Research Article
Wei Zheng, Lei Wang and Moh
Abstract
The Lambert guidance method has been widely used to steer the ballistic missile in the boost phase. However, only the two-body dynamics-based Lambert algorithm is valid in most practical applications due to the high requirement for computing efficiency. To deal with this problem, an analytical state deviation prediction model of missile subject to J2 perturbation term is proposed in this paper. The differential equation with respect to state deviation vector of missile is built in the Local-Vertical-Local- Horizontal (LVLH) frame, and the state transition matrix of this differential equation obtained in previous work is used to derive the analytical state deviation prediction model based on the linear system theory. The J2 term gravitational acceleration is regarded as perturbing term in this differential equation and is also expressed in the LVLH frame by using the knowledge of spherical trigonometry to satisfy the conditions of analytical solution derivation. By using this analytical model, the impact deviation of missile caused by the J2 term can be calculated in each guidance cycle. Then the velocity required to hit the target is modified by a feedback algorithm. Simulations conducted in this paper have verified the accuracy of this analytical model and its effectiveness in the missile guidance applications