Research on Accelerating Single-Frequency Precise Point Positioning Convergence with Atmospheric Constraint  
[PERSON]  
1 NASG Key Laboratory of Land Environment and Disaster Monitoring, China University of Mining and Technology, Xuzhou 221116, China; [EMAIL_ADDRESS] (R.W. ); [EMAIL_ADDRESS] (Z.L. ); [EMAIL_ADDRESS] (L.Z. ); [EMAIL_ADDRESS] (Y.W). 2 School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China
* 2  
[PERSON]  
1 NASG Key Laboratory of Land Environment and Disaster Monitoring, China University of Mining and Technology, Xuzhou 221116, China; [EMAIL_ADDRESS] (R.W. ); [EMAIL_ADDRESS] (Z.L. ); [EMAIL_ADDRESS] (L.Z. ); [EMAIL_ADDRESS] (Y.W). 2 School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China
* 3  
College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, China; [EMAIL_ADDRESS] *  
Correspondence: [EMAIL_ADDRESS] (J.G. ); [EMAIL_ADDRESS] (N.Z. ); Tel. : +86-135-0521-8387 (J.G. ); +86-159-5216-7986 (N.Z.) 2019; 2020;  
for instance, determines the precise orbit, surface ice flow speed, as well as positioning, navigation and timing (PNT) applications [2; 3; 4]. The traditional PPP models are based on Ionosphere-Free (IF) combinations with dual-frequency raw phase and code observations for the removal of the first-order effect of ionospheric refraction [5]. However, the second- and third-order ionospheric effects still exist and they may cause measurements errors of sub-centimeters in GPS [6; 7]. Therefore, traditional PPP technology based on IF combinations cannot obtain ionospheric information, and the ionospheric error is not completely eliminated. In the last few years, PPP used raw observations has received an increasing amount of research attention because of its several advantages as compared to traditional IF PPP, particularly the development of new multi-frequency GNSS [8]. The ionosphere refers to the atmospheric space starting at 60 km above the ground and extending to the magnetosphere. The Global Navigation Satellite System (GNSS) signal will generate ionospheric delay after passing through the ionosphere. A large number of models are currently being used to describe the delay that the ionosphere produces for electromagnetic signals propagating from satellites to receivers. If the delay is not corrected, it can have an important impact on the positioning accuracy of GNSS [9], especially for single-frequency PPP (SF PPP). [PERSON] et al. proposed an improved method in which the deterministic representation is further refined by a stochastic process for each satellite with an empirical model for its power density [10]. The results of this method show that the single- and dual-frequency PPP exhibited enhanced convergence time, and the positioning accuracy of SF data is only improved by 25% [11]. [PERSON] et al. [12] developed an SF PPP model, and the improved model uses between-satellite-single-difference quasi-phase constrained GNSS observations. The GROup and PHase Ionospheric Correction (GRAPHIC) method uses an SF code and carrier phase data to form an IF combined observation [13]. The positioning accuracy can reach several centimeters based on the GRAPHIC method, but the method requires two hours of convergence time [14]. The International GNSS Service (IGS) Ionosphere Working Group (IWG) was created in 1998. Several analysis centers (CODE (Center for Orbit Determination in Europe), ESA (European Space Agency), JPL (Jet Propulsion Laboratory), UPC (Universitat Politecnica de Catalunya), CAS (Chinese Academy of Sciences), and WHU (Wuhan University)) produce and release the post-processed Global Ionospheric Map (GIM) products, where the format is IONosphere EXchange (IONEX) [15; 16].