بررسی ‌تأثیر مدل‌های تصادفی مبتنی بر زاویه ارتفاعی ماهواره‌ها در روش تعیین موقعیت مطلق دقیق

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار، دانشکده مهندسی نقشه‌برداری و اطلاعات مکانی، پردیس دانشکده‌های فنی، دانشگاه تهران، تهران، ایران

2 استاد، دانشکده مهندسی نقشه‌برداری و اطلاعات مکانی، پردیس دانشکده‌های فنی، دانشگاه تهران، تهران، ایران

3 دانشجوی دکتری، دانشکده مهندسی نقشه‌برداری و اطلاعات مکانی، پردیس دانشکده‌های فنی، دانشگاه تهران، تهران، ایران

چکیده

در روش کمترین‌مربعات نیازمند به‌کارگیری دو مدل تابعی و مدل تصادفی برای برآورد دقیق مجهولات هستیم. در این تحقیق به‌بررسی و مقایسه 9 مدل تصادفی مبتنی بر زاویه ارتفاعی ماهواره‌ها پرداخته شده است. این ۹ مدل تصادفی در قالب معادلاتی از چهار خانواده توابع مثلثاتی ، ، توابع مثلثاتی بهبودیافته و توابع نمایی بیان شده‌اند. برای این منظور از مشاهدات ماهواره­ای مربوط به‌یک نقطه در دو اپک زمانی استفاده شده که جابه‌جایی کنترل‌شده آن توسط ابزار دقیق به آن اعمال شده است. با توجه به نتایج ارائه‌شده بالاترین دقت مربوط به استفاده از مدل تصادفی توابع مثلثاتی بهبودیافته می‌باشد. نهایتاً به‌کمک مدل‌ انتخاب شده، میانگین دقت برای مختصات به‌دست آمد. میانگین دقت برای مؤلفه شرقی بین 03/0 تا 8/2 میلی‌متر و برای مؤلفه شمالی بین 04/0 تا 1/3 میلی‌متر به‌دست آمد. با توجه به دقت به‌دست آمده برای مؤلفه‌های مختصاتی افقی به‌کمک مدل هشت به‌عنوان بهترین مدل تصادفی، تعداد اپک‌های کمتری برای رسیدن به سطح دقت دسی‌متر، سانتی‌متر و میلی‌متر مورد نیاز می‌باشد. به‌گونه‌ای که برای نقطه موردنظر تعداد ۲۷۷ اپک برای مؤلفه شرقی و تعداد ۴۰۵ اپک برای مؤلفه شمالی برای رسیدن به سطح دقت میلی‌متر مورد نیاز می‌باشد. در ادامه با درنظرگرفتن شرط همگرایی ۵ سانتی‌متر (درنظرگرفتن اختلاف 5 سانتی‌متر برای دو اپک متوالی و برقراری این شرط تا اپک انتهایی) برای مؤلفه‌های افقی شرقی و شمالی با توجه به مدل هشت، شرط همگرایی بعد از ۵ دقیقه و ۵۰ ثانیه برای مؤلفه شرقی و بعد از ۸ دقیقه و ۵ ثانیه برای مؤلفه شمالی قابل‌دست‌یابی می‌باشد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Evaluation of statistical models of precise point positioning based on satellites elevation angles

نویسندگان [English]

  • Saeed Farzaneh 1
  • Abdolreza Safari 2
  • Kamal Parvazi 3
1 Assistant Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran
2 Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran
3 Ph.D. Student Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran
چکیده [English]

