Tracking and orbit determination performance of the GRAS instrument on MetOp-A

The global navigation satellite system receiver for atmospheric sounding (GRAS) on MetOp-A is the first European GPS receiver providing dual-frequency navigation and occultation measurements from a spaceborne platform on a routine basis. The receiver is based on ESA’s AGGA-2 correlator chip, which implements a high-quality tracking scheme for semi-codeless P(Y) code tracking on the L1 and L2 frequency. Data collected with the zenith antenna on MetOp-A have been used to perform an in-flight characterization of the GRAS instrument with focus on the tracking and navigation performance. Besides an assessment of the receiver noise and systematic measurement errors, the study addresses the precise orbit determination accuracy achievable with the GRAS receiver. A consistency on the 5 cm level is demonstrated for reduced dynamics orbit solutions computed independently by four different agencies and software packages. With purely kinematic solutions, 10 cm accuracy is obtained. As a part of the analysis, an empirical antenna offset correction and preliminary phase center correction map are derived, which notably reduce the carrier phase residuals and improve the consistency of kinematic orbit determination results.

Kalman-filter-based GPS clock estimation for near real-time positioning

In this article, an algorithm for clock offset estimation of the GPS satellites is presented. The algorithm is based on a Kalman-filter and processes undifferenced code and carrier-phase measurements of a global tracking network. The clock offset and drift of the satellite clocks are estimated along with tracking station clock offsets, tropospheric zenith path delay and carrier-phase ambiguities. The article provides a brief overview of already existing near-real-time and real-time clock products. The filter algorithm and data processing scheme is presented. Finally, the accuracy of the orbit and clock product is assessed with a precise orbit determination of the MetOp satellite and compared to results gained with other real-time products.

EPN coordinate time series monitoring for reference frame maintenance

The EUREF permanent network (EPN) is a network of continuously operating global navigation satellite system (GNSS) stations, primarily installed for reference frame maintenance. In order to ensure the long term reliability of the EPN products, a thorough station performance monitoring has been initiated and carried out in addition to the routine GNSS data management, processing and analysis. This paper addresses the main factors influencing the quality of the coordinate time series in a permanent GNSS network. Relevant examples, based on the EPN experience are given, the analysis strategy is introduced, the estimated coordinate offsets are published and the importance of this analysis for site velocity estimation is demonstrated. The results are derived from the analysis of the EPN weekly combined solutions covering the period from 1996 to 2003. Our target is the identification, interpretation and elimination of offsets and outliers present in the EPN coordinate time series in order to estimate reliable coordinates and velocities and consequently maintain a high quality kinematic reference network.

A data archive of GPS navigation messages

Since 18 June 2007 navigation data messages transmitted by the GPS constellation are recorded by five receivers within GeoForschungsZentrum’s global groundstation network. We describe the recording, processing, validation, analysis and archiving of the navigation data. During the 197 days between 18 June 2007 and 31 December 2007 a total of 125,723,666 subframes were collected. By taking into consideration that the same data set frequently is observed by two or more receivers concurrently, 65,153,955 unique subframes could be extracted from the observations. With an estimated 88,099,200 subframes transmitted by the constellation during this time period a data yield of about 74% was achieved. Simulation studies suggest that with two additional GPS receivers, which are scheduled for addition to the network in 2008, about 95% of the transmitted subframes will be retrieved. The message data archive is open to the scientific community for non-commercial purposes and may be accessed through GFZ’s Information System and Data Center ().

Simplified equivalent multiple baseline solutions with elevation-dependent weights

Since the assumption of all stations tracking the same satellites with identical weights was previously employed by Shen and Xu (GPS Solut 12:99–108, 2008) to derive the simplified GNSS single- and double-differenced equivalent equations, this supplementary paper expands these simplified equations in the case of each station tracking different satellites with elevation-dependent weights. Numerical experiments are performed to demonstrate the computational efficiency of the simplified equivalent algorithm relative to the traditional method in various scenarios of multi-baseline solutions with tracking different satellites. The fast computational speed of the simplified equivalent algorithm will potentially benefit the local, regional and even global GNSS multi-baseline solutions as well as the combined GNSS application.

Correction of apparent position shifts caused by GNSS antenna changes

Antenna changes at GNSS reference stations frequently produce discontinuities in the coordinate time series. These apparent position shifts are mainly caused by changes of carrier-phase multipath effects and different errors in the antenna phase center corrections. A monitoring method was developed and successfully tested, which requires additional GNSS observations from a local, temporary reference station. Changes of carrier-phase measurement errors due to the antenna change are determined and stored in L1 and L2 phase maps. These phase maps provide corrections to be applied either to the observation data obtained before the antenna change or to the observation data obtained after the antenna change. The observation corrections are able to remove coordinate discontinuities independent of the selected coordinate estimation algorithm.

