Ionosphere TEC and TEC Gradients Estimation Using a Regional GNSS Network

C. Wang, Y. Morton

Abstract:	Ionosphere total electron content (TEC) is an important parameter for both satellite navigation and scientific studies of the ionosphere. For satellite navigation receiver designers, TEC determines the first order ionosphere induced range error, which is a dominant error source in GNSS generated navigation solutions. For ionosphere researchers, TEC describes the background state of the ionosphere. For these reasons, there are a number of GNSS networks whose main task is to provide measurements to allow assimilation of TEC maps. There are four prominent IGS Ionosphere Associate Analysis Centers (IAACs) that have been generating global TEC maps for over one decade. They are the Center for Orbit Determination in Europe (CODE), European Space Operations Center of ESA (ESOC), Jet Propulsion Laboratory (JPL), and Technical University of Catalonia (UPC)[1]. However, global TEC maps have limited precision and resolution which are often inadequate to describe detailed features of local ionosphere. There is the need for regional ionosphere models to provide high precision ionosphere delay correction. Existing regional ionosphere model typically relies on modeling of measurements from a dense local GNSS network in order to achieve high precision [2-5]. Various models, such as polynomial, grid model, and spherical harmonics model have been used in establishing regional models. In addition to the need for a dense local GNSS network, which is often unavailable, these models also lack sound physical and scientific support. In this paper, we propose a data driven approach that can generate regional ionosphere TEC map with improved precision. In this approach, the ionosphere model is described by TEC gradients in the latitude and longitude directions. In this paper, we treat these gradients as the first-order derivatives of the TEC. For a given regional network having m receivers, it there are a total of n ionosphere piercing points (IPP) for m receivers at a given measurement epoch, then the TEC difference between any two IPPs can be treated as combined contributions from the latitude and longitude gradient in the region. The latitude and longitude gradient contributions are directly proportional to the IPPs latitude and longitude differences respectively. A total of n(n-1)/2 pairs of IPP TEC difference relationships can be established to solve for the TEC gradients. For a sparse regional network, it is possible that the number of satellites in direct view of the receivers may lead to a small number of IPPs, especially if the region is located in high latitude areas. As a result, there may be epochs when there is not sufficient number of equations available to solve for the TEC gradients. Linear interpretations between nearby time epochs solutions are used to generate results for these “missing” data points. These TEC gradients are then used generate regional TEC maps. The paper will present the detailed algorithm to establish the TEC gradient and resulting TEC maps and compare the TEC values obtained using the proposed TEC gradient with that obtained using existing global TEC maps. Our preliminary results show that there is less than 2 TEC units average differences between our approach and the global TEC map over northern Europe covering 46 to 53 degree latitude and 10 to 23 longitude areas with 0.5 degree latitude and 1 degree longitude grid size over a 24 hour period. The standard deviation of difference is about 1.5 TEC units. A total of seven GNSS stations were used to generate our TEC map. More quantitative analysis for stations at other geographical locations using different configurations of GNSS stations will be conducted and compared with existing regional network solutions in the paper. Additionally, the paper will analyze position error residuals using the TEC values obtained from the gradient with that of the global TEC map, and with PPP algorithms. The proposed TEC gradient method has the potential to produce high accuracy regional TEC maps for precision positioning applications and for ionospheric monitoring using relatively sparsely located GNSS receivers measurements. The methodology presented in the paper can be easily modified to incorporate other multi-GNSS measurements such as GLONASS, Galileo, and BeiDou. With the increased number of satellite in space, the TEC gradients can be expanded to higher order terms to capture more complicated structures in the ionosphere, further improve the TEC map resolution and precision. References [1] Global Ionosphere Maps[EB/OL]. http://aiuws.unibe.ch/ionosphere, 2012 [2] Giorgiana De Franceschi and Bruno Zolesi. Regional ionospheric mapping and modelling over Antarctica. Annali di Geofisica, 1998, 41:813-818 [3] S. Lejeune, G. Wautelet and R. Warnant. Ionospheric effects on relative positioning within a dense GPS network. GPS Solutions, 2012,16(1):105-116 [4] A.B.O. Jensen, O. Ovstedal and G. Grinde. Development of a Regional Ionosphere Model for Norway. Proceedings of the 2008 National Technical Meeting of the Insitute of Navigation, San Diego, CA , January, 2008, pp. 893-902 [5] Sakai, Takeyasu, Matsunaga, et al, Mitigating Ionospheric Threat Using a Dense Monitoring Network, Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Fort Worth, TX, September 2007, pp. 927-938.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	1875 - 1880
Cite this article:	Wang, C., Morton, Y., "Ionosphere TEC and TEC Gradients Estimation Using a Regional GNSS Network," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 1875-1880.
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