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.

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.

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.

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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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.

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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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.

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.

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.

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.

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.

Hidden negative spatial autocorrelation

Mostly lip service treatments of negative spatial autocorrelation (NSA) appear in the literature, although spatial scientists confront it in practice. NSA was detected serendipitously in recalcitrant empirical analyses containing a sizeable amount of global positive spatial autocorrelation (PSA) unaccounted for by standard spatial statistical models, and labeled hidden because conventional spatial statistical tools detected only PSA while giving absolutely not hint of NSA existing. The meaning of this phenomenon is explored empirically, with findings including: a better understanding of NSA, spatial filter model construction guidelines, effective illustrations of NSA, and how hidden NSA furnishes a diagnostic for model misspecification.

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.

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.

Show me the code: spatial analysis and open source

This paper considers the intersection of academic spatial analysis with the open source revolution. Its basic premise is that the potential for cross-fertilization between the two is rich, yet some misperceptions about these two communities pose challenges to realizing these opportunities. The paper provides a primer on the open source movement for academicians with an eye towards correcting these misperceptions. It identifies a number of ways in which increased adoption of open source practices in spatial analysis can enhance the development of the next generation of tools and the wider practice of scientific research and education.

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.

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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Nonlinear regional economic dynamics: continuous-time specification,estimation and stability analysis

This paper presents an innovative approach to the study of regional economic dynamics within a nonlinear continuous-time econometric framework—a generalized specification of the Lotka–Volterra system of equations. This specification, which accounts for interdependent behavior of three industrial sectors and spillover effects of activities in neighboring regions, is employed in an analysis of five Italian regions between 1980 and 2003. For these regions, we report estimation results, characterize the varying systems dynamics, analyze the models’ local and global stability properties, and determine via sensitivity analyses which structural features appear to exert the greatest influence on these properties.