Nadir-Dependent GNSS Code Biases and Their Effect on 2D and 3D Ionosphere Modeling

Abstract

Recent publications have shown that group delay variations are present in the code observables of the BeiDou system, as well as to a lesser degree in the code observables of the global positioning system (GPS). These variations could potentially affect precise point positioning, integer ambiguity resolution by the Hatch-Melbourne-Wübbena linear combination, and total electron content estimation for ionosphere modeling from global navigation satellite system (GNSS) observations. The latter is an important characteristic of the ionosphere and a prerequisite in some applications of precise positioning. By analyzing the residuals from total electron content estimation, the existence of group delay variations was confirmed by a method independent of the methods previously used. It also provides knowledge of the effects of group delay variations on ionosphere modeling. These biases were confirmed both for two-dimensional ionosphere modeling by the thin shell model, as well as for three-dimensional ionosphere modeling using tomographic inversion. BeiDou group delay variations were prominent and consistent in the residuals for both the two-dimensional and three-dimensional case of ionosphere modeling, while GPS group delay variations were smaller and could not be confirmed due to the accuracy limitations of the ionospheric models. Group delay variations were, to a larger extent, absorbed by the ionospheric model when three-dimensional ionospheric tomography was performed in comparison with two-dimensional modeling.computerized ionospheric tomography (CIT) [2][3][4], techniques that were inspired by and have emerged from computerized tomography (CT) for medical applications [5].GNSS hardware biases [6], and especially biases in the code observations, are well-known to affect the estimation of TEC from GNSS observations [7][8][9]. These biases, referred to as differential code biases (DCBs), are regarded as constant offsets between code observations associated with two signals transmitted between the same satellite and receiver. Thereby, an offset exists in addition to the expected offset due to different ionospheric influence caused by the difference in carrier frequencies. However, even though these biases have been assumed to be constant, recent findings by Hauschild et al. [10], Wanninger and Beer [11], and Wanninger et al. [12] show that the code biases also have a nadir-dependent component, with the largest effects shown for BeiDou [11], but with measurable effects also shown for other GNSSs [12]. These varying biases of the code observables are also referred to as group delay variations (GDV).Previous studies by Wanninger and Beer [11] and Wanninger, Sumaya, and Beer [12] have shown that nadir-dependent GDV affect precise point positioning (PPP) based on the single frequency ionosphere-free combination, wide-lane ambiguity fixing based on the Hatch-Melbourne-Wübbena linear combination [13][14][15], as well as TEC estimation of the ionosphere. The latter is an important characteristic of the ionosphere and is necess...

A sequential calibration approach based on the ensemble Kalman filter (C-EnKF) for forecasting total electron content (TEC)

“…As our reference, the SPP coordinates, whose ionosphere effect was corrected by the final IONEX TEC products are considered as reference. This is chosen following the recommendation of previous studies who found the IONEX TEC to be well suited for the SPP experiments (Rovira-Garcia et al, 2020;Rovira-Garcia et al, 2015;Liu, 2016;Håkansson, 2020). This means that each SPP coordinates of other four scenarios that are closer to the reference (smaller RMSE) can be considered as the desired approach.…”