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.

Different types of GPS clock and orbit data provided by the International GPS Service (IGS) have been used to assess the accuracy of rapid orbit determination for satellites in low Earth orbit (LEO) using spaceborne GPS measurements. To avoid the need for reference measurements from ground-based reference receivers, the analysis is based on an undifferenced processing of GPS code and carrier-phase measurements. Special attention is therefore given to the quality of GPS clock data that directly affects the resulting orbit determination accuracy. Interpolation of clock data from the available 15 min grid points is identified as a limiting factor in the use of IGS ultra-rapid ephemerides. Despite this restriction, a 10-cm orbit determination accuracy can be obtained with these products data as demonstrated for the GRACE-B spacecraft during selected data arcs between 2002 and 2004. This performance may be compared with a 5-cm orbit determination accuracy achievable with IGS rapid and final products using 5 min clock samples. For improved accuracy, high-rate (30 s) clock solutions are recommended that are presently only available from individual IGS centers. Likewise, a reduced latency and more frequent updates of IGS ultra-rapid ephemerides are desirable to meet the requirements of upcoming satellite missions for near real-time and precise orbit determination.

With the proposition for the adoption of Geocentric Reference System for the Americas (SIRGAS) as a terrestrial reference frame for South America, the need for temporal monitoring of station coordinates used in its materialization has become apparent. This would provide a dynamic characterization of the frame. The Brazilian Network for Continuous Monitoring of GPS (RBMC) has collected high accuracy GPS measurements since 1996. The Brazilian Institute of Geography and Statistics (IBGE) maintains this network in collaboration with several universities and organizations. Most of the stations are also part of the SIRGAS network. The RBMC also contributes data to the International Terrestrial Reference System (ITRS) to densify the global frame. Two of the RBMC stations are also part of the International GPS Service (IGS). This paper reports initial results from these stations. To estimate the velocity field defined by these stations, ten IGS stations located on the border of the South American plate and in adjacent plates, along with nine RBMC stations, were used. Observations covering five groups of 15 days each were used. These groups of observations were at epochs 1997.3, 1997.9, 1998.3, 1998.9 and 1999.2. Seven IGS stations were chosen to have their coordinates constrained to those epochs. IGS products (precise ephemeris and clocks) were used to process the daily solutions, which were carried out with Bernese software. Carrier phase double differences were formed using the ionospheric-delay free observable. The troposphere was modeled using a combination of the Saastamoinen model and the Niell mapping function. A tropospheric parameter was estimated every two hours. The results of the daily baseline solutions were combined using the summation of normal equations technique, in which the final coordinates and velocities were estimated. The results were compared with various models, such as the NNR-NUVEL1 and the APKIM8.80. Velocity vectors estimated for the RBMC stations show good agreement with those two models, with rates approximately equal to 2 cm/year.

The latest evolution in digital wireless technology, third-generation (3G) Code Division Multiple Access/Single Carrier (CDMA2000/1X) wireless network, is applicable for transmitting real-time kinematic (RTK) GPS correction messages. Fast and reliable, publicly available wireless networks, combined with highly accessible Internet connectivity, allows the multicasting of messages to mobile users, who are no longer restricted to traditional private UHF wireless networks. Nationwide public wireless network systems continue to expand and can provide an inexpensive infrastructure for the emerging multi-reference network system. Transmission performance via the Internet-based CDMA2000/1X outperforms UHF technology in transmission throughput and latency, as well as in the RTK initialization time and positional accuracy.

