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The tensor of gravitation is traceless as the gravitational field of the Earth is harmonic outside the Earth’s surface. Therefore, summation of the 2nd-order horizontal derivatives on its diagonal components should be equal to the radial one but with the opposite sign. The gravity field can be recovered locally from either of them, or even their combination. Here, we use the in-orbit diagonal components of the gravitational tensor measured by the gravity field and steady state ocean circulation explorer (GOCE) mission for recovering gravity anomaly with a resolution of 1°×1° at sea level in Ethiopia. In order to solve the system of equations, derived after discretisation of integral equations, the Tikhonov regularisation is applied and the bias of this regularisation is estimated and removed from the estimated gravity anomalies. The errors of the anomalies are estimated and their significance of recovery from these diagonal components is investigated. Statistically, the difference between the recovered anomalies from each scenario is not significant comparing to their errors. However, their joint inversion of the diagonal components improved the solution by about 1 mGal. Furthermore, the inversion processes are better stabilised when using errors of the input data compared with its exclusion, but at the penalty of degradation in accuracy of the estimates.

The establishment of the Continuously Operating Reference Stations (CORS) network as a national positioning service enables high precision in surveying, mapping, and navigation applications, thanks to developments in Global Navigation Satellite System (GNSS) technology. In this study, we determined the best CORS network site in Ethiopia by taking into account aspects such as accessibility, internet coverage, and network geometry. We chose an excellent location for Ethiopia out of 228 options based on these parameters. The CORS network's performance was validated by using a network of triangles as a reference station and a virtual reference station (VRS) within the triangles. To validate the performance of the selected networks, simultaneous GNSS observations are conducted on the reference and VRS stations. The idea of VRS generated GNSS observation data utilizing reference station observation data and the location of VRS station using Wav2 Software. For observations based on genuine and created data, we compared the precise coordinates of the VRS station.The comparison showed a standard deviation of 0.65 cm and 2.7 cm in the horizontal and up directions. Therefore, this CORS network design can be used for different applications with 3D accuracy less than 3 cm.