SBAS Ionospheric Modeling with the Quadratic Approach: Reducing the Risks

Hyunho Rho, Richard B. Langley and Atilla Komjathy

Abstract:	In principle, the quadratic approach can portray ionospheric total electron content (TEC) better than the linear approach by introducing the non-linear spatial variation terms into the model. The previous research [Rho et al., 2004] has shown that the most improvement in the quadratic approach is in the improvement of r.m.s. of residuals. This approach was tested in a batch process using data from 48 reference stations in North America. The algorithm ensures that the estimator is free from the main risks, such as uneven distribution of data and even data holes which can lead to spurious spikes and unphysical features in the resulting models. However, we are left with several issues to properly use the quadratic approach in SBAS. First, the quadratic model with a batch process requires significant computational power when more and more GPS stations providing more and more data are used to determine the model parameters at each epoch. Second, since the batch process uses all the collected ionospheric measurements from all the stations in the network, the modeled results are smoothed over the network and are less sensitive to the local ionospheric variations at each station. And third, as long as a limited number of reference stations are used to estimate the ionospheric vertical delays at the specific grid points of an SBAS ionospheric model, there exist some difficulties, such as a limited density of measurements and geometry issues. To help address these issues, we tested two different approaches, the single station approach and the grid approach. The single station approach with the quadratic model can estimate the ionospheric vertical delays using only single station data since we separately estimated the satellite and receiver inter-frequency biases and use them as a set of fixed IFBs in the estimator. The advantage of the single station approach might be that it is more sensitive to the local variation than the grid approach. We also extended our ionospheric modeling technique by combining a grid-based ionospheric modeling approach with the quadratic approach. We have tested the new approach with data from 25 stations of the Continuously Operating Reference Stations (CORS) and International GNSS Service (IGS) networks in the U.S. To see the difference in performance of the extended quadratic approach on ionospherically quiet and storm days, we selected two sample days. On November 20, 2003 (DOY 324), there was a significant geomagnetic disturbance.
Published in:	Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005) September 13 - 16, 2005 Long Beach Convention Center Long Beach, CA
Pages:	723 - 734
Cite this article:	Rho, Hyunho, Langley, Richard B., Komjathy, Atilla, "SBAS Ionospheric Modeling with the Quadratic Approach: Reducing the Risks," Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), Long Beach, CA, September 2005, pp. 723-734.
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