Much of the research into multipath detection and mitigation has not considered the carrier phase delay between the line of sight (LOS) and reflected signals. A new variable referred to as early late phase (ELP) has recently been proposed to exploit this phase difference. It has been found that in a receiver tracking the L1 GPS signal, the probability of detecting multipath is lower when the carrier phase difference between the LOS and a reflected signal is an integer multiple of π. Since the pseudorange error caused by the multipath’s presence is the highest in this case, we propose to exploit the coexistence of another GPS civilian signal, the L2C. We present an analysis of ELP for the L1 and L2C signals, and a combination of both, for detecting multipath. The multipath detection performance has been compared using probabilities of false alarm and detection. An ideal algorithm should have lower probability of false alarm and higher probability of detection. However, it has been found that using dual-frequency ELP increases both probabilities. Thus, receiver operator characteristics (ROC) curves, and the area under the ROC curves, have been used for effective comparison. It has been found that the L2C signal individually gives worse performance than L1 because of its weaker signal strength. However, the combination of L1 and L2C gives the best overall performance, and thus it can be claimed that ELP using dual-frequency receivers is a more effective approach for detecting multipath.

Over the past decades, a number of methods have been proposed to handle cycle slips in the carrier phase measurements, but few researches have investigated receiver clock jumps, which may produce undesirable effects on GPS data processing. Such events are generally ignored in double-differenced positioning. For undifferenced processing, such as precise point positioning (PPP) techniques, it is unwise to neglect the impact of clock jumps. Failure to properly detect and account for receiver clock jumps may sometimes cause unexpected behavior of the GPS software and large errors in the resulting PPP solution. This is particularly troublesome when there are irregular (types 2 or 3) millisecond clock jumps represented in RINEX observation files. In this study, we first provide an intuitive description of the receiver clock jump phenomenon, and a comprehensive classification of clock jumps is presented according to its influence on three fundamental quantities (time tag, pseudorange, and carrier phase) of RINEX observation files. To follow the RINEX convention, the observable consistency is analyzed for various types of clock jump; and a simple but robust real-time clock jump compensation (RTCJC) method is proposed for reconstructing a consistent set of observables. Numerous validation tests with various GPS data show that the method is applicable to millisecond clock jumps. Without RTCJC, clock jumps are prone to cause failure of gross error and cycle slip detection algorithms and so result in repeated re-initialization or even non-convergent solutions, which lead to gross errors in the PPP solution. When RTCJC is applied, all clock jumps present in the GPS data can be effectively identified and repaired accurately, and the problem of re-initialization in PPP will no longer be triggered by receiver clock jumps, which results in significant improvement of PPP accuracy and reliability.

Several procedures for solving, in a closed form the GPS pseudo-ranging four-point problem P4P in matrix form already exist. We present here alternative algebraic procedures using Multipolynomial resultant and Groebner basis to solve the same problem. The advantage is that these algebraic algorithms have already been implemented in algebraic software such as “Mathematica” and “Maple”. The procedures are straightforward and simple to apply. We illustrate here how the algebraic techniques of Multipolynomial resultant and Groebner basis explicitly solve the nonlinear GPS pseudo-ranging four-point equations once they have been converted into algebraic (polynomial) form and reduced to linear equations. In particular, the algebraic tools of Multipolynomial resultant and Groebner basis provide symbolic solutions to the GPS four-point pseudo-ranging problem. The various forward and backward substitution steps inherent in the clasical closed form solutions of the problem are avoided. Similar to the Gauss elimination techniques in linear systems of equations, the Multipolynomial resultant and Groebner basis approaches eliminate several variables in a multivariate system of nonlinear equations in such a manner that the end product normally consists of univariate polynomial equations (in this case quadratic equations for the range bias expressed algebraically using the given quantities) whose roots can be determined by existing programs (e. g., the roots command in MATLAB). © 2002 Wiley Periodicals, Inc.

