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.

GPS performance in the quantification of integrated water vapor in Amazonian regions

The Amazonian regions are characterized by large space-time variability in the humidity fields due to the intense convective process in those areas associated with the great humidity potential generated by high temperatures. An experiment denominated RACCI/DRY-TO-WET (RAdiation, Cloud, and Climate Interactions in the Amazonia during the DRY-TO-WET Transition Season) was carried out in the Brazilian Amazonian Region in 2002. The IWV values from GPS and other techniques, such as radiosondes, radiometer and humidity sounding satellites were used in this experiment to supply subsidies to evaluate the aerosols influence in the associated processes modifications to seasonality of atmospheric water vapor. Those regions are one of the most humid of the planet, where IWV (Integrated Water Vapor) average values are in the order of 50 kg/m2. As according the literature the IWV quantification using GPS has not been explored in those circumstances, the objective this paper is to present the preliminary results obtained in the evaluation of the GPS performance in Amazonian Regions when comparing with other techniques. The tendency measurement values indicated that the IWV values from GPS tend to be larger than those from radiosondes and smaller than those from radiometer. On the other hand, IWV values from GPS are very close of the average values supplied by radiosondes and radiometer. Due to the great amount of atmospheric water vapor existent in this region, the results obtained in the experiment in percentile terms are quite better than those found in the literature, which are around of 10%.

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.

The use of the two-body energy to study problems of escape/capture Ernesto Vieira Neto1

The problem of escape/capture is encountered in many problems of the celestial mechanics -the capture of the giants planets irregular satellites, comets capture by Jupiter, and also orbital transfer between two celestial bodies as Earth and Moon. To study these problems we introduce an approach which is based on the numerical integration of a grid of initial conditions. The two-body energy of the particle relative to a celestial body defines the escape/capture. The trajectories are integrated into the past from initial conditions with negative two-body energy. The energy change from negative to positive is considered as an escape. By reversing the time, this escape turns into a capture. Using this technique we can understand many characteristics of the problem, as the maximum capture time, stable regions where the particles cannot escape from, and others. The advantage of this kind of approach is that it can be used out of plane (that is, for any inclination), and with perturbations in the dynamics of the n-body problem. © 2005 International Astronomical Union.

End-to-end validation of EPS / MetOp GOME-2 trace gas data

Within the next decade, the improved version 2 of Global Ozone Monitoring Experiment (GOME-2), a ultraviolet-visible spectrometer dedicated to the observation of key atmospheric trace species from space, will be launched successively on board three EUMETSAT Polar System (EPS) MetOp satellites. Starting with the launch of MetOp-1 scheduled for summer 2006, the GOME-2 series will extend till 2020 the global monitoring of atmospheric composition pioneered with ERS-2 GOME-1 since 1995 and enhanced with Envisat SCIAMACHY since 2002 and EOS-Aura OMI since 2004. For more than a decade, an international pool of scientific teams active in ground-and space-based ultraviolet-visible remote sensing have contributed to the successful post-launch validation of trace gas data products and the associated maturation of retrieval algorithms for the latter satellites, ensuring that geophysical data products are/become reliable and accurate enough for intended research and applications. Building on this experience, this consortium plans now to develop and carry out appropriate validation of a list of GOME-2 trace gas column data of both tropospheric and stratospheric relevance: nitrogen dioxide (NO 2), ozone (O 3), bromine monoxide (BrO), chlorine dioxide (OClO), formaldehyde (HCHO), and sulphur dioxide (SO 2). The proposed investigation will combine four complementary approaches resulting in an end-to-end validation of expected column data products.

Modernizing the Brazilian active control network

The Brazilian Network for Continuous Monitoring of GPS - RBMC, since its foundation in December of 1996, has been playing an essential role for the maintenance and user access of the fundamental geodetic frame in the country,. It provides users with a direct link to the Brazilian Geodetic System - SGB. Its role has become more relevant with the increasing use of space navigation technology in the country. Recently, Brazil adopted a new geodetic system, SIRGAS2000, in February 2005, fully compatible with GNSS technology. The paper provides an overview of the recent modernization phases the RBMC network has undergone highlighting its future steps. From its current post-mission mode, the RBMC will evolve into a real-time network, providing real-time data and real-time correction to users. The network enhanced with modern GPS receivers and the addition of atomic clocks will be used to compute WADGPS-type corrections to be transmitted, in real time, to users in Brazil and surrounding areas. It is estimated that users will be able to achieve a horizontal accuracy around 0.5 m (1σ) in static and kinematic positioning and better for dual frequency users. The availability of the WADGPS service will allow users to tie to the new SIRGAS2000 system in a more rapid and transparent way for positioning and navigation applications. It should be emphasized that support to post-mission static positioning will continue to be provided to users interested in higher accuracy levels. In addition to this, a post-mission Precise Point Positioning (PPP) service will be provided based on the one currently provided by the Geodetic Survey Division of NRCan (CSRS-PPP). The modernization of the RBMC is under development based on a cooperation signed at the end of 2004 with the University of New Brunswick, supported by the Canadian International Development Agency and the Brazilian Cooperation Agency. The Geodetic Survey Division of NRCan is also participating in this modernization effort under the same project.

