An Improved Approximate Calculation Method of Earth Gravity Suitable for Space-Borne GPS Real-Time Onboard Orbit Determination

We present an improved gravity acceleration approximation function (IGAAF) suitable for space-borne GPS real-time onboard orbit determination. The test of analyzing IGAAF's performances demonstrates that IGAAF maintains the truncation error in the magnitude of 1×10²-1×10³ nm/s² only with the computational burden less than a 45×45 spherical model and a 200-320 kB RAM requirement for fitting coefficients, and that its accuracy is slightly superior to the spherical models with optimal degree and order for autonomous orbit determination (105×105 model for GOCE, 85×85 for CHAMP, 65×65 for GRACE-A and 55×55 for ZY3 and TerraSAR-X). Compared to the spherical model, IGAAF does not decrease the orbit accuracies. The IGAAF method attains a good trade-off between computational efficiency and coefficient capacity without decreasing the orbit accuracy, so it is of strong engineering value for space-borne GPS autonomous orbit determination.