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.

Ionospheric climatology derived from gps occultation observations made by the ionospheric occultation experiment

The ionospheric occultation experiment (IOX) is a GPS occultation sensor with an ionospheric mission focus. IOX measurements of GPS L1 and L2 carrier phase during Earth limb views of setting GPS satellites are used together with the Abel transform to determine vertical profiles of electron density from which F-region peak parameters are determined. Data from a four and a half month period beginning in November 2001 are statistically binned and compared with a climatological model. To account for potential errors in interpretation that could arise from violation of the Abel transform assertion of spherical symmetry, the data are compared to both the climatology and to statistics of simulated ionospheric inversions using the climatological model. General characteristics of the climatology are reproduced by the occultation data. However, several significant discrepancies between the model and the data are observed during this near-solar maximum time period. In particular, average mid-latitude daytime densities are shown to be higher than the climatological prediction and the height of F2 layer in the post-sunset equatorial region is underestimated by up to 150 km.

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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.

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.

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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Performance of the L2C civil GPS signal under various ionospheric scintillation effects

As GPS is modernizing, there are currently fourteen satellites transmitting L2C civil code and seven satellites transmitting L5 signal. While the GPS observables are subject to several sources of errors, the ionosphere is one of the largest error sources affecting GPS signals. Small irregularities in the electrons density along the GPS radio signal propagation path cause ionospheric scintillation that is characterized by rapid fluctuations in the signal amplitude and phase. The ionospheric scintillation effects are stronger in equatorial and high-latitude geomagnetic latitude regions and occur mainly due to equatorial anomaly and solar storms. Several researchers have analyzed the L2C signal quality since becoming available in December, 2005. We analyze the performance of L2C using GPS data from stations in the equatorial region of Brazil, which is subject of weak, moderate and strong ionospheric scintillation conditions. The GPS data were collected by Septentrio PolaRxS–PRO receivers as part of the CIGALA/CALIBRA network. The analysis was performed as a function of scintillations indexes S4 and Phi60, lock time (time interval in seconds that the carrier phase is tracked continuously without cycle slips), multipath RMS and position variation of precise point positioning solutions. The analysis shows that L2C code solutions are less affected by multipath effects than that of P2 when data are collected under weak ionospheric scintillation effects. In terms of analysis of positions, the kinematic PPP results using L2C instead P2 codes show accuracy improvements up to 33 % in periods of weak or strong ionospheric scintillation. When combining phase and code collected under weak scintillation effects, the results by applying L2C against P2 provide improvement in accuracy up to 59 %. However, for data under strong scintillation effects, the use of L2C for PPP with code and phase does not provide improvements in the positioning accuracy.     

Fast direct GPS P-Code acquisition

GPS P-Code has a higher chipping rate, better accuracy, and anti-jamming property than C/A code. Traditionally, GPS P-Code acquisition depends on handover from C/A code. This potentially needs long acquisition time. Moreover, when C/A code is not available, it is no longer possible to acquire GPS P-Code through handover from C/A code. The purpose of this paper is to describe a new overlap average method to facilitate hardware design of fast direct P-Code acquisition. It allows the rapid code phase search to acquire GPS P-Code signals, and also decreases the hardware resource requirement. The small size FFT in the proposed methods is very promising for fast FPGA hardware system design using FFT cores. The simulation results and theoretical analysis are included demonstrating the overall performance of the proposed method.

Analysis of high-frequency multipath in 1-Hz GPS kinematic solutions

High-frequency multipath would be problematic for studies at seismic or antenna dynamical frequencies as one could mistakenly interpret them as signals. A simple procedure to identify high-frequency multipath from global positioning system (GPS) time series records is presented. For this purpose, data from four GPS base stations are analyzed using spectral analyses techniques. Additional data, such as TEQC report files of L1 pseudorange multipath, are also used to analyze the high-frequency multipath and confirmation of the high-frequency multipath inferred from the phase records. Results show that this simple procedure is effective in identification of high-frequency multipath. The inferred information can aid interpretation of multipath at the GPS site, and is important for a number of reasons. For example, the information can be used to study GPS site selections and/or installations.

An ANN–RTS smoother scheme for accurate INS/GPS integrated attitude determination

Digital mobile mapping, the method that integrates digital imaging with direct geo-referencing, has developed rapidly over the past 15 years. The Kalman filter (KF) is considered an optimal estimation tool for real-time INS/GPS integrated kinematic positioning and orientation determination. However, the accuracy requirements of general mobile mapping applications cannot be easily achieved even when using the KF scheme. Therefore, this study proposes an intelligent scheme combining ANN and RTS backward smoother to overcome the limitations of KF and to enhance the overall accuracy of attitude determination for tactical grade and MEMS INS/GPS integrated systems.

