Study on the influence of stochastic properties of correction terms on the reliability of instantaneous Network RTK

• Autorzy: Próchniewicz D.

Identyfikatory

DOI

10.2478/arsa-2014-0001

• Języki publikacji: EN

Abstrakty

EN

The reliability of precision GNSS positioning primarily depends on correct carrier-phase ambiguity resolution. An optimal estimation and correct validation of ambiguities necessitates a proper definition of mathematical positioning model. Of particular importance in the model definition is the taking into account of the atmospheric errors (ionospheric and tropospheric refraction) as well as orbital errors. The use of the network of reference stations in kinematic positioning, known as Network-based Real-Time Kinematic (Network RTK) solution, facilitates the modeling of such errors and their incorporation, in the form of correction terms, into the functional description of positioning model. Lowered accuracy of corrections, especially during atmospheric disturbances, results in the occurrence of unaccounted biases, the so-called residual errors. The taking into account of such errors in Network RTK positioning model is possible by incorporating the accuracy characteristics of the correction terms into the stochastic model of observations. In this paper we investigate the impact of the expansion of the stochastic model to include correction term variances on the reliability of the model solution. In particular the results of instantaneous solution that only utilizes a single epoch of GPS observations, is analyzed. Such a solution mode due to the low number of degrees of freedom is very sensitive to an inappropriate mathematical model definition. Thus the high level of the solution reliability is very difficult to achieve. Numerical tests performed for a test network located in mountain area during ionospheric disturbances allows to verify the described method for the poor measurement conditions. The results of the ambiguity resolution as well as the rover positioning accuracy shows that the proposed method of stochastic modeling can increase the reliability of instantaneous Network RTK performance.

Słowa kluczowe

EN

network RTK; stochastic model of GNSS observations; instantaneous ambiguity resolution

• Wydawca: Centrum Badań Kosmicznych PAN ; De Gruyter
• Czasopismo: Artificial Satellites : Journal of Planetary Geodesy
• Rocznik: 2014
• Tom: Vol. 49, No. 1
• Strony: 1--19
• Opis fizyczny: Bibliogr. 52 poz., rys., tab.

Twórcy

autor

Próchniewicz D.

• Warsaw University of Technology Department of Geodesy and Geodetic Astronomy pl. Politechniki 1, 00-661 Warsaw, Poland

