Design of Strictly Repeat Ground-Track Orbit Under J4 Perturbation Based on Newton's Iteration Method with Adaptive Correction Step Size

In order to solve the problem of Differential Interferometric Synthetic Aperture Radar(D-InSAR) satellite precision repeat ground-track orbit design in complex spatial ingestion environment, this paper proposes a strictly repeat ground-track orbit method based on a Newton iteration method with adaptive correction step size in view of the slow convergence speed and long solution time of the traditional fixed step size Newton iteration method. Firstly, the model of the repeat ground-track orbit under the J2 perturbation is established and the initial values of the orbit elements of the sun-synchronous strictly repeat ground-track orbit are designed by analytical method. Secondly, based on the Propagator module of STK, a mathematical model of the orbit semi-long axis, the orbit inclination and the difference in latitude and longitude of nadir points before and after the revisit period was established. Thirdly, the traditional fixed-step Newton iteration method requires a high step size setting, which can lead to slow convergence and local optimum solutions if the step size is not selected appropriately. Therefore, adaptive step size is introduced to improve the Newton iteration method and enable it to better approximate the optimum solution by calculating an appropriate correction step size based on the current gradient information in each iteration. Finally, orbit elements of the strictly repeat ground-track orbits are obtained by using the improved Newton's iteration method to make differential corrections to the orbit semi-major axis and the orbit inclination angle. Simulation results show that the orbit design method proposed in this paper can achieve a sun-synchronous strictly repeat ground-track orbit design with a revisit accuracy of the order of meters under the J2/J4 perturbation. Furthermore, the method is faster in computation and requires fewer iterations to reach the convergence condition than the conventional Newtonian iterative method.