Propagation mechanism analysis of navigation errors caused by initial state errors for long-range vehicles

The inertial navigation system is aligned and leveled before the launch of a long-range vehicle. However, the non-uniformity of the Earth can lead to initial state errors including initial positioning errors and initial orientation errors, causing navigation errors in flight dynamics and eventually impact-point deviations up to approximately 1 km. In order to analyze the propagation mechanisms of initial state errors and rapidly estimate their influence magnitudes, navigation perturbation equation subject to apparent acceleration coupling is established based on state space perturbation theory in the launch inertial coordinate system. Afterwards, a series of analytical form of deviations are derived including gravitational acceleration deviation, apparent acceleration projection deviation, apparent acceleration coupling deviation, initial velocity errors and initial position errors. Then, the analytical propagation model of engine-cutoff state deviations and impact-point deviations are acquired by solving the navigation perturbation equation. In the simulations, computer codes are programmed to calculate the propagation matrices of engine-cutoff state deviations and impact-point deviations in the case of fixed launch azimuth, followed by the propagation mechanism analyses of initial state errors. Next, two more scenarios of different launch azimuths and different launch points are simulated to further verify the reliability of the proposed analytical propagation model. The results show that analytical solutions of the propagation model proposed in this paper can well coincide with numerical solutions, with relative errors being all less than 1%, which is also suitable for multiple distinct simulation scenarios compared with previous methods.