Integer Ambiguity Fixing Research Articles

Ionospheric path delay models for spaceborne GPS receivers flying in formation with large baselines

GPS relative navigation filters could benefit notably from an accurate modeling of the ionospheric delays, especially over large baselines (>100 km) where double difference delays can be higher than several carrier wavelengths. This paper analyzes the capability of ionospheric path delay models proposed for spaceborne GPS receivers in predicting both zero-difference and double difference ionospheric delays. We specifically refer to relatively simple ionospheric models, which are suitable for real-time filtering schemes. Specifically, two ionospheric delay models are evaluated, one assuming an isotropic electron density and the other considering the effect on the electron density of the Sun aspect angle. The prediction capability of these models is investigated by comparing predicted ionospheric delays with measured ones on real flight data from the Gravity Recovery and Climate Experiment mission, in which two satellites fly separated of more than 200 km. Results demonstrate that both models exhibit a correlation in the excess of 80% between predicted and measured double-difference ionospheric delays. Despite its higher simplicity, the isotropic model performs better than the model including the Sun effect, being able to predict double differenced delays with accuracy smaller than the carrier wavelength in most cases. The model is thus fit for supporting integer ambiguity fixing in real-time filters for relative navigation over large baselines. Concerning zero-difference ionospheric delays, results demonstrate that delays predicted by the isotropic model are highly correlated (around 90%) with those estimated using GPS measurements. However, the difference between predicted and measured delays has a root mean square error in the excess of 30 cm. Thus, the zero-difference ionospheric delays model is not likely to be an alternative to methods exploiting carrier-phase observables for cancelling out the ionosphere contribution in single-frequency absolute navigation filters.

Regional reference network augmented precise point positioning for instantaneous ambiguity resolution

Integer ambiguity fixing can significantly shorten the initialization time and improve the accuracy of precise point positioning (PPP), but it still takes approximate 15 min of time to achieve reliable integer ambiguity solutions. In this contribution, we present a new strategy to augment PPP estimation with a regional reference network, so that instantaneous ambiguity fixing is achievable for users within the network coverage. In the proposed method, precise zero-differenced atmospheric delays are derived from the PPP fixed solution of the reference stations, which are disseminated to, and interpolated at user stations to correct for L1, L2 phase observations or their combinations. With the corrected observations, instantaneous ambiguity resolution can be carried out within the user PPP software, thus achieving the position solutions equivalent to the network real-time kinematic positioning (NRTK). The strategy is validated experimentally. The derived atmospheric delays and the interpolated corrections are investigated. The ambiguity fixing performance and the resulted position accuracy are assessed. The validation confirms that the new strategy can provide comparable service with NRTK. Therefore, with this new processing strategy, it is possible to integrate PPP and NRTK into a seamless positioning service, which can provide an accuracy of about 10 cm anywhere, and upgrade to a few centimeters within a regional network.

Integer Ambiguity Resolution on Undifferenced GPS Phase Measurements and Its Application to PPP and Satellite Precise Orbit Determination

Integer ambiguity fixing is routinely applied to double-differenced GPS phase measurements to achieve precise positioning. Double-differencing is interesting because it removes most of the common errors between the different signal paths. However, if common errors can be estimated it becomes attractive to fix integer ambiguities on undifferenced measurements. Phase measurements then become pseudorange-like measurements with a noise level of a few millimeters. This paper introduces a new method for fixing dual-frequency GPS ambiguities on undifferenced phase measurements either locally or globally. The clocks for the GPS constellation obtained during this process can be used for precise point positioning of ground based receivers and for precise orbit determination of low Earth orbiting satellites. The resulting positioning precision is comparable to that of standard differential positioning without the need for a reference station. Ambiguity-fixed satellite orbits for the GRACE and Jason satellites are more precise than the most precise solution available today.

Estimates of ocean tide loading displacements and its impact on position time series in Hong Kong using a dense continuous GPS network

Three-dimensional ocean tide loading (OTL) displacements of eight diurnal and semidiurnal constituents at 12 sites in Hong Kong were estimated using 3–7 years of continuous global positioning system (GPS) observations. OTL displacements were estimated using the precise point positioning (PPP) technique on a daily basis and then combined. The OTL displacements obtained by GPS were compared with predictions using seven recent global ocean tide models. The effect of OTL displacements on GPS position time series was also investigated. The study shows that the GPS-derived OTL displacements (excluding K1 and K2 constituents) agree best with those predicted by the GOT4.7 and NAO99b models. The GPS/model agreement is generally at the sub-millimeter level, except for S2, K1, and K2 constituents with relatively large errors. After systematic biases between the GPS and model values are removed, the misfits of all sites for M2, S2, N2, O1, P1, and Q1 are less than 0.5 and 1.0 mm in the horizontal and vertical components, respectively, while larger misfits (within 2.5 mm) are observed for K1 and K2. Integer ambiguity fixing slightly improves the east component of OTL displacement estimates. The study also finds that GPS-derived OTL corrections, instead of model predicts, can be used in daily data processing with the exception of K1 and K2. Including K2 corrections, a secular vertical rate of up to 1 mm/year in position time series can be induced, which needs to be confirmed by further studies.

Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations

Precise Point Positioning (PPP) has been demonstrated to be a powerful tool in geodetic and geodynamic applications. Although its accuracy is almost comparable with network solutions, the east component of the PPP results is still to be improved by integer ambiguity fixing, which is, up to now, prevented by the presence of the uncalibrated phase delays (UPD) originating in the receivers and satellites. In this paper, it is shown that UPDs are rather stable in time and space, and can be estimated with high accuracy and reliability through a statistical analysis of the ambiguities estimated from a reference network. An approach is implemented to estimate the fractional parts of the single-difference (SD) UPDs between satellites in wide- and narrow-lane from a global reference network. By applying the obtained SD-UPDs as corrections to the SD-ambiguities at a single station, the corrected SD-ambiguities have a naturally integer feature and can therefore be fixed to integer values as usually done for the double-difference ones in the network mode. With data collected at 450 stations of the International GNSS Service (IGS) through days 106 to 119 in 2006, the efficiency of the presented ambiguity-fixing strategy is validated using IGS Final products. On average, more than 80% of the independent ambiguities could be fixed reliably, which leads to an improvement of about 27% in the repeatability and 30% in the agreement with the IGS weekly solutions for the east component of station coordinates, compared with the real-valued solutions.

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.

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 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.