Mitigating systematic errors for single frequency GPS receivers employing a penalized least squares methodology

Among the positioning systems that compose GNSS (Global Navigation Satellite System), GPS has the capability of providing low, medium and high precision positioning data. However, GPS observables may be subject to many different types of errors. These systematic errors can degrade the accuracy of the positioning provided by GPS. These errors are mainly related to GPS satellite orbits, multipath, and atmospheric effects. In order to mitigate these errors, a semiparametric model and the penalized least squares technique were employed in this study. This is similar to changing the stochastical model, in which error functions are incorporated and the results are similar to those in which the functional model is changed instead. Using this method, it was shown that ambiguities and the estimation of station coordinates were more reliable and accurate than when employing a conventional least squares methodology.

Evaluation of tropospheric and ionospheric effects on the geographic localization of data collection platforms

The Brazilian National Institute for Space Research (INPE) is operating the Brazilian Environmental Data Collection System that currently amounts to a user community of around 100 organizations and more than 700 data collection platforms installed in Brazil. This system uses the SCD-1, SCD-2, and CBERS-2 low Earth orbit satellites to accomplish the data collection services. The main system applications are hydrology, meteorology, oceanography, water quality, and others. One of the functionalities offered by this system is the geographic localization of the data collection platforms by using Doppler shifts and a batch estimator based on least-squares technique. There is a growing demand to improve the quality of the geographical location of data collection platforms for animal tracking. This work presents an evaluation of the ionospheric and tropospheric effects on the Brazilian Environmental Data Collection System transmitter geographic location. Some models of the ionosphere and troposphere are presented to simulate their impacts and to evaluate performance of the platform location algorithm. The results of the Doppler shift measurements, using the SCD-2 satellite and the data collection platform (DCP) located in Cuiabá town, are presented and discussed.

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.

GPS ambiguity resolution and validation under multipath effects: Improvements using wavelets

Integer carrier phase ambiguity resolution is the key to rapid and high-precision global navigation satellite system (GNSS) positioning and navigation. As important as the integer ambiguity estimation, it is the validation of the solution, because, even when one uses an optimal, or close to optimal, integer ambiguity estimator, unacceptable integer solution can still be obtained. This can happen, for example, when the data are degraded by multipath effects, which affect the real-valued float ambiguity solution, conducting to an incorrect integer (fixed) ambiguity solution. Thus, it is important to use a statistic test that has a correct theoretical and probabilistic base, which has became possible by using the Ratio Test Integer Aperture (RTIA) estimator. The properties and underlying concept of this statistic test are shortly described. An experiment was performed using data with and without multipath. Reflector objects were placed surrounding the receiver antenna aiming to cause multipath. A method based on multiresolution analysis by wavelet transform is used to reduce the multipath of the GPS double difference (DDs) observations. So, the objective of this paper is to compare the ambiguity resolution and validation using data from these two situations: data with multipath and with multipath reduced by wavelets. Additionally, the accuracy of the estimated coordinates is also assessed by comparing with the ground truth coordinates, which were estimated using data without multipath effects. The success and fail probabilities of the RTIA were, in general, coherent and showed the efficiency and the reliability of this statistic test. After multipath mitigation, ambiguity resolution becomes more reliable and the coordinates more precise. © Springer-Verlag Berlin Heidelberg 2007.

An interplanetary mission to Neptune system: Gravitational capture and maneuvers around triton

The gravitational capture was initially used to understand the capture of planetary satellites. However, in the 90's decade, this phenomenon was applied in spacecraft trajectories. Belbruno and Miller studied missions in the Earth-Moon system that uses this technique to save fuel during the insertion of the spacecraft in its final orbit around the Moon. Using a parameter defined as twice the two-body energy of the planet-particle system, Yamakawa also studied the gravitational capture in the Earth-Moon system. In the present paper, this technique is used to study a mission that goes to the Neptune system and perform a gravitational capture in the satellite Triton. The results show direct and retrograde trajectories, for different values of the initial conditions.

