Multilayer Ionospheric Model Constrained by Physical Prior Based on GNSS Stations

Abstract

The need for accurate modeling of the ionosphere plays an important role in the global navigation satellite system (GNSS) positioning. The traditional multi-layer 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 paper, the data enhancement method by virtual observations is proposed to build the constrained multi-layer VTEC model to capture physical features from empirical ionospheric models. The extraction methods of physical knowledge have been developed by prior VTEC based on principal component analysis and model coefficients based on emulated basis function. The constrained multi-layer modeling has been verified based on simulation and real measurement of GNSS data in Yunnan, China collected from Qianxun Ground-based Augmentation System on November 3, 2021. The receiver DCB error estimated by the multi-layer model with prior constraint is significantly lower than that of the single-layer model and the traditional multi-layer model. The experimental test shows that the constrained multi-layer model achieves the accuracy of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.5 \,\rm {TECU}$</tex-math></inline-formula> for the independent reference station. The dSTEC of the proposed two multi-layer models are significantly lower than those of the single-layer model for low elevation angles, and the RMSE of dSTEC is reduced by 63 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> with the cutoff elevation angle of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{\circ }$</tex-math></inline-formula> . The spatial distribution of the multi-layer VTEC model shows consistency with the tomography model to verify vertical feature capturing capability. Compared with the Un-differenced and Un-combined Precise Point Positioning (UCPPP) without ionospheric constraint, the multi-layer constrained model based on the test data improves the convergence time approximately by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$36.55\%$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$18.78\%$</tex-math></inline-formula> in the horizontal (H), up (U) directions, respectively. These results demonstrate that the proposed multi-layer models not only improve ionospheric delay estimation precision but also can obtain the VTEC distribution capturing the physical characteristics of the ionosphere. The proposed multi-layer models may be valuable for the ionospheric delay modeling of satellite navigation systems in harsh variable ionospheric conditions.