Bibliografia

• Al-Shaery A., Lim S., and Rizos C. (2010). Functional models of ordinary kriging for medium range real-time kinematic positioning based on Virtual Reference Station technique. Proceedings of the 23th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2010, 2513-2521.
• Al-Shaery A., Lim S., and Rizos C. (2011). Investigation of different interpolation models used in Network-RTK for the Virtual Reference Station technique. Journal of Global Positioning Systems, 10(2), 136-148.
• Bartels J. (1957). The technique of scaling indices K and Q of geomagnetic activity. Annales of the International Geophysical Year, 4, 215-226.
• Booz-Allen and Hamilton (1996). Second draft for-working group review, proposed European Baseline Radionavigation Plan, appendix b. Technical report, ICAO AllWeather Operations Panel.
• Chang X., Yang X., and Zhou T. (2005). MLAMBDA: a modified LAMBDA method for integer least-squares estimation. Journal of Geodesy, 79, 552-565.
• Chen X., Landau H., and Vollath U. (2003). New tools for Network RTK integrity monitoring. Proceedings of the 16th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GPS/GNSS 2003, 1355-1360.
• Counselman C.C. and Abbot R. (1989). Method of resolving radio phase ambiguity in satellite orbit determination. Journal of Geophysical Research, 94(B6), 7058-7064.
• Dai L., Han S., Wang J., and Rizos C. (2004). Comparison of interpolation algorithms in network-based GPS techniques. Journal of the Institute of Navigation, 50(4), 277-294.
• Dai L., Wang J., Rizos C., and Han S. (2003). Predicting atmospheric biases for real-time ambiguity resolution in GPS/GLONASS reference station networks. Journal of Geodesy, 76, 617-628.
• De Jonge P.J. and Tiberius C.C.J.M. (1996). The LAMBDA method for integer ambiguity estimation: implementation aspects. Technical report, Delft Geodetic Computing Centre, Delft University of Technology.
• Euler H.J. and Schaffrin B. (1991). On a measure for the discernability between different ambiguity solutions in static-kinematic GPS mode. IAG Symposia no. 107, Kinematic Systems in Geodesy, Surveying, and Remote Sensing, 285-295.
• Fotopoulos G. and Cannon M.E. (2001). An overview of multireference station methods for cm-level positioning. GPS Solutions, 4(3), 1-10.
• Gao Y., Li Z., and McLellan J.F. (1997). Carrier phase based regional area differential GPS for decimeter-level positioning and navigation. Proceedings of the 10th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GPS 1997, 1305-1313.
• Geisler I. (2006). Performance improvement of Network RTK positioning. Proceedings of the 2006 National Technical Meeting of The Institute of Navigation, 869-880.
• Grejner-Brzezinska D.A., Wielgosz P., Kashani I., Smith D.A., Spencer P.S.J., Robertson D.S., and Mader G.L. (2004). An analysis of the effects of different network-based ionosphere estimation models on rover positioning accuracy. Journal of Global Positioning Systems, 3(1-2), 115-131.
• Han S. (1997). Quality-control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning. Journal of Geodesy, 71, 351-361.
• Han S. and Rizos C. (1996). GPS network design and error mitigation for real-time continuous array monitoring systems. Proceedings of the 9th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GPS 1996, 1827-1836.
• Han S. and Rizos C. (1997). Instantaneous ambiguity resolution for medium-range GPS kinematic positioning using multiple reference stations. Proceedings of the International Association of Geodesy Symposia, 118, Advances in Positioning and Reference Frames, 283-288.
• Hein G.W. (2000). From GPS and GLONASS via EGNOS to Galileo - positioning and navigation in the third millennium. GPS Solutions, 3(4), 39-47.
• Hofmann-Wellenhof B., Lichtenegger H., and Wasle E. (2008). GNSS Global Navigation Satellite Systems: GPS, GLONASS, Galileo & more. Springer-Verlag, Wien.
• Lachapelle G. and Alves P. (2002). Multiple reference station approach: overview and current research. Journal of Global Positioning Systems, 1(2), 133-136.
• Landau H., Chen X., Kipka A., and Vollath U. (2007). Latest developments in Network RTK modeling to support GNSS modernization. Journal of Global Positioning Systems, 6(1), 47-55.
• Landau H., Vollath U., and Chen X. (2003). Virtual Reference Stations versus broadcast solutions in Network RTK - advantages and limitations. Proceedings of GNSS 2003 The European Navigation Conference, Graz, Austria.
• Marel van der H. (1998). Virtual GPS reference stations in the Netherlands. Proceedings of the 11th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GPS 1998, 49-58.
