When tracking and intercepting ballistic missile at free-flight phase,ballistic missile suffers not only gravity,but also maneuver control force or atmospheric disturbance.In order to track ballistic missile at free-flight phase accurately,both gravity and atmospheric disturbance should be considered and analyzed when establishing the state equation of ballistic missile at free-flight phase.Currently,we mainly considered the gravity when tracking ballistic missile at free-flight phase,while there was no proper model or algorithm upon the analysis of the maneuver force.Maneuvering of ballistic missile is a quite complex question,so it is not accurate to track ballistic missile at free-flight phase when it is maneuvering while only gravity is considered,and ballistic missile is easy to get lost.This paper conducts an analysis on maneuver control force or the atmospheric disturbance which ballistic missile suffers by Singer model based on inverse-square gravitational acceleration model.And this paper describes ballistic missile's state equation and observation equation in mixed coordinate system,and carries out real time estimation on ballistic missile's state of motion with EKF algorithm.The results of simulation show that the tracking error of ballistic missile in mixed coordinate system is small when considering its maneuvering.Combined with Singer model,tracking accuracy on ballistic missile gets improved.%在对自由段飞行的弹道导弹进行跟踪拦截时,弹道导弹不仅受重力作用,而且受到机动控制力或大气扰动.因此为了准确地对自由段弹道导弹进行跟踪,建立自由段弹道导弹状态方程时,不仅需要考虑弹道导弹受到的重力,而且需要对弹道导弹受到的机动控制力或大气扰动进行分析.目前,对自由段弹道导弹的跟踪主要考虑导弹受到的重力,而针对弹道导弹的机动力分析没有比较合适的模型或算法,弹道导弹的机动是一个比较复杂的问题,因此对只考虑重力的作机动的自由段飞行的弹道导弹的跟踪不准确,容易丢失,在平方反比重力加速度模型的基础上结合Singer模型,对弹道导弹受到的机动控制力或大气扰动进行了分析.对自由段弹道导弹的状态方程和观测方程的描述是在混合坐标系下进行的,并采用EKF扩展卡尔曼滤波算法对弹道导弹的运动状态进行实时估计,仿真结果表明在混合坐标系下对考虑机动的弹道导弹跟踪误差较小.结合Singer模型之后,跟踪弹道导弹的精度得以提高.
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