Due to the importance of using an accurate stochastic model in estimation of the coordinates of points using the GNSS observation method, this study investigates the role of the elevation angle-dependent stochastic model. The least-squares estimation method is usually used in processing GNSS observations. This method requires the use of two essential models, one is functional model and the other is stochastic model. The functional model illustrates the relationship between observations and unknown parameters. The stochastic model presents the covariance matrix and the statistical properties (expectation) and dispersion of errors in observation, which expresses the accuracy and the correlation between the types of observations. A precise and detailed stochastic model for observations, expresses the receiver's internal noise, residual errors, and the correlation between the variables. Moreover, by choosing a suitable stochastic model, we can provide the necessary preconditions for solving the reliable phase ambiguity and precise positioning. In this study, we investigate and compare 9 stochastic models based on the satellite elevation angle. These 9 models are expressed as equations of four families of trigonometric functions , , improved trigonometric functions, and exponential functions. To do this, we use observations of a single point in two time epoch where simulated displacement was applied to it very precisely by the device. First, by using precise point positioning method, the horizontal coordinates of the point in two epochs were estimated by using 9 stochastic models. According to the accomplished comparison, we present the closest estimated value to the simulated real value of the stochastic models which are trigonometric functions , improved trigonometric functions and exponential functions respectively. Among these four models, The results of exponential function is closest to the simulated real value. Online services are then used to process point-of-view observations, according to which the two OPUS and AUSPOS services are most closest to the simulated real observations. Then the estimation of the accuracy of the horizontal components is examined by means of 9 presented stochastic models. According to the presented results, the highest accuracy and least error are related to the use of stochastic model  (improved trigonometric functions). Then, two stochastic models and matrix weights  and  (exponential functions) showed the highest accuracy. Using these three models with the highest accuracy, the average accuracy obtained for the East component is between 0.03 mm and 2.8 mm and for the North component is between 0.04 mm and 3.1 mm. In the next section, due to the accuracy obtained for the horizontal coordinate components in all epochs (sampling interval of 5 s) using these three stochastic models, fewer epochs are required to reach the level of accuracy of Dosimeter, Centimeter and Millimeter. In such a way that, for desired point, 277 epochs for the East component and 405 epochs for the North component are required to reach the millimeter precision level. Finally, considering the 5cm convergence condition for the horizontal components East and North, due to the three models used, this convergence condition is achievable after 5 minutes and 50 seconds for the East component and after 8 minutes and 5 seconds for the component North.

کلیدواژه‌ها [English]

  • Global Navigation Satellite Systems (GNSS)
  • Precise Point Positioning
  • PPP accuracy
  • Convergence period
  • Stochastic model

