Evaluation of ionospheric-constrained single-frequency PPP enhanced with an improved stochastic model

Ionospheric delay is the most important environmental factor affecting the positioning performance of single-frequency precise point positioning (SF-PPP). If external ionospheric information is introduced and the weight of ionospheric pseudo-observation is reasonably set, positioning performance can be improved. In this paper, the stochastic model of ionospheric-constrained (IC) SF-PPP, as well as the positioning performances of ionospheric-unconstrained (IU) SF-PPP, ionospheric-free (IF) SF-PPP and IC SF-PPP models were studied. Multi-Global Navigation Satellite System (GNSS) observations of 42 stations from the Multi-GNSS Experiment (MGEX) for 7 days were processed. Firstly, the four classical stochastic models of IC SF-PPP were optimized based on the posterior residual correction (PRC) method. The results show that the PRC method has the highest positioning accuracy improvement (42.4%, 51%, and 56.1%) in the east, north, and up (E, N, U) directions on the IC model. The positioning accuracy results of the IC SF-PPP model using the optimal stochastic model in the E, N, and U directions are 59.8, 42.1 and 31.2% higher than those of the IU SF-PPP model for a one-day period. Second, the short-term positioning performances of three SF-PPP models were compared. The experiments show that the IU SF-PPP model has higher positioning accuracy than the IF model, but the convergence performance is opposite. The IC model has the best positioning performance, especially in dynamic mode. In addition, the short-term positioning performance of IC model in E and N directions is slightly changed when adding multi-GNSS observations and does not differ much in static and dynamic modes. Therefore, IC model using the improved stochastic model is the most cost-effective model for dynamic single-system users in SF-PPP.