Single-frequency precise point positioning with optimal filtering

The accuracy of standalone GPS positioning improved significantly when Selective Availability was turned off in May 2000. With the availability of various public GPS related products including precise satellite orbits and clocks, and ionosphere maps, a single-frequency standalone user can experience even a further improvement of the position accuracy. Next, using carrier phase measurements becomes crucial to smoothen the pseudorange noise. In this contribution, the most critical sources of error in single-frequency standalone positioning will be reviewed and different approaches to mitigate the errors will be considered. An optimal filter (using also carrier phase measurements) will be deployed. The final approach will then be evaluated in a decently long static test with receivers located in different regions of the world. Kinematic experiments have also been performed in various scenarios including a highly dynamic flight trial. The accuracy, in general, can be confirmed at 0.5 m horizontal and 1 m vertical, with static tests. Ultimate results demonstrate an accuracy close to 2 dm (95%) for the horizontal position components and 5 dm (95%) for the vertical in the flight experiment.

Analyzing the shear strength parameters of the Chiu-fen-erh-shan landslide: integrating strong-motion and GPS data to determine the best-fit accelerogram

This study adopts the Chiu-fen-erh-shan landslide as a case study for incorporating comprehensive accelerograph and global positioning system (GPS) data to determine the best-fit acceleration data for analyzing a rock avalanche. Previous investigations indicate that the distance from an accelerograph to a landslide site is crucial to determining the best-fit acceleration data to use in conducting a seismic analysis. Unfortunately, the Chiu-fen-erh-shan landslide and its nearest accelerograph station are located in different geological zones. Thus, GPS data were compared to the displacements derived from the accelerograms of nearby monitoring stations to help select the best accelerograph data. This emphasizes that a high density distribution of accelerographs and GPS installations are essential to acquire the best data for the seismic analysis, especially in complex geological zones. After applying the best-fit accelerogram to Newmark’s sliding model and an empirical displacement attenuation formula to back-calculate the shear strength parameters of the sliding surface, a cohesion of 0 kPa and friction angle of the sliding surface of 24.8° were found for this landslide.

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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A constrained LAMBDA method for GPS attitude determination

An improved method to obtain fixed integer ambiguity in GPS attitude determination is presented. Known conditions are utilized as constraints to acquire attitude information when the float solution and its variance–covariance matrix are not accurate enough. The searching ellipsoidal region is first expanded to compensate for errors caused by the inaccurate float solution. Then the constraints are used to shrink the region to a proper size, which maintains the true integer ambiguity. Experimental results demonstrate that this scheme gives a fast search time and a higher success rate in determining the fixed integer ambiguity than the unconstrained method. The accuracy of attitude angles is also improved.

Impact of systematic errors on precise long-baseline kinematic GPS positioning

Many kinematic GPS applications rely on high accuracy, which usually requires the ambiguities to be fixed. Normally, a reference station in the rover’s vicinity is needed for successful ambiguity resolution. Alternatively, a network surrounding the rover and allowing one to derive area correction parameters is needed. Unfortunately, both approaches are not feasible in certain situations. This paper is a contribution to precise kinematic positioning over long baselines. Atmospheric refraction becomes critical in the error budget, but progress has been made to use numerical weather models to derive tropospheric corrections, for instance. The spatial correlation of both ionospheric and tropospheric propagation delays is investigated in this paper and special attention is paid on the systematic error behavior of tropospheric refraction. The principles developed are applied to an extended reliability test of the ambiguities. Finally, it is demonstrated in positioning experiments that kinematic positioning retrieval with fixed ambiguities is actually possible for baselines between 150 and 300 km with an accuracy of approximately 2 cm in post-mission processing.

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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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Income distribution dynamics and cross-region convergence in Europe

This paper presents a continuous version of the model of distribution dynamics to analyse the transition dynamics and implied long-run behaviour of the EU-27 NUTS-2 regions over the period 1995–2003. It departs from previous research in two respects: first, by introducing kernel estimation and three-dimensional stacked conditional density plots as well as highest density regions plots for the visualisation of the transition function, based on Hyndman et al. (J Comput Graph Stat 5(4):315–336, 1996), and second, by combining Getis’ spatial filtering view with kernel estimation to explicitly account for the spatial dimension of the growth process. The results of the analysis indicate a very slow catching-up of the poorest regions with the richer ones, a process of shifting away of a small group of very rich regions, and highlight the importance of geography in understanding regional income distribution dynamics.

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.

Analysis of inversion errors of ionospheric radio occultation

The retrieved electron density profile of ionospheric radio occultation (RO) simulation data can be compared with the background model value during the simulation and the inversion error can be obtained exactly. This paper studies the inversion error of ionospheric RO through simulation. The sources of the inversion errors are analyzed. The impacts of measurement errors, such as the errors in phase measurements and satellite orbits, are very small and can be neglected. The approximation of straight-line propagation introduces errors at the height of the F1 layer under solar maximum condition. The spherical symmetry approximation of the electron density distribution is found to be the main source of the inversion error. The statistical results reveal some characteristics of the inversion errors. (1) The relative error increases with enhanced solar activity. (2) It is larger in winter than in equinox season, and it is smallest in summer. (3) For all seasons, it is smaller at middle latitude than at other latitudes. (4) For all seasons and geomagnetic latitudes, it is smaller at daytime than at other times. The NmF2 of the ROs from COSMIC are compared with the measurements of ionosondes, and the relative differences show the same dependencies on season, geomagnetic latitude and local time, as the relative errors of the simulated ionospheric ROs.