مراجع

Abdel-salam, M. A. T., 2005, Precise point positioning using un-differenced code and carrier phase observations. PhD Thesis, Department of Geomatics Engineering, University of Calgary, Alberta, Canada.
Afifi, A. and El-Rabbany, A., 2013, Stochastic modeling of Galileo E1 and E5a signals. International Journal of Engineering and Innovative Technology (IJEIT), 3(6), pp.188-192.
Afifi, A., El-Rabbany, A., 2015, An innovative dual frequency PPP model for combined GPS/Galileo observations. Journal of Applied Geodesy, 9(1), 27-34.
Amiri-Simkooei, A., 2007, Least-squares variance component estimation: theory and GPS applications. Delft University of Technology: Delft, The Netherlands.
Amiri-Simkooei, A.R., Teunissen, P.J.G. and Tiberius, C.C.J.M., 2009, Application of least-squares variance component estimation to GPS observables. Journal of Surveying Engineering, 135(4), pp.149-160.
Amiri-Simkooei, A.R., 2013, Application of least squares variance component estimation to errors-in-variables models. Journal of geodesy, 87(10-12), pp.935-944.
Amiri-Simkooei, A.R., Zangeneh-Nejad, F. and Asgari, J., 2013, Least-squares variance component estimation applied to GPS geometry-based observation model. Journal of Surveying Engineering, 139(4), pp.176-187.
Amiri-Simkooei, A.R., Jazaeri, S., Zangeneh-Nejad, F. and Asgari, J., 2016, Role of stochastic model on GPS integer ambiguity resolution success rate. GPS solutions, 20(1), pp.51-61.
Böhm, J., Niell, A., Tregoning, P. and Schuh, H., 2006, Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data. Geophysical Research Letters, 33(7).
Bona, P., 2000, Precision, cross correlation, and time correlation of GPS phase and code observations. GPS solutions, 4(2), pp.3-13.
Cai, C., Gao, Y., 2013, Modeling and assessment of combined GPS/GLONASS precise point positioning. GPS solutions, 17(2), 223-236. Euler, H. J., and Goad, C. 1991, On optimal filtering of GPS dual frequency observations without using orbit information Bulletin Géodésique, 65, 130–143.
Chen, J., Zhang, Y., Wang, J., Yang, S., Dong, D., Wang, J. and Wu, B., 2015, A simplified and unified model of multi-GNSS precise point positioning. Advances in Space Research, 55(1), 125-134.
Daneshmand, S., Broumandan, A., Sokhandan, N. and Lachapelle, G., 2013, GNSS multipath mitigation with a moving antenna array. IEEE Transactions on Aerospace and Electronic Systems, 49(1), pp.693-698.
Defraigne, P., Baire, Q., 2011, Combining GPS and GLONASS for time and frequency transfer. Advances in Space Research, 47(2), 265-275.
Dow, J.M., Neilan, R.E. and Rizos, C., 2009, The international GNSS service in a changing landscape of global navigation satellite systems. Journal of geodesy, 83(3-4), pp.191-198.
El-Rabbany, A.E., 1996, The effect of physical correlations on the ambiguity resolution and accuracy estimation in GPS differential positioning.
Elsobeiey, M. and El-Rabbany, A., 2010, On stochastic modeling of the modernized global positioning system (GPS) L2C signal. Measurement science and technology, 21(5), p.055105.
Eueler, H.J. and Goad, C.C., 1991, On optimal filtering of GPS dual frequency observations without using orbit information. Bulletin géodésique, 65(2), pp.130-143.
Geng, J., Teferle, F. N., Meng, X. and Dodson, A. H., 2011, Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning. Advances in space research, 47(10), 1664-1673.
Gerdan, G.P., 1995, A comparison of four methods of weighting double difference pseudorange measurements. Australian surveyor, 40(4), pp.60-66.
Han, S., 1997, Quality-control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning. Journal of Geodesy, 71(6), pp.351-361.
Hofmann-Wellenhof, B., Lichtenegger, H. and Wasle, E., 2007, GNSS–global navigation satellite systems: GPS, GLONASS, Galileo, and more. Springer Science & Business Media.
Jin, X.X. and de Jong, C.D., 1996, Relationship between satellite elevation and precision of GPS code observations. The Journal of Navigation, 49(2), pp.253-265.
Jonkman, N., 1988, Integer GPS-Ambiguity Estimation without the Receiver-Satellite Geometry; Delft University of Technology: Delft, The Netherlands.
Karaim, M., Elsheikh, M., Noureldin, A. and Rustamov, R.B., 2018, GNSS error sources. In Multifunctional Operation and Application of GPS,69-85, Intech.
Koch, K.R., 1999, Parameter estimation and hypothesis testing in linear models. Springer Science & Business Media.
Kouba, J., 2009, A guide to using International GNSS Service (IGS) products.
