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.

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.

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.

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.

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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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.

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.

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.

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.

Specifying a joint space- and time-lag using a bivariate Poisson distribution

Separate space- or time-lags have been considered regularly in data analyses; as space–time models are more recently being studied extensively in data analytic fashion, joint estimation of both lags has to be considered explicitly. This paper addresses this issue, taking into special consideration parametric parsimony together with specification richness; use of the bivariate Poisson frequency distribution is advocated and applied to an empirical case. The relation of this approach to random effects specifications is investigated. Data for Belgian regional products constitute the empirical case study.

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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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.

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.

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.

A sampling approach to estimate the log determinant used in spatial likelihood problems

Likelihood-based methods for modeling multivariate Gaussian spatial data have desirable statistical characteristics, but the practicality of these methods for massive georeferenced data sets is often questioned. A sampling algorithm is proposed that exploits a relationship involving log-pivots arising from matrix decompositions used to compute the log determinant term that appears in the model likelihood. We demonstrate that the method can be used to successfully estimate log-determinants for large numbers of observations. Specifically, we produce an log-determinant estimate for a 3,954,400 by 3,954,400 matrix in less than two minutes on a desktop computer. The proposed method involves computations that are independent, making it amenable to out-of-core computation as well as to coarse-grained parallel or distributed processing. The proposed technique yields an estimated log-determinant and associated confidence interval.

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.

Incorporating spatial variation in housing attribute prices: a comparison of geographically weighted regression and the spatial expansion method

Hedonic house price models typically impose a constant price structure on housing characteristics throughout an entire market area. However, there is increasing evidence that the marginal prices of many important attributes vary over space, especially within large markets. In this paper, we compare two approaches to examine spatial heterogeneity in housing attribute prices within the Tucson, Arizona housing market: the spatial expansion method and geographically weighted regression (GWR). Our results provide strong evidence that the marginal price of key housing characteristics varies over space. GWR outperforms the spatial expansion method in terms of explanatory power and predictive accuracy.

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.