A summary of the main concepts on global ionospheric map(s) [hereinafter GIM(s)] of vertical total electron content (VTEC), with special emphasis on their assessment, is presented in this paper. It is based on the experience accumulated during almost two decades of collaborative work in the context of the international global navigation satellite systems (GNSS) service (IGS) ionosphere working group. A representative comparison of the two main assessments of ionospheric electron content models (VTEC-altimeter and difference of Slant TEC, based on independent global positioning system data GPS, dSTEC-GPS) is performed. It is based on 26 GPS receivers worldwide distributed and mostly placed on islands, from the last quarter of 2010 to the end of 2016. The consistency between dSTEC-GPS and VTEC-altimeter assessments for one of the most accurate IGS GIMs (the tomographic-kriging GIM ‘UQRG’ computed by UPC) is shown. Typical error RMS values of 2 TECU for VTEC-altimeter and 0.5 TECU for dSTEC-GPS assessments are found. And, as expected by following a simple random model, there is a significant correlation between both RMS and specially relative errors, mainly evident when large enough number of observations per pass is considered. The authors expect that this manuscript will be useful for new analysis contributor centres and in general for the scientific and technical community interested in simple and truly external ways of validating electron content models of the ionosphere.

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Methodology and consistency of slant and vertical assessments for ionospheric electron content models

Within the last decade, GNSS Precise Point Positioning (PPP) has generated unprecedented interest among the GNSS community and is being used for a number of scientific and commercial applications today. Similar to the conventional relative positioning technique, PPP could provide positioning solutions at centimeter-level precision by making use of the precise carrier phase measurements and high-accuracy satellite orbits and clock corrections provided by, for example, the International GNSS Service. The PPP technique is attractive as it is computationally efficient; it eliminates the need for simultaneous observations at both the reference and rover receivers; it also eliminates the needs for the rover receiver to operate within the vicinity of the reference receiver; and it provides homogenous positioning quality within a consistent global frame anywhere in the world with a single GNSS receiver. Although PPP has definite advantages for many applications, its merits and widespread adoption are significantly limited by the long convergence time, which restricts the use of the PPP technique for many real-time GNSS applications. We provide an overview of the current performance of PPP as well as attempt to address some of the common misconceptions of this positioning technique--considered by many as the future of satellite positioning and navigation. Given the upcoming modernization and deployment of GNSS satellites over the next few years, it would be appropriate to address the potential impacts of these signals and constellations on the future prospect of PPP.

Uncovering common misconceptions in GNSS Precise Point Positioning and its future prospect

Fast precise point positioning (Fast-PPP) is a satellite-based navigation technique using an accurate real-time ionospheric modeling to achieve high accuracy quickly. In this paper, an end-to-end performance assessment of Fast-PPP is presented in near-maximum Solar Cycle conditions; from the accuracy of the Central Processing Facility corrections, to the user positioning. A planetary distribution of permanent receivers including challenging conditions at equatorial latitudes, is navigated in pure kinematic mode, located from 100 to 1300 km away from the nearest reference station used to derive the ionospheric model.
It is shown that satellite orbits and clocks accurate to few centimeters
and few tenths of nanoseconds, used in conjunction with an ionosphere with an accuracy better than 1 Total Electron Content Unit (16 cm in L1) reduce the convergence time of dual-frequency Precise Point Positioning, to decimeter-level (3-D) solutions. Horizontal convergence times are shortened 40% to 90%, whereas the vertical components are reduced by 20% to 60%. A metric to evaluate the quality of any ionospheric model for Global Navigation Satellite System is also proposed. The ionospheric modeling accuracy is directly translated to mass-market single-frequency
users. The 95th percentile of horizontal and vertical accuracies is shown to be 40 and 60 cm for single-frequency users and 9 and 16 cm for dual-frequency users. The tradeoff between the formal and actual positioning errors has been carefully studied to set realistic confidence levels to the corrections.

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A Worldwide Ionospheric Model for Fast Precise Point Positioning

The characterization of the accuracy of ionospheric models currently used in global navigation satellite systems (GNSSs) is a long-standing issue. The characterization remains a challenging problem owing to the lack of sufficiently accurate slant ionospheric determinations to be used as a reference. The present study proposes a methodology based on the comparison of the predictions of any ionospheric model with actual unambiguous carrier-phase measurements from a global distribution of permanent receivers. The differences are separated as hardware delays (a receiver constant plus a satellite constant) per day. The present study was conducted for the entire year of 2014, i.e. during the last solar cycle maximum. The ionospheric models assessed are the operational models broadcast by the global positioning system (GPS) and Galileo constellations, the satellite-based augmentation system (SBAS) (i.e. European Geostationary Navigation Overlay System (EGNOS) and wide area augmentation system (WAAS)), a number of post-process global ionospheric maps (GIMs) from different International GNSS Service (IGS) analysis centres (ACs) and, finally, a more sophisticated GIM computed by the research group of Astronomy and GEomatics (gAGE). Ionospheric models based on GNSS data and represented on a grid (IGS GIMs or SBAS) correct about 85 % of the total slant ionospheric delay, whereas the models broadcasted in the navigation messages of GPS and Galileo only account for about 70 %. Our gAGE GIM is shown to correct 95 % of the delay. The proposed methodology appears to be a useful tool to improve current ionospheric models.

