A common assumption in real-time kinematic (RTK) techniques is that the differential ionospheric delay between a GNSS transmitter and each of the roving or reference receivers is negligible. However, increased position uncertainty — spatial decorrelation — is usually allocated to the baseline receivers as baseline distances increase.
A refinement of this assumption comes with the network RTK (NRTK) using a set of permanent receivers to mitigate atmospheric dependent effects, such as the ionospheric delay, over distance.
A common assumption in real-time kinematic (RTK) techniques is that the differential ionospheric delay between a GNSS transmitter and each of the roving or reference receivers is negligible. However, increased position uncertainty — spatial decorrelation — is usually allocated to the baseline receivers as baseline distances increase.
A refinement of this assumption comes with the network RTK (NRTK) using a set of permanent receivers to mitigate atmospheric dependent effects, such as the ionospheric delay, over distance.
These two approaches work well for baselines up to 10-20 kilometers (RTK) and to 50–70 kilometers (NRTK), requiring only one extra equation per satellite in-view. They both allow quick carrier phase ambiguity fixing and the corresponding real-time sub-decimeter error level positioning for high precision applications such as civil engineering. But both techniques restrict themselves to satellites with fixed double-differenced ambiguities, without exploiting the full geometry of the observations in a real-time ionospheric model of the slant delay.
The WARTK concept was introduced in the late 1990s to address these deficiencies. The method dramatically increases the RTK/NRTK service area, with permanent stations separated by up to 500–900 kilometers — all while requiring 100 to 1,000 times fewer receivers covering a given region.
This is accomplished thanks to combining at a Central Processing Facility (CPF) new ionospheric tomography and travelling ionospheric disturbance models with real-time geodetic undifferenced processing of measurements from widely separated permanent GNSS receivers, which is able to provide to the users undifferenced accurate ionospheric corrections that are used as additional information with its corresponding estimated standard deviation.
An example of such a permanent receiver network is the network of European Geostationary Navigation Overlay Service (EGNOS) ranging and monitoring station (EGNOS RIMS). This service would be able to provide WARTK corrections to navigation users, resulting in typical accuracies of around 10 centimeters of error, within a short convergence time. The availability of precise ionospheric corrections helps to decisively fix the real-time carrier phase ambiguities of the WARTK user.
Over the last 10 years, many experiments demonstrated the feasibility of WARTK using both actual and simulated data, while the technique evolved.
This article summarizes the present state and key results of the WARTK technique. We discuss the expected performance of future multi-frequency/multi-constellation GNSS scenarios using both WARTK CPF and associated products, including WARTK user accuracy, convergence time, and integrity. We detail our analysis using recently simulated multi-frequency Galileo data derived from a number of R&D projects funded by the European Space Agency (ESA).
Background to WARTK
ESA has been funding several R&D projects to evaluate the feasibility of a future high-precision positioning service based on a new augmentation system. Data gathered by the existing EGNOS RIMS — originally designed to guarantee integrity in safety-of-life GNSS usage for civil aviation — would feed into this service.
Several projects carried out since 2000 have focused on finding accurate ways of modeling the ionosphere in real-time, profiting from the well-known coordinates of the permanent RIMS receivers. To date, this has been done only notionally by processing data from permanent receivers at the network’s central processing facility (CPF) and roving receivers (users), emulating real-time conditions. In these trials, the typically static receivers of users are treated as roving ones, as well as occasionally truly roving.
A future Wide Area RTK (WARTK) system would extend the sub-decimeter error level for GNSS navigation across continental regions and reduce the cost of existing high-precision positioning applications such as civil engineering, while creating opportunities for new applications.
. . .
GNSS RF Simulator Experiment
In order to investigate the feasibility of WARTK feasibility using multiple constellations and multi-frequency signals, we first defined a representative network of permanent GNSS receivers to generate the WARTK corrections for the users. This step was needed in order to generate realistic signals from which to gather corresponding measurements, with various error sources emulating as much as possible actual conditions.
. . .
Central Processing Facility
Similar to the GPS Master Control Station or the EGNOS processing facility, the WARTK Central Processing Facility has the fundamental mission of generating in real-time the required WARTK user products for the precise, fast, and reliable navigation. One important difference, however, is that the WARTK user’s real-time positioning is based on the carrier phase measurements and precise modeling. Moreover, a user’s real-time ambiguity fixing (or constraining) is closely linked to the availability of very precise ionospheric corrections, to be provided as well by the WARTK CPF.
. . .
