Monthly gravitational field solutions as spherical harmonic coefficients produced by the GRACE satellite mission require post-processing to reduce the effects of shortwave-length noises and north–south stripe errors. However, the spatial smoothing and de-striping filter commonly used in the post-processing step will either reduce spatial resolution or remove short-wavelength features of geophysical signals, mainly at high latitudes. Here, by using prior covariance information that reflects the spatial and temporal features of the geophysical signals and the correlated errors derived from the synthetic model, together with the covariance matrix of the formal errors for the monthly gravity spherical harmonic coefficients, we apply the Kalman filter to separate the geophysical signal from GRACE Level-2 data and simultaneously to estimate the correlated errors. By increasing the number of observations, the iterative process is applied to update the state vector and covariance in the Kalman filter because the prior information is not accurate. Due to the inevitable truncation error, multiple gridded-gain factors method considering different temporal frequencies has been developed to recover the geophysical signal. The results show that the Kalman filter can reduce the high-frequency noises and correlated errors remarkably. When compared with the commonly used filter, no spatial filter (such as Gaussian filter) is used in the Kalman filter. Therefore, the estimated signal preserves its natural resolution, and more detailed information is retained. It shows good consistency when compared with mascon solutions in both secular trend and annual amplitude.
Spatial Filter Bank in the Spherical Harmonic Domain: Reconstruction and Application
