Impacts of Interpolation Formula, Correlation Coefficient and Sampling Interval on the Accuracy of Grace Follow‐on Intersatellite Range‐Acceleration

Abstract

AbstractThis paper presents our studies of the impacts of the interpolation formula, correlation coefficient and sampling interval on the accuracies of the GRACE Follow‐On intersatellite range‐acceleration using the Intersatellite Range‐Acceleration Method (IRAM). The results of numerical simulation show that the interpolation accuracy can be efficiently improved with appropriately increasing the number of the interpolation points from the numerical differential formula. The interpolation error of intersatellite range‐acceleration is 4.401×10–13 m·s–2 using the nine‐point Newton's interpolation formula, and errors are enhanced 1.192 times, 6.912 times and 274.029 times based on the seven‐point, five‐point, three‐point interpolation formulas, respectively. The error of intersatellite range‐acceleration is observably decreased with the proper increase of the correlation coefficients. The variance of intersatellite range‐acceleration is 3.777×10–24 m2·s–4 using a correlation coefficient of 0.99, and the variances are respectively increased 9.780 times, 22.404 times, 26.217 times and 26.820 times based on the correlation coefficients 0.90, 0.70, 0.50 and 0.00, respectively. With increasing sampling intervals, the variances of intersatellite range‐acceleration gradually decrease, while the spatial resolution of satellite observations will be simultaneously reduced. Therefore, the accuracy of the Earth's gravitational field can be improved by a preferred selection of sampling intervals. Finally, the Earth's gravitational field from GRACE Follow‐On complete up to degree and order 120 is accurately and rapidly recovered using the nine‐point Newton's interpolation formula, correlation coefficients (0.85 in intersatellite range and intersatellite range‐rate, 0.95 in orbital position and orbital velocity, and 0.90 in non‐conservative force) and a sampling interval of 10 s based on the Pre‐Conditioned Conjugate‐Gradient (PCCG) approach, and the cumulative geoid height error is 4.602×10–4 m at degree 120.