An Enhanced UNB Ionospheric Modeling Technique for SBAS: the Quadratic Approach

Hyunho Rho, Richard B. Langley, Attila Komjathy

Abstract:	Several satellite-based augmentation systems (e.g., WAAS, EGNOS, and CDGPS) have recently started operations and more are planed for the future. With a view towards further improving the accuracy of such systems, the associated ionospheric modeling technique is capturing the attention of the scientific community. As long as the ionosphere is the biggest error source in single-frequency GPS, the accuracy of ionospheric modeling remains a critical issue in satellite-based augmentation systems. In terms of modeling the ionosphere, the current UNB approach uses a bi-linear approximation and so ignores the non-linear spatial variation of the ionosphere over the monitoring stations. Efficiency and an acceptable level of accuracy are the main reasons for using a simplified linear model. However, we are left with the questions: Is the linear model sufficient to explain the temporal and spatial variations of the ionosphere? What are the effects of ignoring the non-linear spatial variations in the ionosphere especially under geomagnetic storm conditions? To provide answers to these questions, we have extended the UNB ionospheric modeling technique from bi-linear to the quadratic form. As the quadratic model is far more sensitive to the distribution of the ionospheric pierce points (IPPs) than the linear model, there are a number of risks in adopting this potentially higher fidelity model. The main risk is associated with the uneven distribution of data and even data holes (although this can be overcome by a threat model which looks at the undersampled and temporal threats) which can lead to spurious spikes and unphysical features in the resulting models. To test our new model, we have mainly used data from the U.S. Continuously Operating Reference Stations (CORS) network and the International GPS Service (IGS) network. With this relatively dense combined network, we have minimized data gaps. A data set spanning one month from October 25 to November 25, 2003 has been used to generate statistics. On October 29, 30, 31 and November 20, 21, 2003, there were significant geomagnetic disturbances. We first examined the effect of “not-monitored satellites” on the estimator. In a global ionospheric model, all the satellites are monitored by a global scale network (all satellites are seen by at least one station at all times). However in a regional ionospheric model, only some of satellites can be seen by the ground network at the given time. We quantified the differences between the global approach and regional approach. On a quiet day, the difference in rms of residuals was about 0.25 TECU and it was 0.5 TECU when the ionosphere was disturbed. We also examined the quantified differences between the two approaches, the quadratic and bi-linear models, using data sets from both quiet days and days when the ionosphere was disturbed. In quiet conditions, the improvements of daily rms of residuals are at about the 1 (maximum 1.5 TECU) TECU level or less. The maximum improvement in rms of residuals happens when the ionosphere is significantly disturbed. The level of improvements is at the 1 to 3 TECU level. We also discuss the advantages and disadvantages of the two approaches that we encountered during the research. For validation purposes and to see if there exist any unphysical or abnormal features in our models, we compared the estimated ionospheric vertical delays from both the bi-linear and quadratic models with those of WAAS. With the quadratic model, there was a better agreement with WAAS at the level of 23cm. However overall peak-to-peak variations of estimated VTECs from both UNB quadratic and bi-linear models are within the uncertainties (one sigma) of WAAS. The presented results could serve as a baseline for further improvements in the GPS-based ionospheric modeling techniques for satellite-based augmentation systems.
Published in:	Proceedings of the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2004) September 21 - 24, 2004 Long Beach Convention Center Long Beach, CA
Pages:	354 - 365
Cite this article:	Rho, Hyunho, Langley, Richard B., Komjathy, Attila, "An Enhanced UNB Ionospheric Modeling Technique for SBAS: the Quadratic Approach," Proceedings of the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2004), Long Beach, CA, September 2004, pp. 354-365.
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