Analytical trajectory prediction for skip re-entry of lifting vehicle

An analytical trajectory prediction method is put forward for skip re-entry of lifting vehicles. First, the 3-D analytical solutions of skip re-entry trajectory are developed, which are crucial to realize the analytical trajectory prediction. To facilitate the derivation, an auxiliary geocentric inertial frame is established to deal with the strong nonlinear problem caused by the Earth’s rotation. Thereafter, the analytical solutions of the downrange, crossrange, and velocity are approximated by the outer solutions of a two-time scale singular perturbation. The analytical solutions of the altitude and flight-path angle are developed using regular perturbation techniques which can decompose the strongly coupled and nonlinear system into a sequence of linear problems. Second, since the analytical solutions are with respect to the lift-to-drag ratio and bank angle, a method based on the EKF technique is proposed to estimate the lift-to-drag ratio and bank angle of the re-entry vehicle. Third, the analytical trajectory prediction schemes for the lifting re-entry vehicle with multiple bank reversals are put forward. The simulations show that the proposed analytical solutions are in good agreement with the numerical solutions, but the computation time of the analytical solutions is about two orders of magnitude less than that of the numerical solutions. In addition, the superior performance of the proposed analytical trajectory prediction method is well demonstrated by the simulation results.