Ambiguity Fixing Research Articles

A New Data Processing Strategy for Huge GNSS Global Networks

In Global Positioning System (GPS) data analyses, large networks are usually divided into sub-networks to solve the conflict between increasing amounts of data and limited computer resources, although an integrated analysis would provide better results. This conflict becomes even more critical with the increasing number of stations, and low-Earth-orbiting satellites and the Galileo system coming into operation. The major reason is that a huge number of ambiguity parameters are kept in the normal equation for sequential integer ambiguity fixing. In this paper, the problem is solved by a special procedure of parameter elimination for both real-valued and ambiguity-fixed solutions, based on an adapted ambiguity-fixing approach where the covariance-matrix of ambiguity parameters is not required anymore. It is demonstrated that, with the new strategy, the required memory can be reduced to one-tenth and the computation time to at least one-third compared to the existing methods, and huge GPS networks with several hundred stations can be processed efficiently on a personal computer.

Hospital volume specialization, guidelines and outcomes in cancer treatment: importance in quality of cancer care

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10 cm accuracy, PPP with ambiguity-fixing of 2–5 cm accuracy, PPP using single-frequency receiver with accuracy of better than 50 cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3 cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.

Improving carrier-phase ambiguity resolution in global GPS network solutions

Integer carrier-phase ambiguity resolution is one of the critical issues for precise GPS applications in geodesy and geodynamics. To resolve as many integer ambiguities as possible, the ‘most-easy-to-fix’ double-difference ambiguities have to be defined. For this purpose, several strategies are implemented in existing GPS software packages, such as choosing the ambiguities according to the baseline length or the variances of the estimated real-valued ambiguities. Although their efficiencies are demonstrated in practice, it is proven in this paper that they do not reflect all effects of varying data quality, because they are based on theoretical considerations of GPS data processing. Therefore, a new approach is presented, which selects the double-difference ambiguities according to their probability of being fixed to the nearest integer. The probability is computed from estimates and variances of wide-lane and narrow-lane ambiguities. Together with an optimized ambiguity fixing procedure, the new approach is implemented in the routine data processing for the International GPS Service (IGS) at GeoForschungsZentrum (GFZ) Potsdam. Within a sub-network of about 90 IGS stations, it is demonstrated that more than 97% of the independent ambiguities are fixed correctly compared to 75% by a commonly used method, and that the additionally fixed ambiguities improve the repeatability of the station coordinates by 10–26% in regions with sparse site distribution.

An analysis of the effects of different network-based ionosphere estimation models on rover positioning accuracy

The primary objective of this paper is to test several methods of modeling the ionospheric corrections derived from a reference GPS network, and to study the impact of the models’ accuracy on the user positioning results. The five ionospheric models that are discussed here are: (1) network RTK (NR) carrier phase-based model — MPGPS-NR, (2) absolute, smoothed pseudorange-based model — MPGPS-P4, (3) IGS Global Ionosphere Model — GIM, (4) absolute model based on undifferenced dual-frequency ambiguous carrier phase data — ICON, and (5) carrier phase-based data assimilation method — MAGIC. Methods 1–4 assume that the ionosphere is an infinitesimal single layer, while method (5) considers the ionosphere as a 3D medium.The test data set was collected at the Ohio Continuously Operating Reference Stations (CORS) network on August 31, 2003. A 24-hour data set, representing moderate ionospheric conditions (maximum Kp = 2o), was processed. The ionospheric reference “truth” in doubledifference (DD) form was generated from the dualfrequency carrier phase data for two selected baselines, ~60 and ~100 km long, where one station was considered as a user receiver at an unknown location (simulated rover). The five ionospheric models were used to generate the DD ionospheric corrections for the rover, and were compared to the reference “truth.” The quality statistics were generated and discussed. Examples of instantaneous ambiguity resolution and RTK positioning are presented, together with the accuracy requirements for the ionospheric corrections, to assure integer ambiguity fixing.

Relative positioning of multiple moving platforms using GPS

To obtain subdecimeter level accuracy in relative kinematic positioning, the use of double differenced GPS carrier phase measurement with carrier phase ambiguities fixed to their correct integer values must be adopted. If multiple platforms are available in the configuration, the redundancy provided by the multiplicity of platforms can speed up the time to integer ambiguity fixing while at the same time improve the reliability of the solution. An approach to effectively construct ambiguity constraints through the multiplicity of platforms is presented herein. The use of these ambiguity constraints to position multiple moving platforms with respect to each other is then discussed. A series of simulations and field tests are designed and conducted to investigate the effects of different system parameters on this approach, with a configuration of up to 10 moving platforms. The test results show that the use of ambiguity constraints can improve the time to integer ambiguity fixing by up to 67%, relative to the case when no constraints are used. In addition, the use of ambiguity constraints is found to enhance the ability of the multiple platform system to detect wrong ambiguity fixes.

A General Criterion of Integer Ambiguity Search

A general criterion for integer ambiguity searching is derived in this paper. The criterion takes into account not only the residuals caused by ambiguity parameter changing, but also the residuals caused by coordinates changing through ambiguity fixing. The search can be carried out in a coordinate domain, in an ambiguity domain or in both domains. The three searching scenarios are theoretically equivalent. The optimality and uniqueness properties of the proposed criterion are also discussed. A numerical explanation of the general criterion is outlined. The theoretical relationship between the general criterion and the commonly used least squares ambiguity search (LSAS) criterion is derived in an equivalent case in detail. It shows that the LSAS criterion is just one of the terms of the equivalent criterion. Numerical examples are given to illustrate the behaviour of the two components of the equivalent criterion.