Assessment of time-series of troposphere zenith delays derived from the Global Data Assimilation System numerical weather model

Troposphere zenith path delays derived from the Global Data Assimilation System (GDAS) numerical weather model (NWM) are compared with those of the International GNSS Service (IGS) solutions over a 1.5-year period at 18 globally distributed IGS stations. Meteorological parameters can be interpolated from the NWM model at any location and at any time after December 2004. The meteorological parameters extracted from the NWM model agree with in situ direct measurements at some IGS stations within 1 mbar for pressure, 3° for temperature and 13% for relative humidity. The hydrostatic and wet components of the zenith path delay (ZPD) are computed using the meteorological parameters extracted from the NWM model. The total ZPDs derived from the GDAS NWM agree with the IGS ZPD solutions at 3.0 cm RMS level with biases of up to 4.5 cm, which can be attributed to the wet ZPDs estimates from the NWM model, considering the less accurate interpolated relative humidity parameter. Based on this study, it is suggested that the availability and the precision of the GDAS NWM ZPD should be sufficient for nearly all GPS navigation solutions.

Ultra-tight GPS/INS/PL integration: a system concept and performance analysis

The architecture of the ultra-tight GPS/INS/PL integration is the key to its successful performance; the main feature of this architecture is the Doppler feedback to the GPS receiver tracking loops. This Doppler derived from INS, when integrated with the carrier tracking loops, removes the Doppler due to vehicle dynamics from the GPS/PL signal thereby achieving a significant reduction in the carrier tracking loop bandwidth. The bandwidth reduction provides several advantages such as: improvement in anti-jamming performance, and increase in post correlated signal strength which in turn increases the dynamic range and accuracy of measurements. Therefore, any degradation in the derived Doppler estimates will directly affect the tracking loop bandwidth and hence its performance. The quadrature signals from the receiver correlator, I (in-phase) and Q (quadrature), form the measurements, whereas the inertial sensor errors, position, velocity and attitude errors form the states of the complementary Kalman filter. To specify a reliable measurement model of the filter for this type of integrated system, a good understanding of GPS/PL signal characteristics is essential. It is shown in this paper that phase and frequency errors are the variables that relate the measurements and the states in the Kalman filter. The main focus of this paper is to establish the fundamental mathematical relationships that form the measurement model, and to show explicitly how the system error states are related to the GPS/PL signals. The derived mathematical relationships encapsulated in a Kalman filter, are tested by simulation and shown to be valid.

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Total electron content processing from GPS observations to facilitate ionospheric modeling

With the increasing global distribution of high rate dual-frequency global positioning system (GPS) receivers, the production of a real-time atmospheric constituent definition, total electron content (TEC), has become a beneficial contributor to the modeling applications used in the assessment of GPS position accuracy and the composition of the ionosphere, plasmasphere, and troposphere. Historically, TEC measurements have been obtained through post processing techniques to produce the quality of data necessary for modeling applications with rigorous error estimate requirements. These procedures necessitated the collection of large volumes of data to address the various abnormalities in the computation of TEC associated with the use of greater data quality controls and source selection while real-time modeling environments must rely on autonomous controls and filtration techniques to prevent the production of erroneous model results. In this paper we present methods for processing TEC in real time, which utilize several procedures including the application of an ionospheric model to automatically perform quality control on the TEC output and the computational techniques used to address receiver multipath, faulty receiver observations, cycle-slips, segmented processing, and receiver calibrations. The resulting TEC measurements are provided with rigorous error estimates validated using the vertical TEC from the Jason satellite mission.

Critical network infrastructure analysis: interdiction and system flow

Effective management of critical network infrastructure requires the assessment of potential interdiction scenarios. Optimization approaches have been essential for identifying and evaluating such scenarios in networked systems. Although a primary function of any network is the distribution of flow between origins and destinations, the complexity and difficulty of mathematically abstracting interdiction impacts on connectivity or flow has been a challenge for researchers. This paper presents an optimization approach for identifying interdiction bounds with respect to connectivity and/or flow associated with a system of origins and destinations. Application results for telecommunications flow are presented, illustrating the capabilities of this approach.

