Abstract: The global surface mass variation obtained by using the unconstrained gravity recovery and climate experiment (GRACE) Level-2 spherical harmonic coefficient inversion has obvious north-south striping noise, which seriously affects the accuracy of regional surface mass anomaly estimation. The decorrelation and denoising kernel (DDK) filter introduced signal covariance matrix and regularization factor to deal with spherical harmonic coefficients to obtain spatial constrained solutions in order to better weaken striping errors and retain more real geophysical signals. DDK filtering ignores the correlation of spherical harmonic coefficients in time, and uses the state space (SS) model to represent the relation between spherical harmonic coefficients in adjacent months, and then realizes noise reduction through Kalman filtering, which is the state space DDK filtering method (SS-DDK). In the SS-DDK method proposed in this paper, the state vector only contains spherical harmonic coefficients, and the covariance matrix reflecting the strip error statistics is used as the observation noise covariance matrix in the state space model. The power law model is used to design the process noise covariance matrix, and the variance component factors are solved by iterative method. Finally, the RTS smooth solution was output instead of the Kalman filter solution as the final data processing result. The results show that there is no significant striping error in SS-DDK results worldwide. The root mean square deviation (RMSD) of the abnormal quality difference between each constraint solution and mascon solution was calculated. The RMSD of SS-DDK is 10.36 cm, which is smaller than that of any DDK filter. By comparing the equivalent water column height, annual amplitude and RMSD of all constraint solutions in the five regions for 135 months, it is found that in Greenland, the signal distortion caused by SS-DDK is less, only 49.8 cm. In other regions, SS-DDK's striping and retention capabilities are somewhat similar to those of DDK3—5 filtering, and superior to all DDK filtering in some time periods. An uncertainty analysis of the estimation results shows that the global uncertainty size of the SS-DDK solution is 2.20 cm, which is between DDK2 and DDK3 in the selected regions. From the point of view of geoid degree error, the noise level of SS-DDK solution is lower than that of DDK4—8, and the signal retention ability is comparable to DDK2—3. The addition of simulation experiments further demonstrates the good performance of SS-DDK in terms of de-striping and signal retention.

Key words: GRACE, strip errors, state space model, RTS smoothing, power law model