The Research on the Regional Precise Troposphere Delay by using Spherical Cap Harmonic Analysis

Chuang Qian, Hui Liu, Changyong He

Abstract:	The troposphere delay is one of the major error resources for the accuracy of GPS positioning. Empirical models were unable to provide sufficient accuracy for the precise positioning with increasing demand of precision, the Continuously Operating Reference Stations (CORS) built around the world shed lights on constructing more precise tropospheric delay model. Based on the analysis of drawbacks of common real-time regional tropospheric delay models, a new regional real-time troposphere model based on spherical cap harmonic analysis (SCHA) was proposed in this paper. Detailed SCHA model calculations was introduced in this paper, and the optimal SCHA area troposphere model was established by experimental comparison analysis. SCHA model’s inner coincident precision has obvious advantage (RMS < 6 mm) and its external coincident precision increases about 50% than four-parameter model (RMS < 1 cm). SCHA model could describe special variations of troposphere more reasonably and is adequate for regional real-time troposphere delay modeling for large areas. Key words: spherical cap harmonic function; zenith troposphere total delay; fitting model; CORS1 Introduction In electromagnetic space technology, before reaching receiver the satellite electromagnetic signals need to travel across the troposphere, during this the signal will be bended and delayed because of the atmospheric refraction effects. The magnitude of troposphere delay is about 2 meters along the zenith direction, reaching up to 25 meters at the elevation angles below 15 degrees [1]. In GNSS navigation and positioning, we usually map the slant delay of the signal propagation path onto zenith direction by mapping function, and model zenith total delay(ZTD) in order to considerably weaken the influence of atmospheric effect on the navigation and positioning. Troposphere delay plays a crucial role in GNSS positioning [2]. Currently, the main methods to eliminate the troposphere delay are: the empirical models, parameter estimation, external correction (e.g., water vapor radiometer) and differential positioning method. The accuracy of empirical model correction cannot meet the requirements of modern high-precision positioning; although external correction method has a high precision, the high cost largely limits its extensive application; the accuracy of parameter estimation method can be millimeter level for long baseline; but both model correction and differential positioning are commonly used for short baseline with small differences both in elevation and weather conditions on each side of stations [3]. With the development of GNSS, Continuously Operating Reference Station System (CORS) has been established over many areas. Regional precise troposphere model has received widespread attention from large amount of individuals and research organizations. It was built with precise ZTD estimated from reference stations. The main methods to establish regional model are: (a) Inverse distance weighted (IDW) method based on the distances between rover station and reference stations; (b) mathematical models considering the horizontal and vertical variations [4]. For the first method, it will increase the pressure of communication and be not convenient in real-time positioning, because ZTDs of the reference stations are required; for the second one, the commonly used methods mainly include four-parameter surface model and linear curve model which only take elevation into account. These models are basically appropriate for Virtual Reference Station (VRS) technology in small scale by establishing a small area model with data of several reference stations. At present, many places have basically completed the construction of CORS. So users can get ZTD on their location to meet the request of precision tropospheric delay correction in precise positioning, with tropospheric delay model established by CORS. Spherical harmonic analysis (SHA) has been widely used in geophysical gravity and magnetic field modeling. But data distribution and convergence speed are two main factors limiting spherical harmonic analysis methods. The spherical cap harmonic analysis (SCHA) requires fewer observation data, and effectively reduces the model coefficients. Since 1985, the spherical cap harmonic analysis method has been widely used in conservative force field, sea surface topography, local gravity field, local quasi geoid, the magnetic field changes, GPS Leveling, regional ionospheric model, distribution characteristics of soil relative humidity and so on [6-14]. Based on the analysis of the commonly used regional tropospheric delay fitting models, a new fitting model is proposed based on spherical cap harmonic with a helpful result.
Published in:	Proceedings of the 27th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2014) September 8 - 12, 2014 Tampa Convention Center Tampa, Florida
Pages:	51 - 59
Cite this article:	Qian, Chuang, Liu, Hui, He, Changyong, "The Research on the Regional Precise Troposphere Delay by using Spherical Cap Harmonic Analysis," Proceedings of the 27th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2014), Tampa, Florida, September 2014, pp. 51-59.
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