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Antenna phase center calibration for precise positioning of LEO satellites

Phase center variations of the receiver and transmitter antenna constitute a remaining uncertainty in the high precision orbit determination (POD) of low Earth orbit (LEO) satellites using GPS measurements. Triggered by the adoption of absolute phase patterns in the IGS processing standards, a calibration of the Sensor Systems S67-1575-14 antenna with GFZ choke ring has been conducted that serves as POD antenna on various geodetic satellites such as CHAMP, GRACE and TerraSAR-X. Nominal phase patterns have been obtained with a robotic measurement system in a field campaign and the results were used to assess the impact of receiver antenna phase patterns on the achievable positioning accuracy. Along with this, phase center distortions in the actual spacecraft environment were characterized based on POD carrier phase residuals for the GRACE and TerraSAR-X missions. It is shown that the combined ground and in-flight calibration can improve the carrier phase modeling accuracy to a level of 4 mm which is close to the pure receiver noise. A 3.5 cm (3D rms) consistency of kinematic and reduced dynamic orbit determination solutions is achieved for TerraSAR-X, which presumably reflects the limitations of presently available GPS ephemeris products. The reduced dynamic solutions themselves match the observations of high grade satellite laser ranging stations to 1.5 cm but are potentially affected by cross-track biases at the cm-level. With respect to the GPS based relative navigation of TerraSAR-X/TanDEM-X formation, the in-flight calibration of the antenna phase patterns is considered essential for an accurate modeling of differential carrier phase measurements and a mm level baseline reconstruction.

Reliability checking for GNSS baseline and network processing

Reliability analysis is inseparably connected with the formulation of failure scenarios, and common test statistics are based on specific assumptions. This is easily overlooked when processing observation differences. Poor failure identification performance and misleading pre-analysis results, mainly meaningless minimum detectable biases and external reliability measures, are the consequence. A reasonable failure scenario for use with differenced GNSS observations is formulated which takes into account that individual outliers in the original data affect more than one processed observation. The proper test statistics and reliability indicators are given for use with correlated observations and both batch processing and Kalman filtering. It is also shown that standardized residuals and redundancy numbers fail completely when used with double differenced observations.

Ionospheric delay corrections for single-frequency GPS receivers over Europe using tomographic mapping

The majority of navigation satellites receivers operate on a single frequency and experience a positioning error due to the ionospheric delay. This can be compensated for using a variety of approaches that are compared in this paper. The study focuses on the last solar maximum. A 4D tomographic imaging technique is used to map the ionospheric electron density over the European region during 2002 and 2003. The electron density maps are then used to calculate the excess propagation delay on the L1 frequency experienced by GPS receivers at selected locations across Europe. The excess delay is applied to correct the pseudo-range single frequency observations at each location and the improvements to the resulting positioning are calculated. The real-time tomographic technique is shown to give navigation solutions that are better than empirical modelling methods and approach the accuracy of the full dual-frequency solution. The improvements in positioning accuracy vary from day to day depending on ionospheric conditions but can be up to 25 m during mid-day during these solar maximum conditions at European mid-latitudes.

Artificial neural networks for predicting DGPS carrier phase and pseudorange correction

Artificial neural networks (ANNs) were used to predict the differential global positioning system (DGPS) pseudorange and carrier phase correction information. Autoregressive moving average (ARMA) and autoregressive (AR) models were bounded with neural networks to provide predictions of the correction. The neural network was employed to realize time-varying implementation. Online training for real-time prediction of the carrier phase enhances the continuity of service of the differential correction signals and, therefore, improves the positioning accuracy. When the correction signal from the DGPS was lost, the artificial neural networks predicted the correction data with good accuracy for the navigation system during a limited period. Comparisons of the prediction results using the two models are given.

The ecological fallacy in a time series context: evidence from Spanish regional unemployment rates

The ecological fallacy (EF) is a common problem regional scientists have to deal with when using aggregated data in their analyses. Although there is a wide number of studies considering different aspects of this problem, little attention has been paid to the potential negative effects of the EF in a time series context. Using Spanish regional unemployment data, this paper shows that EF effects are not only observed at the cross-section level, but also in a time series framework. The empirical evidence obtained shows that analytical regional configurations are the least susceptible to time effects relative to both normative and random regional configurations, while normative configurations are an improvement over random ones.