With the introduction of a third frequency on GPS Block IIF satellites and the implementation of Galileo, there will be three freely available carrier phase measurements transmitted from each system. This change in satellite navigation infrastructure will enable the use of linear combinations of the original measurements that are not currently available. As a result, it is conceivable that there may be an optimal choice of combination coefficients for a given positioning campaign. This article outlines some of the motivations of using linear combinations of Global Navigation Satellite System (GNSS) data. For example, linear combinations can be used to eliminate or mitigate individual sources of error, they can be used to alleviate excessive computational burdens, and they can be used to reduce the necessary bandwidth in communication systems. Upon establishing the motivations for using linear combinations of data, the mathematical theory involved in creating linear combinations is given. The variance of the combined signal is shown to be a weighted sum of the variances of the error sources in the untransformed signals. The weights depend on the choice of combination coefficients and the nominal frequencies of the carrier signals. As a result, there are certain choices of combination coefficients that eliminate or mitigate individual sources of error. Three categories of combinations are developed: those that eliminate the ionospheric effect, those that mitigate the effects of thermal noise and multipath, and those that mitigate the tropospheric effects. The relationships between these various categories of linear combinations are shown geometrically and the concept of optimal linear combinations of data is discussed. Finally, experimental results using optimal linear combinations of data are shown. The results are obtained using a commercially available software simulator and a GNSS processing engine from the Mobile Multi-Sensor Research Group in the Geomatics Engineering Department of the University of Calgary. It is shown that there indeed exist combinations that produce approximately the same ambiguity estimation accuracy as the pure L1 (or E1) signals, but that deliver far better baseline precision results. However, like the pure L1 (or E1) signals, instantaneously resolving integer ambiguities with these combinations will be impossible for baselines longer than about 15 km depending on the existing ionospheric conditions.

Acceptance testing or ambiguity validation is a key step in global navigation satellite system (GNSS) ambiguity resolution, which combined with integer estimator is the so-called integer aperture (IA) estimator. The difference test and ratio test are the two most popular tests. In order to compare the performances of both IA estimators, their differences in different GNSS models are analyzed from algebraic and geometrical perspectives. Furthermore, both tests are connected by comparing with the optimal acceptance test, and then, they can be transformed each other based on certain numerical conditions. As to the instantaneous applications, both tests are first compared with their corresponding instantaneous approaches, including the fixed failure rate approach for ratio test IA (RTIA) and the instantaneous and controllable approach for difference test IA (DTIA). Advantages and drawbacks of both IA estimators in theory and application are analyzed based on these comparisons. In order to verify these conclusions, typical multi-frequency, multi-GNSS situations are constructed to evaluate the performances of DTIA and RTIA ambiguity resolution. Then, both IA estimators are compared based on their instantaneous approaches in the field test. All the simulation experiments and field test results indicate that DTIA has more advantages and is better than RTIA not only in theory, but also in the practical applications.

The squat phenomenon, that is, the sinkage of a vessel due to its motion can affect the safety of navigation and reduce the accuracy of hydrographic bathymetry. Therefore, it is necessary to model and predict the squat of vessels as a function of cruise speed. We present a Global Navigation Satellite Systems–based squat modeling method for both hydrographic and navigation applications. For implementation of the proposed method, onboard GPS antennae configurations are offered to model bow squat for full-form ships such as supertankers or ore–bulk–oil carriers as well as stern squat for fine-form vessels such as passenger liners or container ships. In the proposed methodology, the onboard GPS observations are used to determine cruise ground speed, heave, attitude, and controlling the quality of kinematic positioning via fixed baselines. The vessel squat is computed from ellipsoidal height differences of the onboard antennae with respect to a reference state, after removal of all disturbing effects due to roll, pitch, heave, tide, vessel load, and geoidal height variations. The final products of the proposed approach are the analytical squat models usable for hydrographic and navigation applications. As the case study, the method is applied to a survey vessel in the offshore waters of Kish harbor. Numerical results indicate that the experimental precision of the derived analytical squat models is in the range of 0.003–0.028 m. The computed navigation squat of the test vessel at a speed of 12.64 knots is 30 % of the vessel draft and about twice its hydrographic squat. Although the field test was performed on a survey vessel, the method can be applied to any ship at any waterway. The proposed method can address the inevitable demand of reliable squat models for delicate hydrographic projects and high-speed marine traffic.