IRG2016: RBF-based regional geoid model of Iran

Abstract

The aim of this research is the optimal determination of the regional geoid model of Iran based on radial basis functions (RBFs). In this case, the type and number of RBFs, their horizontal positions, depths, and unknown coefficients must be properly determined. The quality of calculations strongly depends on the correct choice of these unknown parameters. Given the precise geocentric position of any point on the Earth’s surface with the beginning of the global navigation satellite system (GNSS), the surface gravity disturbances were used to calculate the height anomaly according to Molodensky’s theory. The residual surface gravity disturbances derived by subtracting the global gravitational model EIGEN-6C4 up to degree and order 360 were applied to determine the unknown RBF parameters using the stabilized orthogonal matching pursuit (SOMP) algorithm. Based on this iterative sparse approach, non-zero components of unknown RBF parameters having the maximum recoverable energy for the desired signal were found at each iteration. The SOMP algorithm was applied for optimal determination of the proper basis functions since each unknown RBF coefficient is related to a specific basis function. Only the RBFs representing the best solution to the problem were selected at each iteration, then several new RBFs were added at suitable positions to enhance the calculation result. The new RBF-based regional geoid model entitled IRG2016 was calculated by applying the geoid-to-quasigeoid corrections to the height anomaly. The IRG2016 was fitted to 1288 GNSS/levelling control points over Iran, by applying the polynomial corrector surface. Relying on this new strategy, the calculated height reference surface shows an RMS value of approximately 0.23 m for the difference in geoidal height at the independent control points, which is comparable with the last Stokes-based geoid model.