Accuracy of ionospheric models used in GNSS and SBAS: methodology and analysis

With the development of precise point positioning (PPP), the School of Geodesy and Geomatics (SGG) at Wuhan University is now routinely producing GPS satellite fractional cycle bias (FCB) products with open access for worldwide PPP users to conduct ambiguity-fixed PPP solution. We provide a brief theoretical background of PPP and present the strategies and models to compute the FCB products. The practical realization of the two-step (wide-lane and narrow-lane) FCB estimation scheme is described in detail. With GPS measurements taken in various situations, i.e., static, dynamic, and on low earth orbit (LEO) satellites, the quality of FCB estimation and the effectiveness of PPP ambiguity resolution (AR) are evaluated. The comparison with CNES FCBs indicated that our FCBs had a good consistency with the CNES ones. For wide-lane FCB, almost all the differences of the two products were within ±0.05 cycles. For narrow-lane FCB, 87.8 % of the differences were located between ±0.05 cycles, and 97.4 % of them were located between ±0.075 cycles. The experimental results showed that, compared with conventional ambiguity-float PPP, the averaged position RMS of static PPP can be improved from (3.6, 1.4, 3.6) to (2.0, 1.0, 2.7) centimeters for ambiguity-fixed PPP. The average accuracy improvement in the east, north, and up components reached 44.4, 28.6, and 25.0 %, respectively. A kinematic, ambiguity-fixed PPP test with observation of 80 min achieved a position accuracy of better than 5 cm at the one-sigma level in all three coordinate components. Compared with the results of ambiguity-float, kinematic PPP, the positioning biases of ambiguity-fixed PPP were improved by about 78.2, 20.8, and 65.1 % in east, north, and up. The RMS of LEO PPP test was improved by about 23.0, 37.0, and 43.0 % for GRACE-A and GRACE-B in radial, tangential, and normal directions when AR was applied to the same data set. These results demonstrated that the SGG FCB products can be produced with high quality for users anywhere around the world to carry out ambiguity-fixed PPP solutions.

Generating GPS satellite fractional cycle bias for ambiguity-fixed precise point positioning

This paper summarizes the main results obtained during the development of an Enhanced Precise Point Positioning (EPPP) Global Navigation Satellite Systems multifrequency user algorithm. The main innovations include the application of precise ionospheric corrections to facilitate the resolution of undifferenced carrier phase ambiguities, ambiguity validation, and integrity monitoring. The performance of the EPPP algorithm in terms of accuracy, convergence time, and integrity is demonstrated with actual GPS and simulated Galileo data. This can be achieved with very limited bandwidth requirements for EPPP users (less than 300 b/s for dual-frequency GPS data).

Enhanced Precise Point Positioning for GNSS Users

The determination of the correct integer number of carrier cycles (integer ambiguity) is the key to high accuracy positioning with carrier phase measurements from Global Navigation Satellite Systems (GNSS). There are a number of current methods for resolving ambiguities including the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method, which is a combination of least-squares and a transformation to reduce the search space. The current techniques to determine the level of confidence (integrity) of the resolved ambiguities (i.e. ambiguity validation), usually involve the construction of test statistics, characterisation of their distribution and definition of thresholds. Example tests applied include ratio, F-distribution, t-distribution and Chi-square distribution. However, the assumptions that underpin these tests have weaknesses. These include the application of a fixed threshold for all scenarios, and therefore, not always able to provide an acceptable integrity level in the computed ambiguities. A relatively recent technique referred to as Integer Aperture (IA) based on the ratio test with a large number of simulated samples of float ambiguities requires significant computational resources. This precludes the application of IA in real time. This paper proposes and demonstrates the power of an integrity monitoring technique that is applied at the ambiguity resolution and positioning stages. The technique has the important benefit of facilitating early detection of any potential threat to the position solution, originating in the ambiguity space, while at the same time giving overall protection in the position domain based on the required navigation performance. The proposed method uses the conventional test statistic for ratio testing together with a doubly non-central F distribution to compute the level of confidence (integrity) of the ambiguities. Specifically, this is determined as a function of geometry and the ambiguity residuals from least squares based ambiguity resolution algorithms including LAMBDA. A numerical method is implemented to compute the level of confidence in real time. The results for Precise Point Positioning (PPP) with simulated and real data demonstrate the power and efficiency of the proposed method in monitoring both the integrity of the ambiguity computation and position solution processes. Furthermore, due to the fact that the method only requires information from least squares based ambiguity resolution algorithms, it is easily transferable to conventional Real Time Kinematic (RTK) positioning.

M. Jofre

Papers

Enhanced Precise Point Positioning for GNSS Users

Integrity Monitoring for Carrier Phase Ambiguities