برآورد دقت ضريب مدل ژيوپتانسيل ماهواره ي GRACE

Accuracy Estimation of GRACE Satellite Geopotential Model

Least Squares Method is a mostly used method for estimating geopotential coefficients. From computational point of view, estimation of the unknown parameters up to degree and order 120 is a highly demanding task due to the sheer number of the unknowns. Direct inversion of the normal matrix of such a big linear system is impossible in a desktop computer. That is why an iterative method must be used for this purpose. On the other hand, an infamous disadvantage of an iterative estimation is that no variance-covariance matrix exists, because the iterative inversion solves the least-squares system without assembling the normal matrix. The high degree aliasing effect is another serious concern for achieving reliable accuracy information of the unknown parameters. In this paper, for the complete least-squares solution with accuracy information, through the simultaneous solution to both problems, unavailable direct inverse of the normal matrix and the aliasing effect, the diagonal elements of the covariance matrix have been computed. The method has been applied in a close-loop simulation to the Gravity Recovery and Climate Experiment (GRACE) data and the achieved results show validity of the proposed method.