An investigation of three dimensional ray tracing method efficiency in precise point positioning by tropospheric delay correction


1 Ph.D. Student, Faculty of Geodesy and Geomatics Engineering, K.N.Toosi University of Technology, Tehran, Iran

2 Assistant Professor, Faculty of Geodesy and Geomatics Engineering, K.N.Toosi University of Technology, Tehran, Iran


Earth's atmosphere has a series of layers, each with its own specific traits. Moving upward from ground level, these layers are named the troposphere, stratosphere, mesosphere, thermosphere and exosphere. The exosphere gradually fades away into the realm of interplanetary space. The troposphere is the lowest layer of our atmosphere. Starting at ground level, it extends upward to about 10 km above sea level. Humans live in the troposphere layer, and nearly all weather occurs in this layer and affects their activities. Ninety nine percent of the water vapor in the atmosphere is found in the troposphere; therefore most clouds appear in this layer. Air pressure and temperature drops in the troposphere with height. The tropospheric path delay is one the main error sources in Global Navigation Satellite System (GNSS) such as Global Positioning System (GPS) observations and reduces the accuracy of GNSS point positioning. Accurate estimation of tropospheric path delay in GNSS signals is necessary for positioning and also its meteorological applications. The tropospheric delay is divided into the dry (hydrostatic) and wet (non-hydrostatic) parts. The dry tropospheric delay depends on the pressure variations between satellite and station on the Earth’s surface and can be determined accurately using experimental models. The wet delay can be determined by subtracting the dry delay from the total GPS derived delay. In this paper the efficiency of 3D ray tracing in increasing the accuracy of point positioning is investigated. The 3D ray tracing technique based on Eikonal equation is the strongest and newest ray tracing method. These equations are solved in order to get the ray path and the optical path length. The Eikonal equation itself is the solution of the so-called Helmholtz equation with respect to electro-magnetic waves. In this method the ray paths are not limited to a certain azimuthally fixed vertical plane. In 2D methods the ray paths are forced to stay within a vertical plane of constant azimuth. European Center for Medium Range Weather Forecasting (ECMWF) is currently publishing ERA-I, a global reanalysis of the meteorological data. This reanalysis provides values of several meteorological parameters on a global gride ∼75 km. The vertical stratification is described on 37 pressure levels. Tropospheric corrections were calculated using 3D ray tracing, 2D ray tracing and Saastamoinen methods in Tabriz and Abarkuh stations using ERA-I meteorological parameters. These corrections were applied to the GPS observations and the stations coordinate were computed. Furthermore, these stations coordinates were determined twice using Bernese GPS processing software, one time the tropospheric delay was not canceled from observations and second time it was considered as unknown parameter and evaluated with stations coordinates. The result of this process was considered as a reference to evaluate the three prescribed correction methods. These comparisons indicate that the correction computed from 3D ray tracing is more efficient than that of 2D ray tracing and Saastamoinen model corrections. Also the correction amount in Tabriz station is meaningful with respect to Abarkuh station, which can be attributed to small variations of water vapor in Abarkuh station.


Main Subjects

Bevis, M., 2010, Researchers Show How far South American Cities Moved in Quake. and http:// researchnews. osu. Edu /archive/chilemoves.htm.
Black, H., 1978, An easily implemented algorithm for the tropospehric range correction. Journal of Geophysical Research, 83.
Böhm, J. and Schuh, H., 2003, Vienna Mapping Functions. Proceedings of the 16th Working Meeting on European VLBI for Geodesy and Astrometry, Leipzig, Verlag des Bundesamtes für Kartographie und Geodäsie, 131 – 143.
Böhm, J., 2004, Troposphärische Laufzeitverzögerungen in der VLBI. PhD thesis. Institut für Geodäsie und Geophysik, Fakultät für Mathematik und Geoinformation, Technische Universität Wien.
Böhm, J., Werl, H. and Schuh, H., 2006a, Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data. Journal of Geophysical Research, 111.
Dach, R., Hugentubler, U., Fridez, P. and Meindl, M., 2007, Bernese GPS Software Version 5.0, Astronomical Institute, University of Berne., p. 612.
Ghaffari Razin, M. R. and Voosoghi, B., 2016, Modeling of ionosphere time series using wavelet neural networks (case study: N-W of Iran). Adv. Space Res.. http:// 10.1016/j.asr. 2016.04.006.
Haji Aghajany, S., Voosoghi, B. and Yazdian, A., 2017, Estimation of north Tabriz fault parameters using neural networks and 3D tropospherically corrected surface displacement field. Geomatics, Natural Hazards and Risk.
Haji Aghajany, S. and Amerian, Y., 2017, Three-dimensional ray tracing technique for tropospheric water vapor tomography using GPS measurements. Journal of Atmospheric and Solar-Terrestrial Physics, 164, 81-88. doi: 10.1016/j.jastp.2017.08.003.
Hopfield, H., 1969, Two-quartic tropospheric refractivity profile for correcting satellite data. Journal of Geophysical Research, 74, 4487-4499.
Hobiger, T., Ichikawa, R., Koyama, Y. and Kondo, T., 2008, Fast and accurate ray-tracing algorithms for real-time space geodetic applications using numerical weather models. Journal of Geophysical Research, 113.
Hofmeister, A., 2016, Determination of path delays in the atmosphere for geodetic VLBI by means of ray-tracing. Ph.D. Thesis. Department of Geodesy and Geoinformation, TU Wien.
Mendes, V. B., 1998, Modeling the neutral-atmosphere propagation delay in radiometric space techniques. U.N.B., p. 353.
Niell, A. E., 1996, Global mapping functions for the atmosphere delay at radio wavelengths. Journal of Geophysical Research, 101, 3227–3246.
Niell, A. E., 2001, Preliminary evaluation of atmospheric mapping functions based on numerical weather models. Physics and Chemistry of the Earth, 26, 475–480.
Saastamoinen, J., 1972, Atmospheric correction for the troposphere and tratosphere in radio ranging of satellites. The Use of Artificial Satellites for Geodesy, American Geophysical Union, Washington, D.C.
Saastamoinen, J., 1973, Contributions to the Theory of Atmospheric Refraction. Bulletin Geodesique, 105, pp. 279-298, 106, pp. 383-397, 107, pp. 113-134. Printed in three parts.
Thayer, G. D., 1967, A rapid and accurate ray tracing algorithm for a horizontally stratified atmosphere, Radio Science, 1(2).
Wallace, J. M., and Hobbs, P. V., 2006, Atmospheric science: an introductory survey Vol. 92, Academic Press.