Precise point positioning (PPP) based on the machine learning-based ionospheric tomography

Undifferenced and Uncombined Precise Point Positioning (UPPP) currently stands as a prominent research area, where the integration of high-precision ionospheric products holds the potential to substantially enhance accuracy and convergence performance in UPPP. Presently, the majority of external ionospheric constraints for UPPP rely on Global Ionospheric Maps (GIM). However, the accuracy and resolution of GIM fall short, imposing significant limitations on the positioning performance of UPPP. Consequently, this paper introduces the application of Computerized Ionospheric Tomography based on Machine Learning (CIT-ML) to enhance UPPP performance (PPP-CIT-ML). In this approach, we convert the three-dimensional electron density of CIT-ML into vertical total electron content (VTEC), and then it is compiled into ionospheric grid files essential for UPPP. Simultaneously, the traditional ionospheric tomography methods based on the improved algebraic reconstruction technique (IART) is also employed for UPPP (PPP-CITIART), alongside the ionospheric grid files broadcasted by the Center for Orbit Determination in Europe (CODE) for UPPP (PPP- CODE), where PPP-CIT-IART and PPP-CODE are used as the reference methods to test the performance of PPP-CIT-ML. In Static and Kinematic UPPP, compared to PPP-CODE, PPP-CIT-IART demonstrated average improvements in positioning accuracy and convergence performance by over 10% and 7%, respectively. PPP-CIT-ML showed average improvements in positioning accuracy and convergence performance by over 26% and 28%, respectively. The extrapolated ionospheric electron density (IED) applied to UPPP (ECITML-PPP) and compared with PPP-CODE displayed average improvements in positioning accuracy by over 21% and convergence performance by over 26%. Compared with PPP-CIT-IART, ECIT-ML-PPP displayed average improvements in positioning accuracy and convergence performance by over 6% and 21%, respectively. These findings highlight that ionospheric error correction information obtained through ionospheric tomography significantly enhances the positioning accuracy and convergence performance of UPPP. Moreover, the performance enhancement achieved through machine learning-based ionospheric tomography is more pronounced. This study provides preliminary validation for the feasibility of applying machine learning-based ionospheric tomography results to navigation positioning.