Mitigation of Ionospheric Mapping Function Error

M.M. Hoque, N. Jakowski

Abstract:	Ionospheric delay is currently considered as a major error source for satellite based navigation systems. The operational standards set by the International Civil Aviation Organization (ICAO) for Wide Area Differential GPS (WADGPS) ensure Space Based Augmentation System (SBAS) users an ionospheric delay correction in addition to satellite clock and orbit corrections. In the current standard, the SBAS broadcasts vertical ionospheric delays in meters at the ionospheric grid points (IGP) located at every five degrees of latitude and longitude. The SBAS user receivers convert them to the slant delay using the so called obliquity factor derived under an assumption of the thin-shell ionosphere at a fixed shell height of 350 km. Although the ionospheric correction is available for all broadcast IGPs, the user does bilinear interpolation between IGPs those surround the ionospheric piercing point (IPP) at the thin-shell height. In the German Aerospace Center (DLR), we recently developed a new mapping function approach to mitigate the vertical to slant ionospheric delay conversion error. Simulation studies using the three dimensional NeQuick model [Nava et al., 2008] show that our approach significantly reduces the slant ionospheric delay differences between the true and mapped values. While the ionospheric shell height is fixed at a certain value, the thin-shell mapping function is solely dependent on the ray path elevation angle. It ignores the vertical structure of the ionosphere as well as horizontal gradients of the ionosphere. It gives the same ionospheric correction for all ray paths those have a collocated ionospheric pierce point regardless ray paths azimuth angles. Komjathy et al. [2004] investigated the errors introduced by the thin-shell mapping function during October 2003 ionospheric storm event. They found the difference between two nearly collocated vertical estimates due to mapping function error as large as 10 meters during October 2003 storm. By varying the ionospheric shell height instead of fixing it at 350 km, the performance of the thin-shell model may be improved [Sakai et al., 2009]. The shell height practically depends on the height of the peak ionospheric electron density which has typical diurnal variation of low values during daytime and high values during nighttime. However, the main drawback of such an approach is that the SBAS must broadcast the shell height in addition to the contents of the current message to reflect the actual peak height. Another ionosphere modeling approach called multi-layer shell was studied by Sakai et al. [2009]. In this approach, multiple layers of the thin-shell are defined at different fixed heights which share the vertical ionospheric delay. Sakai et al. [2009] found that the root mean squared (RMS) residual of a double-layer model is roughly half of a single-layer model while a triple-layer model reduces the RMS residual further. In such an approach, each IGP broadcast must include multiple (e.g., 2/3) set of vertical ionospheric delays. We developed a multi-layer mapping function approach for vertical to slant ionospheric delay conversion. The advantage of our method is that the SBAS does not require broadcasting additional ionospheric information. To compare the performance of our approach with the thin-shell approach we have selected a number of IPPs distributed over the globe. The IPP height is fixed at 350 km above the earth’s surface. Numerous user positions surrounding each IPP are obtained varying the ground-IPP elevation and azimuth angles. Now using the NeQuick model [Nava et al., 2008] we have calculated vertical total electron content (TEC) at each IPP as well as slant TECs (called STEC true) piercing the IPP at different elevation and azimuth angles. The simulations are done for daytime and nighttime hours considering low and high solar activity levels. Additionally, we have computed global vertical TEC maps by the NeQuick model at different local time and solar activity levels. Again the slant TECs are calculated by the thin-shell model and also by our approach using the NeQuick global TEC map. The computed slant TECs are called the STEC mapped. The differences between the STEC true and STEC mapped are computed for both the thin-shell and our approach. Then we computed histograms of STEC differences at different elevation angles for the thin-shell approach and our approach. Each histogram includes data points from all considered IPPs of all local time hours. For statistical comparisons we computed the mean, standard deviation (STD), RMS and maximum (MAX) estimates of STEC differences for each histogram. We have found that at low elevation angles, e.g., 5° and 20°, the benefit of using our approach is very significant in comparison to the thin-shell approach. Using our approach instead of the thin-shell approach we can reduce the mean, STD, RMS and MAX values by more than 50% during high solar activity time as well as low solar activity time. By mitigating the mapping function error the SBAS may reduce broadcast grid ionosphere vertical errors (GIVEs) and thus may improve the availability of its navigation services. References: Komjathy A., L. Sparks, A. J. Mannucci, A. Coster (2004) The Ionospheric Impact of the October 2003 Storm Event on WAAS, 17th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS, Long Beach, California, September 21-24, 2004. Nava B., P. Coisson, S. M. Radicella (2008) A new version of the NeQuick ionosphere electron density model, JASTP, 70(15), 1856-1862, doi:10.1016/j.jastp.2008.01.015 Sakai T., T. Yoshihara, S. Saito, K. Matsunaga and K. Hoshinoo, T. Walter (2009) Modeling Vertical Structure of Ionosphere for SBAS, 22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, September 22-25
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:	1848 - 1855
Cite this article:	Hoque, M.M., Jakowski, N., "Mitigation of Ionospheric Mapping Function Error," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 1848-1855.
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