Comparative Analysis of Models for Signal Delays in Ionosphere

E. A. Roshchina, A. V. Saltsberg

Transactions of IAA RAS, issue 75, 12–20 (2025)

DOI: 10.32876/ApplAstron.75.12-20

Keywords: GNSS, GLONASS, ionospheric delay, vertical electron content, pseudorange

Abstract

The paper compares two approaches to estimating ionospheric delays used in GLONASS and GPS systems, and evaluates the impact of these modelson pseudorange determination errors. While the considered models reduce ionospheric delay effects, during periods of high solar activity or in certain regions, the influence of ionospheric delays on signal propagation remains a primary source of pseudorange errors for users. The GLONASS system employs a model with harmonic approximation, accounting for diurnal and semi-diurnal variations in electron density. In contrast, the Klobuchar model used in GPS is based on a simplified empirical approach, describing diurnal variations with a cosine function. Models used in BeiDou and Galileo were not analyzed in this study. BeiDou's model is a modified version of the Klobuchar model, making it methodologically similar to GPS. The Galileo model, NeQuick, is structurally akin to the GLONASS approach in its parameterization and in describing global vertical electron content variations, with particular emphasis on regional features and harmonic components. This similarity allows us to categorize Galileo's and GLONASS's models within the same class. The model values of vertical electron content for eight ground-based sites were obtained using navigation messages data. Also, the values were derived from ionospheric maps provided by the Information and Analytical Center for Coordinate-Time and Navigation Support (JSC “TsNIIMash”). These values were compared with those calculated from the interfrequency difference of pseudorange code observations using GLONASS. The comparison revealed discrepancies between the model-derived vertical electron content values (GLONASS/GPS), actual data (inter-frequency code measurements), and vertical electron content maps during daily maxima of electron content. These discrepancies correlate with the solar activity index and geographic latitude for GLONASS. The analysis also identified inaccuracies in the GLONASS model that could potentially be corrected by revising certain formulas. This research emphasizes the need for further improvements in ionospheric modeling to enhance navigation accuracy, especially in the context of advancing autonomous vehicle technologies and high-precision positioning systems.

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