WARTK User
As mentioned earlier, WARTK user navigation employs multi-frequency carrier phase data, combined with accurate corrections provided by the CPF, most importantly, ionospheric delay. With the ionospheric correction a user may add an extra equation to quickly estimate and fix the carrier phase ambiguities in real-time.
. . .
Single-Epoch Full Ambiguity Fixing with LAMBDA
In the previous results we have basically used a TCAR like approach for user ambiguity fixing. In fact, the double difference of the extra-wide lane (or just widelane for GPS), widelane and shortlane ambiguities are constrained to its integer value, in order to facilitate the usage of all the available observations, no just the ones with fixed ambiguities, to take the full profit of the GNSS satellites observing geometry.
. . .
Conclusions
Our results confirm the maturity of the wide area real-time kinematic technique. Using a wide area permanent network of GNSS receivers, the technique provides not only outstanding accuracy at the decimeter level, but also integrity with protection levels of the order of one meter.
These results are typically achieved after a few minutes in the case of a dual-frequency single constellation user, or real scenario with GPS, and almost instantaneously with future three-frequency GNSS data, once the initial convergence of the user tropospheric delay is achieved. In both cases the WARTK technique also used the LAMBDA method to complete single-epoch real-time user carrier phase ambiguity fixing.
These results have been obtained with a GPS+Galileo receiver, gathering simultaneous simulated signals of Galileo and GPS satellites, and are being confirmed with large actual datasets in an on-going project.
Critical to the demonstration of these results, we acknowledge two key points: understanding the main factors influencing the estimation of the ionospheric delays (by the WARTK CPF) and transmitting these data to users (by means of the WARTK user interpolation method), and the use of optimal precise ionospheric and geodetic models and measurements at both the CPF and user levels in order to maximize the efficiency in real-time long-baseline carrier phase ambiguity fixing, and hence user accuracy and integrity.
This can be done with an affordable bandwidth, especially by using the recently proposed space-state representation requiring a bandwidth of less than 600 bps for a single constellation, corresponding to 40 ground receivers tracking 30 satellites (M. Hernández-Pajares et alia, 2009b).
Moreover, we should note that the WARTK CPF may be used to support precise navigation while at the same time generating accurate real-time data products for many different user communities, including those with such interests as precise ionospheric models for space weather, instantaneous tropospheric delay determination for weather forecasting, and improvements in satellite clocks and orbits.
For the complete story, including figures, graphs, and images, please download the PDF of the article, above.
Additional Resources
[1] Agrotis L., IGS Real Time Pilot Project progress meeting, June 24, 2009
[2] Bilitza D., International Reference Ionosphere 2000, Radio Science 36, #2, pp. 261-275, 2001
[3] Colombo, O.L., and M. Hernández-Pajares, J. M. Juan, J. Sanz, and J. Talaya, “Resolving Carrier-Phase Ambiguities On the Fly, at More Than 100 km from Nearest Reference Site, with the Help of Ionospheric Tomography,” Institute of Navigation ION GPS-99, Nashville, Tennessee, USA, September 1999
[4] Hernández-Pajares M., and J. M. Juan, J. Sanz and O.L. Colombo (1999a), “Precise Ionospheric Determination and its Application to Real-Time GPS Ambiguity Resolution,” Institute of Navigation ION GPS-99, Nashville, Tennessee, USA, September 1999
[5] Hernández-Pajares M., and J. M. Juan, J. Sanz (1999b), “New Approaches in Global Ionospheric Determination Using Ground GPS Data,” Journal of Atmospheric and Solar-Terrestrial Physics 61, pp. 1237-1247,1999
[6] Hernández-Pajares, M., and J. M. Juan, J. Sanz, and O.L. Colombo, “Application of Ionospheric Tomography to Real-Time GPS Carrier-Phase Ambiguities Resolution, at Scales of 400–1000 km, and with High Geomagnetic Activity,” Geophysical Research Letters, 27, pp. 2009-2012, 2000.
[7] Hernández-Pajares, M., J.M. Juan, J. Sanz and O.L. Colombo (2001), “Tomographic modeling of GNSS ionospheric corrections: Assessment and real-time applications”, ION GPS-2001, Salt-Lake, Utah, USA, September 2001.
