An analytical method for error analysis of GRACE-like missions based on spectral analysis

The aim of this paper is to present an analytical relationship between the power spectral density of GRACE-like mission measurements and the accuracies of the gravity field coefficients mainly from the point of view of theory of signal and system, which indicates the one-to-one correspondence between spherical harmonic error degree variances and frequencies of the measurement noise. In order to establish this relationship, the average power of the errors due to gravitational acceleration difference and the relationship between perturbing forces and range-rate perturbations are derived, based on the orthogonality property of associated Legendre functions and the linear orbit perturbation theory, respectively. This method provides a physical insight into the relation between mission parameters and scientific requirements. By taking GRACE-FO as the object of research, the effects of sensor noises and time variable gravity signals are analyzed. If LRI measurements are applied, a mission goal with a geoid accuracy of 7.4 cm at a spatial resolution of 101 km is reachable, whereas if the KBR measurement error model is applied, a mission goal with a geoid accuracy of 10.2 cm at a spatial resolution of 125 km is reachable. Based on the discussion of the spectral matching of instrument accuracies, an improvement in accuracy of accelerometers is necessary for the match between the range errors and accelerometer noises in the future mission. Temporal aliasing caused by the time variable gravity signals is also discussed by this method.