One important ionosphere element that impacts radio signal transmission is the Vertical Total Electron Content (VTEC). Accurate estimation of VTEC is important for diverse applications such as satellite positioning, space weather forecasting, satellite communication. In regions with a sparse network of receivers, especially Nigeria, the spatial and temporal resolutions of the Global Ionospheric Maps (GIM) regularly provided by the International GNSS Service (IGS), Center for Orbit Determination in Europe (CODE), and the International Reference Ionosphere (IRI) are limited. This limits their potential to uncover local ionospheric phenomena in such areas. To address this limitation, we have developed a VTEC model for estimating high temporal-resolution VTEC and Differential Code Bias (DCB) over Nigeria using spherical harmonic expansions with an orthogonal transformation solution. Our novel method makes use of GNSS measurements from the Global Positioning System (GPS) and Global Navigation Satellite System (GLONASS) to precisely estimate VTEC and DCB. GNSS datasets in Receiver Independent EXchange (RINEX), satellite orbit (SP3) and Ionospheric Exchange (IONEX) formats from 2011 across 9 GNSS receivers in the Nigerian Geodetic Network sampled at 30-second intervals were used for this study. For this investigation, code pseudo-range observations were also smoothed using carrier phase observations. To assure data quality, we also carried out several preprocessing procedures utilizing the Melbourne-Wubbena linear and geometry-free linear combinations using an internal ITB-GNSSTEC FORTRAN application based on batch processing and least squares approaches. To validate our model, we compared the estimates with the IGS, CODE, and IRI-2020 models. Results demonstrated strong agreement with the other models with a standard deviation between 2.80 and 6.50 TECU and a correlation coefficient of not less than 0.92 at the evaluation stations. Notably, the new model aligned more closely with CODE and IGS than the IRI model. Also, the new model enabled the detection of local ionospheric VTEC post-sunset enhancement missed by GIM models. Our model also showed a strong positive correlation with the other models for quiet and disturbed days of geomagnetic activity. In Conclusively, this research has developed a high-resolution VTEC method for areas with sparse distribution of GNSS receivers, achieving a temporal resolution of 10 minutes. The ionospheric modeling in areas like Nigeria with sparse GNSS networks has greatly benefited from this research. The approach improves the precision of GNSS-based applications, such as location and navigation, by precisely calculating VTEC and DCBs. It also addresses the issue of sparse observational data in equatorial regions, offering insightful information for atmospheric and geodetic research.
