Assimilation of the total electron content obtained from GNSS to a model of the ionosphere using a hierarchical Bayesian network

Ionospheric data assimilation aims to address the uneven spatiotemporal distribution of observational data and errors in numerical models. This paper proposes an ionospheric data assimilation model using the hierarchical Bayesian network (HBN) algorithm. We use the International Reference Ionosphere (IRI) 2016 as a background model. The HBN method assimilates global navigation satellite system (GNSS) observational data from approximately 260 stations within the Crustal Movement Observation Network of China (CMONOC). For this analysis, we use the total electron content (TEC) data from the Center for Orbit Determination in Europe (CODE) and BeiDou Navigation Satellite System (BDS) geostationary earth orbit (GEO) experiments. We evaluate the HBN assimilation effect through single-frequency precise point positioning (PPP). The results demonstrate that the HBN algorithm closely aligns with the BDS GEO TEC, regardless of geomagnetic conditions. Statistical results show that, with BDS GEO TEC data as the ground truth reference, the HBN model improves the correlation coefficient by approximately 14% and reduces the root mean square error (RMSE) by around 33% compared to the IRI model. The assimilation effect is significantly superior to that of the Kalman filter. Additionally, the HBN-based PPP method demonstrates slightly improved GNSS positioning accuracy compared to CODE-based PPP, with a reduction in RMSE observed under both geomagnetically disturbed and quiet conditions. Thus, the HBN method is effective for ionospheric data assimilation.