Eliminating Potential Errors Caused by the Thin Shell Assumption: An Extended 3D UNB Ionospheric Modelling Technique

W. Zhang, R.B. Langley, A. Komjathy, S. Banville

Abstract:	Ionospheric modelling plays an important role in improving the accuracies of positioning and navigation, especially for current civil aircraft navigation and mass-market single-frequency users. Mathematical data-driven models are considered to be among the best candidates for real-time single-frequency positioning owing to their real-time applicability and relatively higher accuracy compared to empirical models, such as the GPS broadcast (also known as Klobuchar) and NeQuick models. A good example of a real-time positioning application is satellite-based augmentation systems (SBASs), such as WAAS, EGNOS, and MSAS. Since the ionosphere can be the largest error source in single-frequency positioning, the accuracy of ionospheric modelling is critical in this kind of single-frequency positioning. Several organizations have been routinely providing ionospheric products to correct errors caused by the ionosphere in the form of ionospheric maps, i.e. vertical total electron content (TEC) at grid points (including regional and global products), such as those from WAAS and the International GNSS Service (IGS), with various processing time delays ranging from near real-time to a couple of weeks. Among the earliest works of ionosphere modelling, the UNB Ionospheric Modelling Technique (UNB-IMT) was developed in the mid-1990s. This technique was demonstrated for effectively deriving both regional and global TEC maps. However, most of these models, including the current version of UNB-IMT, approximate the ionosphere using a single thin shell approach with an altitude set at e.g., 350 km, which may introduce additional modelling errors up to several TECU (1 TECU = 1016 electrons/m2), corresponding to scores of metres of measurement delay or advance at the GPS L1 frequency. To overcome any downside of such models, three-dimensional (3D) ionospheric tomographic modelling methods have been proposed and implemented by several groups since the early 2000s. Different from the two-dimensional (2D) single thin shell ionospheric models where the parameter to be estimated is the TEC, the modelled variable in the tomographic model is the electron density function. Therefore, a more complex structure of electron densities (such as that observed during ionospheric storms or in the highly variable equatorial anomaly) may be expected to be revealed by the models. A commonly-accepted modelling approach is to describe the ionospheric horizontal (longitudinal and latitudinal) variability by a spherical harmonic (SH) expansion up to a specific degree and its vertical dimension modelled by empirical orthogonal functions (EOFs). The performance of such modelling approaches has been demonstrated by several research groups. However, SH models are not ideal for capturing local variability in the ionosphere as each basis function of spherical harmonics exists over the entire geographic region of interest, such as the entire globe in the case of global modelling. That is to say, localized measurements will have influence on the estimated state across the whole globe. As alternative approaches, wavelet and finite element (meshes/pixels) models were proposed and implemented to capture the localized information content in the measurements and pass this information on to the end user. On the other hand, the inversion process can occasionally become singular as many of the parameters to be estimated tend to be ineffective and less meaningful. This is especially the case when our goal is to obtain better accuracies with higher order wavelet bases or smaller meshes/pixels. Due to the potential computing and transmitting burden, the two modelling techniques may have more difficulties associated with real-time applications, such as real-time single-frequency positioning, although they have advantages for capturing localized structures in the ionosphere. In this paper, aiming for potential real-time applications of 3D tomographic models, we extend the UNB-IMT from 2D to 3D by modelling the vertical dimension of the ionosphere using EOFs, and compare its performance with the 3D SH approach. The 3D UNB-IMT was demonstrated to work with various network sizes: regional, baseline by baseline, and even single standalone stations. Therefore, it is expected that this technique will help in capturing localized ionospheric structures above small regional networks or above a single standalone station compared to the 3D SH approach. Additional benefits may be expected for disturbed ionospheric conditions. For assessing the two modelling techniques, a small regional network was chosen to perform network and station-by-station processes. The performance of both methods with the two processing scenarios is compared by analyzing the post-fit residuals and TEC of the state estimation process, as well as the repeatability of estimates of differential code biases (DCBs) for both quiet and disturbed ionospheric conditions.
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:	2447 - 2462
Cite this article:	Zhang, W., Langley, R.B., Komjathy, A., Banville, S., "Eliminating Potential Errors Caused by the Thin Shell Assumption: An Extended 3D UNB Ionospheric Modelling Technique," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 2447-2462.
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