Prediction of Regional Ionospheric Delays with Spherical Cap Harmonic Analysis and Vector Auto-Regressive Models.

M. Ohashi, K. Nishimoto, T. Sakai, Y. Kubo, S. Sugimoto

Abstract:	In this paper, we present Japanese regional ionospheric delay models and show a prediction method of the ionospheric delay. The ionospheric delay models derived in this paper are based on the SCHA (Spherical Cap Harmonic Analysis). By using the SCHA ionospheric models, we investigate to the ionospheric delay prediction and the prediction errors are examined through the experiments by using GPS observation data obtained from GEONET (Gnss Earth Observation NETwork) of the GSI (Geospatial Information Authority of Japan). It is well known that the ionospheric delay is one of the dominant error sources in GNSS (Global Navigation Satellite System) positioning. Thus, high positioning accuracy requires accurate correction of ionospheric delay. Moreover, real time positioning require 2 to 24 hours ahead prediction of ionospheric delay. Especially, the regional ionospheric model and prediction have been paid much attention with recent development of regional satellite systems in the world. The methods to model the ionospheric delays based on regional VTEC (Vertical Total Electron Content) estimation method applied by GR (GNSS Regressive) model [1-3], have been presented by the authors[4-6]. In [5,6], the SCHA as well as the SHF are applied to model the regional VTEC distributions. The regional ionosphere is assumed as a part of sphere, and thus it is considered that SCHA is more appropriate to the regional ionospheric model than SHF. In the experiments of [5,6], the ionospheric delays (or advances) over Japan were modeled and evaluated by the measurement data obtained from GEONET, and it was shown that the SCHA model has a high ability to model the regional VTEC. In this paper, the prediction methods of regional VTEC are motivated and proposed based on the method in [6]. In the method in [6], the coefficients of SCHA (hereinafter referred to as SCHA coefficients) are estimated to model the ionospheric VTEC and the ionospheric VTEC at arbitrary point is calculated from the estimated SCHA coefficients. Thus, predicting the SCHA coefficients, we can model the prediction of regional ionospheric VTEC. In this paper, the statistical properties of the SCHA coefficients are focused on. By using the method in [6], the estimated SCHA coefficients data are maintained for several years are stored to analyze their statistical characteristics. In the experiments, GPS data obtained from over 30 GEONET stations are analyzed, and the coefficients from the SCHA model are obtained with time resolution of 2 hours as same as GIM (Global Ionosphere Maps) provided by IGS (International GNSS Service) to compare proposed (SCHA) model with GIM. Statistical properties of time-series data with 2 hours sampling interval for each SCHA coefficient are analyzed. We show that these time series data have strong correlation for 24 hours. Therefore we attempt to model these time series data for each SCHA coefficient by the 12 dimensional Vector (i.e. one day data) Auto-Regressive (VAR) model. Once we estimate the AR coefficient matrices by the least square method for one year's SCHA coefficient data, we can predict the one-step ahead prediction which means 2 to 24 hours ahead prediction of each SCHA coefficient. Finally, by collecting all predicted SCHA coefficients for each SCHA coefficients in the same day, we can predict the SCHA coefficients for one day which provide 2 to 24 hours ahead predicted VTEC values. In the experiments, the SCHA coefficients of the next day are predicted and compared with those obtained from the original SCHA model, final and prediction products of GIMs provided by IGS and CODE (Center for Orbit Determination in Europe). The positioning accuracy of PPP (Precise Point Positioning) applied by the predicted ionosphere correction information are also evaluated. As a result, the predicted VTEC values are similar to actual VTEC values and the accurate positioning results are obtained. Therefore, we can consider that the proposed method can provide good ionospheric prediction in the regional area such as the sky over Japan. References: [1] S. Sugimoto and Y. Kubo: GNSS Regressive Models and Precise Point Positioning, Proc. of 36th ISCIE Int. Symp. on Stochastic Systems Theory and Its Applications, pp. 159-164, Hatoyama, Saitama, Japan, Nov. (2004). [2] Y. Kubo, S. Kitao, S. Fujita and S. Sugimoto: A New RTK Algorithm for Carrier-Phase-Based Precise Point Positioning Based on GNSS Regression Models, Proc. ION GNSS 2005, pp. 1492-1499, Long Beach, CA (2005). [3] S. Sugimoto and Y. Kubo: Unified Methods of Point and Relative Positioning Based on GNSS Regression Equations, Proc. ION-GNSS 2006, pp. 345-358, Fort Worth, Texas (2006) . [4] S. Sugimoto, Y. Kubo, S. Fujita, T. Imamura and T. Kazuno: Ionospheric Estimation over Japan Based on GNSS Regressive Models and GEONET Data, ION GNSS 2007, pp. 2346-2356, Sept. (2007). [5] S. Otsuki, M. Kamimura, M. Ohashi, Y. Kubo and S. Sugimoto: Local Models for Ionospheric VTEC Estimation Based on GR Models and Spherical Cap Harmonic Analysis, Journal of Aeronautics, Astronautics and Aviation, Vol. 43, No. 1, pp. 1-7 (2011). [6] M. Ohashi, T. Hattori, Y. Kubo and S. Sueo: Multi-Layer Ionospheric VTEC Estimation for GNSS Positioning, Transactions of The Institute of Systems, Control and Information Engineers, Vol. 26, No. 1, pp. 16-24 (2013).
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:	1840 - 1847
Cite this article:	Ohashi, M., Nishimoto, K., Sakai, T., Kubo, Y., Sugimoto, S., "Prediction of Regional Ionospheric Delays with Spherical Cap Harmonic Analysis and Vector Auto-Regressive Models.," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 1840-1847.
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