[8] Hernández-Pajares, M., and J. M. Juan, J. Sanz, and O.L. Colombo, “Improving the Real-Time Ionospheric Determination from GPS Sites at Very Long Distances over the Equator,” Journal of Geophysical Research, V.107, No. A10, 1296, 2002
[9] Hernández-Pajares, M., and J. M. Juan, J. Sanz, and O.L. Colombo, “Feasibility of Wide-Area Subdecimeter Navigation with GALILEO and Modernized GPS,” IEEE Transactions on Geoscience and Remote Sensing, V. 41, No. 9, 2003
[10] Hernández-Pajares, M., and J. M. Juan, J. Sanz, A. García-Rodríguez, and O.L. Colombo, “Wide Area Real Time Kinematics with Galileo and GPS Signals,” ION GNSS-2004, Long Beach, California, USA, September 2004
[11] Hernandez-Pajares M., and J.M. Juan, J. Sanz (2006a), “Medium Scale Traveling Disturbances Affecting GPS Measurements: Spatial and Temporal Analysis,” Journal of Geophysical Research, doi:10.1029/2005JA011471, Vol. 111, A07 S11, 2006
[12] Hernandez-Pajares, M., and J.M. Juan, and J. Sanz (2006b), Real time MSTIDs modelling and application to improve the precise GPS and GALILEO navigation, Proceeedings of ION GNSS-2006, September 2006
[13] Hernández-Pajares, M., and J. M. Juan, J. Sanz, A. García-Rigo, R. Chen, X. Li, J. Talaya, E. Bosch, T. Schueler, E. Schueler, S. Soley, and M. Reche, “WARTK-EGAL: WARTK Based on EGNOS and Galileo: Technical Feasibility Study,” invited presentation at Growing Galileo Conference & Exhibition, European GNSS Supervisory Authority, Brussels, November 14–15, 2007
[14] Hernández-Pajares, M., and J. M. Juan, J. Sanz, A. Aragón-Angel, P. Ramos-Bosch, D. Odijk, P. F. de Bakker, H. van der Marel, S. Verhagen, I. Fernández-Hernández, M. Toledo, and J. Samson, “TN3.1: WARTK Algorithms and messages at PF level”, page 60, report of the project “Feasibility study of a Wide Area High-precision Navigation Service (WARTK) for EGNOS & Galileo (FES-WARTK)”, funded by ESA, September 2007b.
[15] Hernández-Pajares, M., and J. M. Juan, J. Sanz, A. Aragón-Angel, P. Ramos-Bosch, D. Odijk, P. F. de Bakker, H. van der Marel, S. Verhagen, I. Fernández-Hernández, M. Toledo, and J. Samson, “Feasibility Study of a European Wide Area Real Time Kinematic System,” invited talk in 4th ESA Workshop on Satellite Navigation User Equipment Technologies (Navitec), ESTEC, Noordwijk, The Netherlands, December 2008
[16] Hernández-Pajares, M., and J. M. Juan, J. Sanz (2009a), “WARTK Evaluation with Real GPS Data Report (GNSS-MRS-TN-UPC-I-070001),” within the ESA GNSS Evolution MRS project, presented at the MRS Progress Meeting, Barcelona, Spain, July 23, 2009
[17] Hernández-Pajares, M., and J. M. Juan, J. Sanz (2009b), UPC Contribution to Enhanced Precise Point Positioning (EPPP) Progress Meeting Number 4, Barcelona, Spain, December 3, 2009
[18] Juan, J.M., and P. Ramos (2009), Techical Notes #2 and #3: “GPS PRTODTS Design and Validation Documents” of ESA funded “Precise Real-time Orbits and Clocks Determination” (PRTODTS) project, Barcelona, December 2009.
[19] Simsky, A., and D. Mertens, J-M. Sleewaegen, W. de Wilde, M. Hollreiser, and M. Crisci, “MBOC vs. BOC(1,1) Multipath Comparison Based on GIOVE-B Data,” Inside GNSS, pp. 36–40, September/October 2008
[20] Teunissen, P. J. G., (1995), “The Least-Squares Ambiguity Decorrelation Adjustment: a Method for Fast GPS Integer Ambiguity Resolution” Journal of Geodesy, 70(1-2): 65-82
[21] Teunissen, P. J. G., (1999): A Theorem on Maximizing the Probability of Correct Integer Estimation,” Artificial Satellites, 34(1), pp. 3-9
[22] Teunissen, P.J.G., and S. Verhagen, “The GNSS Ambiguity Ratio-Test Revisited,” Survey Review, Vol. 41, No. 312, pp. 138-151, 2009
[23] Wanninger, L., “Introduction to Network RTK,” from <http://www.network.info/intro/introduction.html> 2008
