Real-Time Kinematic Precise Point Positioning (PPP–RTK) is inextricably linked to external ionospheric information. The PPP–RTK performances vary much with the accuracy of ionospheric information, which is derived from different network scales, given different prior variances, and obtained under different disturbed ionospheric conditions. This study investigates the relationships between the PPP–RTK performances, in terms of precision and convergence time, and the accuracy of external ionospheric information. The statistical results show that The Time to First Fix (TTFF) for the PPP–RTK constrained by Global Ionosphere Map (PPP–RTK-GIM) is about 8–10 min, improved by 20%–50% as compared with that for PPP Ambiguity Resolution (PPP-AR) whose TTFF is about 13–16 min. Additionally, the TTFF of PPP–RTK is 4.4 min, 5.2 min, and 6.8 min, respectively, when constrained by the external ionospheric information derived from different network scales, e.g. small-, medium-, and large-scale networks, respectively. To analyze the influences of the optimal prior variances of external ionospheric delay on the PPP–RTK results, the errors of 0.5 Total Electron Content Unit (TECU), 1 TECU, 3 TECU, and 5 TECU are added to the initial ionospheric delays, respectively. The corresponding convergence time of PPP–RTK is less than 1 min, about 3, 5, and 6 min, respectively. After adding the errors, the ionospheric information with a small variance leads to a long convergence time and that with a larger variance leads to the same convergence time as that of PPP-AR. Only when an optimal prior variance is determined for the ionospheric delay in PPP–RTK model, the convergence time for PPP–RTK can be shorten greatly. The impact of Travelling Ionospheric Disturbance (TID) on the PPP–RTK performances is further studied with simulation. It is found that the TIDs increase the errors of ionospheric corrections, thus affecting the convergence time, positioning accuracy, and reliability of PPP–RTK.

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The global navigation satellite system (GNSS) is characterized by continuous and global coverage at low cost, high temporal and spatial resolution, and high accuracy, thus being widely used as a significant tool for global or regional ionospheric modeling and monitoring (

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Large-scale TIDs (LSTIDs) have been widely observed and studied both experimentally and theoretically for decades (

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High-reliable ionospheric prediction information is of great significance for precise positioning and navigation, space weather monitoring, as well as wireless communication (Schunk & Sojka, 1996;Zhang et al., 2022). Many models have been proposed to model the ionosphere and predict its changes. However, the prediction accuracy is limited due to the irregular characteristics and the complicated mechanism of ionospheric variations (Liu et al., 2022;Mcgranaghan et al., 2018). In recent years, the rapidly developed deep learning technique has been steadily applied to ionospheric prediction with an increase in long-term ionospheric observation data (Camporeale, 2019;Ren et al., 2022).Since the mid-1990s, artificial neural networks (ANN), the forerunner of deep learning, provide a new efficient solution for ionospheric modeling and prediction (Joselyn et al., 1993;Oyeyemi et al., 2005). Cander (1998) used different artificial neural networks to simulate and predict the temporal-spatial variations of ionospheric key parameters, such as f0F2 and total electron content (TEC). The prediction results proved the promising prospect of artificial neural networks in ionospheric prediction. Zeng et al. (2002) used Global Positioning System (GPS) occultation data to predict the ionospheric electron density. The results showed that the ANN was an effective

The precise description of the topside ionosphere using an ionospheric empirical model has always been a work in progress. The NeQuick topside model is greatly enhanced by adopting radio occultation data from the FORMOSAT-7/COSMIC-2 constellation. The topside scale height H formulation in the NeQuick model is simplified into a linear combination of an empirically deduced parameter H0 and a gradient parameter g. The two-dimensional grid maps for the H0 and g parameters are generated as a function of the foF2 and hmF2 parameters. Corrected H0 and g values can be interpolated easily from two grid maps, allowing a more accurate description of the topside ionosphere than the original NeQuick model. The improved NeQuick model (namely NeQuick_GRID model) is statistically validated by comparing it to Total Electron Content (TEC) integrated from COSMIC-2 electron density profiles and space-borne TEC derived from onboard Global Navigation Satellite System observations, respectively. The results show that the NeQuick_GRID model can reduce relative errors by 38% approximately when compared to the integrated TEC from COSMIC profiles and by 15% approximately when compared to the space-borne TEC. Furthermore, a long-term statistical analysis during years of both high and low solar activities reveals that grid maps of the scale factor H0 and the gradient parameter g have very similar features, allowing rapid and efficient acquisition of high-precision electron density during different solar activity.