Multilayer Ionospheric Model Constrained by Physical Prior Based on GNSS Stations

The need for accurate modeling of the ionosphere plays an important role in the global navigation satellite system (GNSS) positioning. The traditional multilayer VTEC model without prior has been used for modeling the ionospheric delay error. However, it is assumed that the electron density of the ionosphere is compressed into multiple thin layers at fixed heights in the lack of capturing ionospheric physics. In this article, the data enhancement method by virtual observations is proposed to build the constrained multilayer VTEC model to capture physical features from empirical ionospheric models. The extraction methods of physical knowledge have been developed by prior VTEC based on the principal component analysis and model coefficients based on the EBF. The constrained multilayer modeling has been verified based on simulation and real measurement of GNSS data in Yunnan, China, collected from Ground-based GNSS stations by Qianxun on November 3, 2021. The receiver DCB error estimated by the multilayer model with prior constraint is significantly lower than that of the single-layer model and the traditional multilayer model. The experimental test shows that the constrained multilayer model achieves the accuracy of
$0.5 \,\rm {TECU}$
for the independent reference station. The dSTEC of the proposed two multilayer models are significantly lower than those of the single-layer model for low elevation angles, and the RMSE of dSTEC is reduced by 63
$\%$
with the cutoff elevation angle of
$10^{\circ }$
. The spatial distribution of the multilayer VTEC model shows consistency with the tomography model to verify vertical feature-capturing capability. Compared with the undifferenced and uncombined precise point positioning without ionospheric constraint, the multilayer-constrained model based on the test data improves the convergence time approximately by 36.55% and 18.78% in the horizontal (H) and up (U) directions, respectively. These results demonstrate that the proposed multilayer models not only improve ionospheric delay estimation precision but also can obtain the VTEC distribution capturing the physical characteristics of the ionosphere. The proposed multilayer models may be valuable for the ionospheric delay modeling of satellite navigation systems under harsh variable ionospheric conditions.