Research On Trajectory Determination And System Stability Of Ballistic Target

As the most threatening weapon in modern warfare,ballistic missiles have been widely used around the world.All great powers are conducting in-depth research and innovation on missile attack and defense technology.Therefore,vigorously developing missile defense system is not only a major trend in today's world,but also a necessary choice to improve national defense capability.One of the most important tasks of the missile defense system is to track and determine the trajectory of ballistic targets in real time,and then to intercept them or predict their landing points.It's crucial for missile defense system to improve the tracking accuracy of ballistic target and stability of trajectory determination.In this paper,the ballistic missile during the reentry phase is taken as the research object,the improvement of tracking accuracy and stability of the trajectory determination system is studied.The modified square root cubature Kalman filter algorithm and the multi-model interaction fusion are employed to track and determine the trajectory of ballistic target during the reentry phase.Moreover,Lyapunov auxiliary function based on the innovation is utilized to analyze the stability of the system,and the reasonable stability criterions are proposed.The main research contents are as follows:(1)Determinate the initial trajectory of the reentry ballistic target.The various coordinate systems commonly used in target tracking and the preprocessing method of radar observation data are studied.Based on the simulation standard trajectory of reentry ballistic missile which is generated by Runge-Kutta algorithm,the improved Laplace method is employed to determine the initial trajectory.It can provide the initial filter value for subsequent precise trajectory determination and accelerate the convergence speed of filtering algorithm.(2)Determinate the precise trajectory of reentry ballistic target based on nonlinear filtering theory.Analyze the state model and measurement model of the reentry ballistic target.Aiming at the influence of observation noise and ballistic coefficient on the tracking of reentry ballistic target,a modified square root cubature Kalman filter algorithm is proposed and embedded in the interactive multi-model algorithm framework,which is composed of several sub-models with different initial ballistic coefficients.Finally,the performance of the proposed algorithm is evaluated by comparing simulation standard trajectory with tracking trajectory.The results show that the proposed algorithm can effectively improve the tracking accuracy of the reentry ballistic target,accelerate the convergence speed of the tracking error,and make the tracking result more accurate.(3)Analyze the stability of trajectory determination system on the basis of Lyapunov stability theory.The true value of the ballistic target state is unknown in the real application environment so that it's impossible to judge whether the trajectory determination system can work stably through estimation error of filtering algorithm.For this reason,a new construction method of the Lyapunov function based on innovation is proposed.Under the premise that the innovation and the estimation error are consistent,the reasonable criterions of the system stability are obtained through the rigorous mathematical derivation and theoretical argumentation,which provide reasonable constraints conditions and theoretical support for the practical application of the trajectory determination system.