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.

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.

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.

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.

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.

A MATLAB toolbox for attitude determination with GPS multi-antenna systems

In this paper a MATLAB toolbox for determining the attitude of a rigid platform by means of multiple non-dedicated antennas using global positioning system is presented. The programs embedded in this toolbox cover the RINEX data analysis, single point positioning, differential positioning, coordinate conversion, attitude determination, and other auxiliary functions. After forming the baselines through double-differenced (carrier phase smoothed) code observables, the attitude parameters are obtained by applying the direct attitude computation and the least squares attitude estimation. The theoretical background is summarized, and some hints regarding the software implementation are given in the paper. Moreover, improvements yielding an expanded functionality are proposed.

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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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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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.

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.

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.

Bringing GPS into harsh environments for fully automated deformation monitoring

Engineering projects that require deformation monitoring frequently utilize geodetic sensors to measure displacements of target points located in the deformation zone. In situations where control stations and targets are separated by a kilometer or more, GPS can offer higher precision position updates at more frequent intervals than can normally be achieved using total station technology. For large-scale deformation projects requiring the highest precision, it is therefore advisable to use a combination of the two sensors. In response to the need for high precision, continuous GPS position updates in harsh deformation monitoring environments, a software has been developed that employs triple-differenced carrier-phase measurements in a delayed-state Kalman filter. Two data sets were analyzed to test the capabilities of the software. In the first test, a GPS antenna was displaced using a translation stage to mimic slow deformation. In the second test, data collected at a large open pit mine were processed. It was shown that the delayed-state Kalman filter developed could detect millimeter-level displacements of a GPS antenna. The actual precision attained depends upon the amount of process noise infused at each epoch to accommodate the antenna displacements. Higher process noise values result in quicker detection times, but at the same time increase the noise in the solutions. A slow, 25 mm displacement was detected within 30 min of the full displacement with sigma values in E, N and U of ±10 mm or better. The same displacement could also be detected in less than 5 h with sigma values in E, N and U of ±5 mm or better. The software works best for detecting long period deformations (e.g., 20 mm per day or less) for which sigma values of 1–2 mm are attained in all three solution components. It was also shown that the triple-differenced carrier-phase observation can be used to significantly reduce the effects of residual tropospheric delay that would normally plague double-differenced observations in harsh GPS environments.

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.

On exact solutions of the multi-constellation GNSS navigation problem

In Global Navigation Satellite System (GNSS) positioning, the receiver measures the pseudorange with respect to each observable navigation satellite and determines the position and clock bias. In addition to the GPS, several other navigation satellite constellations including Glonass, Galileo and Compass can/will also be used to provide positioning, navigation, and timing information. The paper is concerned with the solvability of the navigation problem when the receiver attempts to process measurements from different constellations. As two different constellations may not be time-synchronized, the navigation problem involves the determination of position of the receiver and clock bias with respect to each constellation. The paper describes an analytic approach to account for the two-constellation navigation problem with three measurements from one constellation and two measurements from another constellation. It is shown that the two-constellation GNSS navigation problem becomes the solving of a set of two simultaneous quadratic equations or, equivalently, a quartic equation. Furthermore, the zero-crossover of the leading coefficient and the sign of the discriminant of the quartic equation are shown to play a significant role in governing the solvability, i.e., the existence and uniqueness of the navigation solutions.

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.

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.

Hierarchical spatial interaction among the Italian regions: a nonlinear relative dynamics approach

Regional interactions and spillover effects should be considered as important factors in growth analysis of regional economies. Using modified versions of the Dendrinos–Sonis model, this paper analyses the spatial hierarchical system of Italy. The interaction among Italian regions is considered at three different levels of spatial aggregation, the NUTS-1, NUTS-2 and NUTS-3 levels. Compared to more popular spatial econometric approaches, the Dendrinos–Sonis model and its extensions provide greater flexibility in the way interaction between regions is handled but the results strongly depend on the choice of a reference region.

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.

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.

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.