• Musa T.A., Wang J., and Rizos C. (2004). A stochastic modelling method for network-based GPS positioning. European Navigation Conference, ECN GNSS2004.
• Musa T.A., Wang J., Rizos C., and Satirapod C. (2003). Stochastic modelling for networkbased GPS positioning. The 6th International Symposium on Satellite Navigation Technology Including Mobile Positioning and Location Serivces, Melbourne, Australia.
• Odijk D. (2000). Weighting ionospheric corrections to improve fast GPS positioning over medium distances. Proceedings of the 13th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GPS 2000, 1113-1123.
• Odijk D. (2001). Instantaneous precise GPS positioning under geomegnetic storm conditions. GPS Solutions, 5(2), 29-42.
• Odijk D. (2008). GNSS solutions: mathematical models. Inside GNSS, 3(2), 22-24.
• Odijk D., Marel van der H., and Song I. (2000). Precise GPS positioning by applying ionospheric corrections from an active control network. GPS Solutions, 3(3), 49-57.
• O’Keefe K., Petovello M., Lachapelle G., and Cannon M.E. (2006). Assessing probability of correct ambiguity resolution in the presence of time-correlated errors. Navigation: Journal of the Institute of Navigation, 53(4), 269-282.
• Próchniewicz D. (2011). A study on mitigation of the distance-dependent biases in the Network RTK technique. Reports on Geodesy, 90(1), 397-407.
• Raquet J.F. (1998). Development of a method for kinematic GPS carrier-phase ambiguity resolution using multiple reference receivers. Ph.D. thesis, The University of Calgary.
• Rizos C. (2002). Network RTK research and implementation - a geodetic perspective. Journal of Global Positioning Systems, 1(2), 144-150.
• Rizos C. and Han S. (2003). Reference station network based RTK systems - concepts and progress. Wuhan University Journal of natural Sciences, 8(2B), 566-574.
• Seeber G. (2003). Satellite Geodesy: foundations, methods, and applications. Walter de Gruyter, Berlin, New York, 2nd completely rev. and extended edition.
• Takasu T. and Yasuda A. (2010). Kalman-filter-based integer ambiguity resolution strategy for long-baseline RTK with ionosphere and troposphere estimation. Proceedings of the 23rd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2010, 161-171.
• Teunissen P.J.G. (1993). Least squares estimation of the integer GPS ambiguities. Invited lecture, Section IV Theory and Methodology, IAG General Meeting, Beijing.
• Teunissen P.J.G. (1995). The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. Journal of Geodesy, 70, 65-82.
• Teunissen P.J.G. (1997). The geometry-free GPS ambiguity search space with a weighted ionosphere. Journal of Geodesy, 71, 730-383.
• Teunissen P.J.G. (1998). Success probability of integer GPS ambiguity rounding and bootstrapping. Journal of Geodesy, 72, 606-612.
• Tiberius C.C.J.M. and De Jonge P.J. (1995). Fast positioning using LAMBDA-method. Proceedings of the 4th International Symposium on Differential Satellite Navigation Systems, DSNS 1995(paper no. 30).
• Tiberius C.C.J.M., Jonkman N., and Kenselaar F. (1999). The stochastics of GPS observables. GPS World, 10(2), 49-54.
• Tiberius C.C.J.M., Teunissen P.J.G., and De Jonge P.J. (1997). Kinematic GPS: performance and quality control. Int. Symp. on Kinematic Systems in Geodesy, Geomatics & Navigation, Banff, Canada, KIS1997, 289-299.
• Verhagen S. (2004). Integer ambiguity validation: an open problem? GPS Solutions, 8, 36-43.
• Verhagen S. (2005). The GNSS integer ambiguities: estimation and validation. Ph.D. thesis, Netherlands Geodetic Commission, Delft.
• Verhagen S., Li B., Teunissen P.J.G., and Tiberius C.C.J.M. (2012). Challenges in ambiguity resolution: biases, weak models, and dimensional curse. Proceedings of 6th ESA Workshop on Satellite Navigation Technologies, NAVITEC 2012, 1-8.
• Wang J., Lee H.K., Lee Y.J., Musa T., and Rizos C. (2005). Online stochastic modelling for network-based GPS real-time kinematic positioning. Journal of Global Positioning Systems, 4(1-2), 113-119.
• Wanninger L. (1995). Enhancing differential GPS using regional ionospheric error models. Bulletin G´eod´esique, 69, 283-291.
• Wanninger L. (2004). Ionospheric disturbance indices for RTK and Network RTK positioning. Proceedings of the 17th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2004, 2849-2854.
• Wielgosz P., Grejner-Brzezinska D.A., and Kashani I. (2003). Regional ionosphere mapping with kriging and multiquadric methods. Journal of Global Positioning Systems, 2(1), 48-55.
• Wielgosz P., Kashani I., and Grejner-Brzezinska D. (2005). Analysis of long-range network RTK during a severe ionospheric storm. Journal of Geodesy, 79, 524-531.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).