinates time series. Experiments were carried out using data from stations Manaus (NAUS) and Fortaleza (BRFT) which belong to the Brazilian Continuous GPS Network (RBMC). The coordinates of these stations were estimated daily using PPP and were analyzed through wavelets for identification of the periods of the seasonal effects (annual and semi-annual) in each time series. These effects were removed by means of a filtering process applied in the series via the least squares adjustment (LSQ) of a periodic function. The results showed that the combination of these two mathematical tools, wavelets and LSQ, is an interesting and efficient technique for removal of seasonal effects in time series.

RINEX_HO: second- and third-order ionospheric corrections for RINEX observation files

When GNSS receivers capable of collecting dual-frequency data are available, it is possible to eliminate the first-order ionospheric effect in the data processing through the ionosphere-free linear combination. However, the second- and third-order ionospheric effects still remain. The first-, second- and third-order ionospheric effects are directly proportional to the total electron content (TEC), although the second- and third-order effects are influenced, respectively, by the geomagnetic field and the maximum electron density. In recent years, the international scientific community has given more attention to these kinds of effects and some works have shown that for high precision GNSS positioning these effects have to be taken into consideration. We present a software tool called RINEX_HO that was developed to correct GPS observables for second- and third-order ionosphere effects. RINEX_HO requires as input a RINEX observation file, then computes the second- and third-order ionospheric effects, and applies the corrections to the original GPS observables, creating a corrected RINEX file. The mathematical models implemented to compute these effects are presented, as well as the transformations involving the earth's magnetic field. The use of TEC from global ionospheric maps and TEC calculated from raw pseudorange measurements or pseudoranges smoothed by phase is also investigated.

On determining spectral parameters, tracking jitter, and GPS positioning improvement by scintillation mitigation

A method of determining spectral parameters p (slope of the phase PSD) and T (phase PSD at 1 Hz) and hence tracking error variance in a GPS receiver PLL from just amplitude and phase scintillation indices and an estimated value of the Fresnel frequency has been previously presented. Here this method is validated using 50 Hz GPS phase and amplitude data from high latitude receivers in northern Norway and Svalbard. This has been done both using (1) a Fresnel frequency estimated using the amplitude PSD (in order to check the accuracy of the method) and (2) a constant assumed value of Fresnel frequency for the data set, convenient for the situation when contemporaneous phase PSDs are not available. Both of the spectral parameters (p, T) calculated using this method are in quite good agreement with those obtained by direct measurements of the phase spectrum as are tracking jitter variances determined for GPS receiver PLLs using these values. For the Svalbard data set, a significant difference in the scintillation level observed on the paths from different satellites received simultaneously was noted. Then, it is shown that the accuracy of relative GPS positioning can be improved by use of the tracking jitter variance in weighting the measurements from each satellite used in the positioning estimation. This has significant advantages for scintillation mitigation, particularly since the method can be accomplished utilizing only time domain measurements thus obviating the need for the phase PSDs in order to extract the spectral parameters required for tracking jitter determination.

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)

Avaliação das previsões do atraso zenital troposférico para a América do Sul, obtidas usando modelo de previsão numérica de tempo com alta resolução espacial

A Center for Weather Forecast and Climatic Studies of National Institute for Space Research (CPTEC/INPE) has provided to the Brazilian Geodetic community, since 2004, an alternative to correct the GNSS observables from the tropospheric refraction. Numerical Weather Prediction (NWP) Model is used to generate Zenital Tropospheric Delay (ZTD). For the version 1, it was developed a model with horizontal resolution of 100 km, which was updated with Eta model, with resolution of 20 km. This paper provides the most significative details of the current version, as well an evaluation of its quality, using for such ZTD estimates from GPS data collect at RBMC. Comparing to the old version, considerable improvement could be observed from the new model, mainly in Brasilia and Curitiba, reaching up to 55% improvement. When all stations were used in the quality control, almost null bias and RMS of about 4 to 5 cm could be observed.

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.

Desempenho do modelo global da ionosfera do IGS: avaliação no posicionamento por ponto na região sul do Brasil em período de alta atividade solar

One of the main drawbacks of the GPS accuracy for L1 users is the error due to ionosphere. This error depends on the total electron content presents in the ionosphere, as well as of the carrier frequency. Some models have been developed to correct GPS observables of the systematic error due to the ionosphere. The model more known and used is the Klobuchar model, which corrected 50-60% of the ionospheric error approximately. Alternatively, IGS (International GNSS Service) also has developed a model called Global Ionospheric Map (GIM). These maps, in format IONEX, are available in the site of the IGS, and one of the applications of them is to correct the GPS observables of the error due to ionosphere. This work aims at evaluating the quality of GPS point positioning using the IGS ionospheric model in the southerm region of Brazil. Tests carried out had shown an average improvement in the horizontal and vertical determination of 44% and 77%, respectively, when GIM is used in the point positioning.

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.