Kouba, J. and Héroux, P., 2001, Precise point positioning using IGS orbit and clock products. GPS solutions, 5(2), pp.12-28.
Kunysz, W., 2000, September. High performance GPS pinwheel antenna. In Proceedings of the 2000 international technical meeting of the satellite division of the institute of navigation (ION GPS 2000) (pp. 19-22).
Leandro, R. F. and M. C. Santos., 2007, Stochastic models for GPS positioning: An empirical approach. GPS World 18(2), 50-56
Leick, A., Rapoport, L. and Tatarnikov, D., 2015, GPS satellite surveying. John Wiley & Sons.
Li, B., Lou, L. and Shen, Y., 2015, GNSS elevation-dependent stochastic modeling and its impacts on the statistic testing. Journal of Surveying Engineering, 142(2), p.04015012.
Li, B., Shen, Y. and Xu, P., 2008, Assessment of stochastic models for GPS measurements with different types of receivers. Chinese Science Bulletin, 53(20), pp.3219-3225.
Li, B., Shen, Y. and Lou, L., 2010, Efficient estimation of variance and covariance components: a case study for GPS stochastic model evaluation. IEEE Transactions on Geoscience and Remote Sensing, 49(1), pp.203-210.
Li, P. and Zhang, X., 2014, Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning. GPS solutions, 18(3), pp.461-471.
Li, B., 2016, Stochastic modeling of triple-frequency BeiDou signals: estimation, assessment and impact analysis. Journal of Geodesy, 90(7), 593-610.
Li, B., Zhang, L. and Verhagen, S., 2017, Impacts of BeiDou stochastic model on reliability: overall test, w-test and minimal detectable bias. GPS solutions, 21(3), pp.1095-1112.
Petit, G. and Luzum, B., 2010, IERS conventions (2010) (No. IERS-TN-36). BUREAU INTERNATIONAL DES POIDS ET MESURES SEVRES (FRANCE).
Qian, K., Wang, J. and Hu, B., 2016, A posteriori estimation of stochastic model for multi-sensor integrated inertial kinematic positioning and navigation on basis of variance component estimation. The Journal of Global Positioning Systems, 14(1), p.5.
Rizos, C., 1997, Principles and practice of GPS surveying. University of New South Wales.
Rizos, C., Janssen, V., Roberts, C. and Grinter, T., 2012, Precise point positioning: is the era of differential GNSS positioning drawing to an end?
Satirapod, C. and Luansang, M., 2008, Comparing stochastic models used in GPS precise point positioning technique. Survey Review, 40(308), pp.188-194.
Schön, S. and Brunner, F.K., 2008, A proposal for modelling physical correlations of GPS phase observations. Journal of Geodesy, 82(10), 601-612.
Seepersad, G. and Bisnath, S., 2014, Challenges in Assessing PPP Performance. Journal of Applied Geodesy, 8(3), 205-222.
Teunissen. PJG., 2006, Testing theory: an introduction, 2nd edn. Delft University Press, Delft.
Teunissen, P.J.G., 2007, Influence of ambiguity precision on the success rate of GNSS integer ambiguity bootstrapping. Journal of Geodesy, 81(5), pp.351-358.
Tiberius, C.C.J.M. and Kenselaar, F., 2000, Estimation of the stochastic model for GPS code and phase observables. Survey Review, 35(277), 441-454.
Tiberius, C. and Kenselaar, F., 2003, Variance component estimation and precise GPS positioning: case study. Journal of surveying engineering, 129(1), pp.11-18.
Wang, J., Stewart, M.P. and Tsakiri, M., 1998, Stochastic modeling for static GPS baseline data processing. Journal of Surveying Engineering, 124(4), 171-181.
Wang, J., Satirapod, C. and Rizos, C., 2002, Stochastic assessment of GPS carrier phase measurements for precise static relative positioning. Journal of Geodesy, 76(2), pp.95-104.
Witchayangkoon, B., 2000, Elements of GPS precise point positioning. In Spatial Information Science and Engineering, University of Maine.
Wu, J.T., Wu, S.C., Hajj, G.A., Bertiger, W.I. and Lichten, S.M., 1992, August. Effects of antenna orientation on GPS carrier phase. In Astrodynamics 1991, 1647-1660.
Xu, G. and Xu, Y., 2016, GPS: theory, algorithms and applications. Springer.
Yang, L., Li, B., Li, H., Rizos, C. and Shen, Y., 2017, The influence of improper stochastic modeling of Beidou pseudoranges on system reliability. Advances in Space Research, 60(12), 2680-2690.
Zumberge, J. F., Heflin, M. B., Jefferson, D. C., Watkins, M. M. and Webb, F. H., 1997, Precise point positioning for the efficient and robust analysis of GPS data from large networks. Journal of geophysical research: solid earth, 102(B3), 5005-5017.
فیزیک زمین و فضا
دوره 46، شماره 2
مرداد 1399
صفحه 205-223

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