Permanent Magnet Hall Thruster for satellite orbit raising with low power energy consumption

Electric propulsion is now a succeful method for primary propulsion of deep space long duration missions and for geosyncronous satellite attitude control. Closed Drift Thruster, so called Hall Thruster or SPT (Stationary Plasma Thruster), was primarily conceived in USSR (the ancient Soviet Union) and, since then, it has been developed by space agencies, space research institutes and industries in several countries such as France, USA, Israel, Russian Federation and Brazil. In this work we present the main features of the Permanent Magnet Hall Thruster (PMHT) developed at the Plasma Laboratory of the University of Brasilia. The idea of using an array of permanent magnets, instead of an electromagnet, to produce a radial magnetic field inside the plasma channel of the thruster is very significant. It allows the development of a Hall Thruster with power consumption low enough to be used in small and medium size satellites. Description of a new vacuum chamber used to test the second prototype of the PMHT (PHALL II) will be given. PHALL II has an aluminum plasma chamber and is smaller with 15 cm diameter and will contain rare earth magnets. We will show plasma density and temperature space profiles inside and outside the thruster channel. Ion temperature measurements based on Doppler broadening of spectral lines and ion energy measurements are also shown. Based on the measured plasma parameters we constructed an aptitude figure of the PMHT. It contains the specific impulse, total thrust, propellant flow rate and power consumption necessary for orbit raising of satellites. Based on previous studies of geosyncronous satellite orbit positioning we perform numerical simulations of satellite orbit raising from an altitude of 700 km to 36000 km using a PMHT operating in the 100 mN - 500 mN thrust range. In order to perform these calculations integration techniques were used. The main simulation paraters were orbit raising time, fuel mass, total satellite mass, thrust and exaust velocity. We conclude comparing our results with results obtainned with known space missions performed with Hall Thrusters. © 2008 by the American Institute of Aeronautics and Astronautics, Inc.

An effective wavelet method to detect and mitigate low-frequency multipath effects

To ensure high accuracy results from GPS relative positioning, the multipath effects have to be mitigated. Although the careful selection of antenna site and the use of especial antennas and receivers can minimize multipath, it cannot always be eliminated and frequently the residual multipath disturbance remains as the major error in GPS results. The high-frequency multipath from large delays can be attenuated by double difference (DD) denoising methods. But the low-frequency multipath from short delays is very difficult to be reduced or modeled. In this paper, it is proposed a method based on wavelet regression (WR), which can effectively detect and reduce the low-frequency multipath. The wavelet technique is firstly applied to decompose the DD residuals into the low-frequency bias and high-frequency noise components. The extracted bias components by WR are then directly applied to the DD observations to correct them from the trend. The remaining terms, largely characterized by the high-frequency measurement noise, are expected to give the best linear unbiased solutions from a least-squares (LS) adjustment. An experiment was carried out using objects placed close to the receiver antenna to cause, mainly, low-frequency multipath. The data were collected for two days to verify the multipath repeatability. The ground truth coordinates were computed with data collected in the absence of the reflector objects. The coordinates and ambiguity solution were compared with and without the multipath mitigation using WR. After mitigating the multipath, ambiguity resolution became more reliable and the coordinates were more accurate.

A study of the relative velocities of small particles that are orbiting the earth

The evolution of the velocity of the particles with respect to the circular orbits of satellites that are around the Earth that the particles will cross, suggests a range of possible velocities of impact as a function of the altitude of the satellite. A study made from those results show that the maximum relative velocities occur at the semi-latus rectum, independent of the initial semi-major axis of the particle. Considering both the solar radiation pressure and the oblateness of the Earth, it is visible that a precession in the orbit occurs and there is also a variation in the eccentricity of the particle as a function of its orbital region and its size. This is important information, because the damage caused in a spacecraft depends on the impact velocity.

Latest Enhancements in the Brazilian Active Control Network

The Brazilian Network for Continuous Monitoring of GPS - RBMC, since its foundation in December of 1996, has been playing an essential role for the maintenance and user access of the fundamental geodetic frame in the country. It provides to users a direct link to the Brazilian Geodetic System. Its role has become more relevant with the increasing use of space navigation technology in the country. Recently, Brazil adopted a new geodetic frame, SIRGAS2000, in February 2005, fully compatible with GNSS technology. The paper provides an overview of the recent modernization phases the RBMC network has undergone highlighting its future steps. From its current post-mission mode, the RBMC will evolve into a real-time network, providing real-time data and real-time correction to users. The network enhanced with modern GPS receivers and the addition of atomic clocks will be used to compute WADGPS-type corrections to be transmitted, in real time, to users in Brazil and surrounding areas. It is estimated that users will be able to achieve a horizontal accuracy around 0.5 m (1 σ) in static and kinematic positioning and better for dual frequency users. The availability of the WADGPS service will allow users to tie to the new SIRGAS2000 frame in a more rapid and transparent way for positioning and navigation applications. It should be emphasized that support to post-mission static positioning, will continue to be provided to users interested in higher accuracy levels. In addition to this, a post-mission Precise Point Positioning (PPP) service will be provided based on the one currently provided by the Geodetic Survey Division of NRCan (CSRS-PPP). The modernization of the RBMC is under development based on a cooperation signed at the end of 2004 with the University of New Brunswick, supported by the Canadian International Development Agency and the Brazilian Cooperation Agency. The Geodetic Survey Division of NRCan is also participating in this modernization effort under the same project. © Springer-Verlag Berlin Heidelberg 2009.