Trajectory characteristic analysis influenced by initial state errors for long-range vehicles

The initial state errors, caused by the Earth’s un-homogeneity through the leveling and alignment of an inertial platform before launching a long-range vehicle, will bring about remarkable flight state deviations and fall point deviations by flight dynamics. In order to analyze the propagation characteristics of the initial state errors and rapidly estimate their influence magnitude, an analytical propagation model of trajectory design is deduced by employing state space perturbation theory in nominal launch coordinate system. Then, propagation matrices of engine-cutoff state deviations and fall point deviations are obtained. In the simulations, deviations of engine-cutoff and fall point are computed in the case of a fixed launch azimuth, different launch azimuths and different launch points. Next, propagation regularities of the initial state errors are analyzed from the launch point to the engine-cutoff as well as to fall point. Conclusions are as follows: (1) the estimation accuracy of flight states deviations during boost phase will be distinctly enhanced when considering the force term deviations; (2) in the case of different launch azimuths, position and velocity deviations of engine-cutoff in the x, y directions and longitudinal deviation of fall point are symmetrical at the azimuth of 45° where these deviations are maximum. Comparatively, position and velocity deviations of engine-cutoff in the z direction and lateral deviation of fall point are symmetrical at the azimuth of −45°; (3) the proposed analytical propagation model of the initial state errors has a high estimation accuracy within the error percentage of 2%, which can improve computational efficiency by 100 times and is more suitable for multiple simulation scenarios.