# Comparison of NeQuick G and Klobuchar Model Performances at Single-Frequency User Level +
## 1 Introduction  
The collaborative study presented in this paper was performed under the European Union Agency for Space Programme (EUSPA) Framework Partnership Agreements (GSA/GRANT/04/2016) involving the entities Galileo Reference Centre (GRC) [1], Norwegian Mapping Authority (NMA), Technische Universitat Wien (TUW), and Space Research Centre (SRC) of Polish Academy of Sciences, whose main objectives were to investigate theGNSS performance at different levels. The ionosphere, the ionized part of the Earth's upper atmosphere, is highly dynamic and is influenced by various space weather phenomena. The presence of free electrons can significantly impact radio wave transmission, altering the electromagnetic radio frequency waves [2]. Satellite communication and navigation systems, such as the Galileo and the Global Positioning System (GPS), rely on radio signals transmitted through the ionosphere. However, the ionosphere can cause significant errors in these signals, which can lead to degraded performance and reduced accuracy, especially at the equatorial and high latitudes. To mitigate the effects of the ionosphere on satellite systems for single-frequency (SF) applications, ionospheric models have been developed [3]. Their final scope is to provide accurate estimates of the total electron content (TEC). Two widely used ionospheric models, enabling the ionospheric delay corrections computations for SF users, are the NeQuick G model, developed for Galileo, and the Klobuchar model, developed for GPS. NeQuick G [3] is a three-dimensional and time-dependent ionospheric electron density model based on an empirical climatological representation of the ionosphere, which predicts monthly mean electron density from analytical profiles, depending on solar-activity-related input values: sunspot number or solar flux, month, geographic latitude and longitude, height, and universal time (UT). On the other side, the Klobuchar model [2] is designed to minimise user computational complexity and user computer storage as well as to keep a minimum number of coefficients to transmit on satellite-user links. In this study, the comparison of NeQuick G and Klobuchar models at the SF user level is shown. Three parameters are used to present the results: the TEC accuracy (also called TEC error) defined as the difference between the model TEC obtained by either the NeQuick G or the Klobuchar model over a given station and the reference TEC based on observations from networks of GNSS receivers; the TEC availability characterization defined as the percentage of time when the TEC error is compliant with the specification of the Galileo Single-Frequency Ionosphere Algorithm (NeQuick G model); the Position, Velocity, and Time (PVT) accuracy characterization used to assess the impact of ionospheric disturbances on the accuracy of PVT estimates. The results are presented for a network of stations distributed worldwide. The computation method used for the TEC estimates is different for the networks of stations used by the involved entities GRC, NMA, TUW, and SRC. The results cover the period from 1 January 2019 to 30 June 2022. The comparison of the performance of the two models in the different networks is the key element of this work, providing a better understanding of the model performances. Moreover, this study provides valuable insights into the performance of the NeQuick G and Klobuchar models at the SF user level.