GPS Attitude Determination Reliability Performance Improvement Using Low Cost Receivers

This paper describes different methods to improve reliability of attitude estimation using low cost GPS receivers. Previous work has shown that low cost receiver attitude determination systems are more susceptible to measurement errors, such as multipath, phase center offsets, and cycle slips. In some cases, these error sources lead to severely erroneous attitude estimates and/or to a lower availability. The reliability control in the attitude determination becomes imperative to users, as most attitude applications require a high level of reliability. The three methods tested herein to improve reliability are the use of a high data rate, fixed angular constraints, and a quality control algorithm implemented with a Kalman filter. The use of high rate measurements improves error detection as well as ambiguity fixing time. Fixed angular constraints in a multi-antenna attitude system is effective to reject incorrect solutions during the ambiguity resolution phase of the process. Utilizing a Kalman filter with a high data rate, e.g. 10 Hz, not only increases reliability through an increase of information, but also can improve accuracy and availability. The simultaneous utilization of the above methods significantly improves reliability, as demonstrated through a series of hardware simulations and field tests. The low cost receiver type selected is the CMC Allstar receiver equipped with a commercially available low cost antenna. Finally, the use of statistically reliability measures, namely internal and external reliability measures, shows the inherent limitations of a low cost system and the need to either use better antennas and/or external aiding in the form of low cost sensors.

AMBIGUITY ONLINE ESTIMATION BY COMBINING DUAL-FREQUENCY PHASE AND CARRIER SMOOTHED CODE MEASUREMENTS: PERFORMANCE ON SHORT BASELINES

For both static and kinematic relative positioning with GPS, the success of baseline resolution depends closely on the reliable fixing of integer ambiguities of carrier phase measurements. Low noise code correlated dual-frequency GPS receivers offer accurate pseudo-range measurements on both carrier frequencies. With the help of a combination of code and carrier phase measurements, wide-lane ambiguities can be easily determined and used for the improvement of ambiguity resolutions on both L1 and L2 frequencies. A carrier smoothing technique is utilized to eliminate the noise of code measurements. Baselines ranging from 1.5 km to 48 km are used to test the proposed method.

Precise GPS Positioning by Applying Ionospheric Corrections from an Active Control Network

In this article, initial results are presented of a method to improve fast carrier phase ambiguity resolution over longer baselines (with lengths up to about 200 km). The ionospheric delays in the global positioning system (GPS) data of these long baselines mainly hamper successful integer ambiguity resolution, a prerequisite to obtain precise positions within very short observation time spans. A way to correct the data for significant ionospheric effects is to have a GPS user operate within an active or permanently operating network use ionospheric estimates from this network. A simple way to do so is to interpolate these ionospheric estimates based on the expected spatial behaviour of the ionospheric delays. In this article such a technique is demonstrated for the Dutch Active Control Network (AGRS.NL). One hour of data is used from 4 of the 5 reference stations to obtain very precise ionospheric corrections after fixing of the integer ambiguities within this network. This is no problem because of the relatively long observation time span and known positions of the stations of the AGRS.NL. Next these interpolated corrections are used to correct the GPS data from the fifth station for its ionospheric effects. Initial conclusions about the performance of this technique are drawn in terms of improvement of integer ambiguity resolution for this baseline. © 1999 John Wiley & Sons, Inc.

A new approach to GPS ambiguity decorrelation

Ambiguity decorrelation is a useful technique for rapid integer ambiguity fixing. It plays an important role in the least-squares ambiguity decorrelation adjustment (Lambda) method. An approach to multi-dimension ambiguity decorrelation is proposed by the introduction of a new concept: united ambiguity decorrelation. It is found that united ambiguity decorrelation can provide a rapid and effective route to ambiguity decorrelation. An approach to united ambiguity decorrelation, the HL process, is described in detail. The HL process performs very well in high-dimension ambiguity decorrelation tests.

An analytical study of ambiguity decorrelation using dual frequency code and carrier phase

In this contribution the integer least-squares estimation of the double differencedL1 andL2 ambiguities is analyzed, under the provision that the relative receiver-satellite geometry is dispensed with. The variance-covariance matrix of the ambiguities is instrumental for gaining insight into the characteristics of the ambiguity fixing process. A qualitative geometric description in detail is therefore given of the ambiguity search space. The elongation, the correlation coefficient and the areas of the ambiguity search space and its enclosing boxes are all given as function of the ratio or product of the carrier phase and code standard deviations. It is shown that the ambiguity search space is very elongated and that the ambiguities are highly correlated. It is also shown how the high correlation between the ambiguities can be used to ones advantage for the transformation to new ambiguities. This is done by means of the least-squares ambiguity decorrelation adjustment method. The improvements in terms of decorrelation, elongation and precision are shown and the corresponding optimal time-invariant ambiguity transformations are given for a practical range of code and measurement precisions.

Evolutionary laws, initial conditions and gauge fixing in constrained systems

We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the fixing of ambiguities in the dynamics and the determination of inequivalent initial data. The Lagrangian discussion is novel, and a proof is given that the final number of degrees of freedom in the two formulations agrees. We give applications to reparameterization invariant theories, where we prove that one of the constraints must be explicitly time dependent. We illustrate our procedure with the examples of trajectories in spacetime and with spatially homogeneous cosmological models. Finally, we comment briefly on Dirac's extended Hamiltonian technique.