Pitch and roll attitude estimation of a small-scaled helicopter using single antenna GPS with gyroscopes

A method is presented for estimating the roll and pitch attitude of a small-scaled unmanned helicopter based on the velocity measurements of the global positioning system (GPS). The small-scaled helicopter is a radio controlled (RC) model which is readily available and affordable for academic laboratories as a research platform. Only one single antenna GPS receiver is equipped on the RC helicopter to acquire the velocity measurements needed for the attitude estimation. The velocity information is recorded by the onboard computer for post-processing. An attitude and heading reference system (AHRS) is used to provide the reference attitudes. The required angular rates and heading for this study are also given by the gyroscopes and compass of the AHRS for the sake of system’s simplification. The Kalman filter is applied to estimate the helicopter’s accelerations by using the GPS velocity measurements. The estimated accelerations form the fundamental elements of synthesizing the pseudo-roll and the pseudo-pitch. With some legitimate simplifications and assumptions, the relation between the helicopter’s attitudes and the accelerations estimated from the GPS velocity measurements can be developed. Furthermore, to enhance the accuracy of the pseudo-attitudes, the angular rates acquired from the gyroscopes are incorporated into the estimation algorithm of pseudo-attitudes by using a complementary filter.

A weighted difference barrier method in landscape genetics

Identifying barriers of species and characterize their effects on spatial distribution provide essential information to research in landscape genetics. We propose a weighted difference barrier (WDB) method as an alternative to maximum difference barriers (MDB), and to initiate and integrate more spatial modeling and methods into the problem solving process. Overall, WDB provides quick and straightforward improvements to the drawbacks of MDB. WDB integrates more sample location relationships into the barrier construction and reveals potential barriers that would otherwise go undetected. WDB incorporates both within group and between group genetic information, and delineates the barriers as a more complex pattern.

Use of C-Band frequencies for satellite navigation: benefits and drawbacks

Although not considered for the first generation of European Galileo satellites, the use of C-Band frequencies for navigation purposes may be taken into account for a future generation of Galileo. For this reason, a frequency band of 20 MHz bandwidth (5,010–5,030 MHz) has been allocated in the course of the World Radio Communications Conference 2000 held in Istanbul, Turkey. The use of C-Band navigation signals offers both advantages and drawbacks. One example is the ionospheric path delay which is inversely proportional to the (squared) carrier frequency and is therefore significantly smaller at C-Band. On the other hand, the use of C-Band frequencies results in increased attenuation effects such as free space loss or rainfall attenuation. It is therefore necessary to provide a detailed analysis of the effects of C-Band frequencies on the navigation process. In order to assess the feasibility of using C-Band frequencies, various aspects of signal propagation and satellite signal tracking at C-Band are examined in the context of this article. In particular, aspects like free space loss, atmospheric effects, foliage attenuation, code and carrier tracking performance, code noise, phase noise and multipath are discussed with respect to their performance at C-Band. In order to allow comparison with the current GPS system, the performance at C-Band is compared to the L-Band performance under similar or identical conditions. The results of this analysis will finally be discussed with respect to their impact on satellite payload and receiver design.

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Carrier phase-based integrity monitoring for high-accuracy positioning

Pseudorange-based integrity monitoring, for example receiver autonomous integrity monitoring (RAIM), has been investigated for many years and is used in various applications such as non-precision approach phase of flight. However, for high-accuracy applications, carrier phase-based RAIM (CRAIM), an extension of pseudorange-based RAIM (PRAIM) must be used. Existing CRAIM algorithms are a direct extension of PRAIM in which the carrier phase ambiguities are estimated together with the estimation of the position solution. The main issues with the existing algorithms are reliability and robustness, which are dominated by the correctness of the ambiguity resolution, ambiguity validation and error sources such as multipath, cycle slips and noise correlation. This paper proposes a new carrier phase-based integrity monitoring algorithm for high-accuracy positioning, using a Kalman filter. The ambiguities are estimated together with other states in the Kalman filter. The double differenced pseudorange, widelane and carrier phase observations are used as measurements in the Kalman filter. This configuration makes the positioning solution both robust and reliable. The integrity monitoring is based on a number of test statistics and error propagation for the determination of the protection levels. The measurement noise and covariance matrices in the Kalman filter are used to account for the correlation due to differencing of measurements and in the construction of the test statistics. The coefficient used to project the test statistic to the position domain is derived and the synthesis of correlated noise errors is used to determine the protection level. Results from four cases based on limited real data injected with simulated cycle slips show that residual cycle slips have a negative impact on positioning accuracy and that the integrity monitoring algorithm proposed can be effective in detecting and isolating such occurrences if their effects violate the integrity requirements. The CRAIM algorithm proposed is suitable for use within Kalman filter-based integrated navigation systems.