比例导引法中剩余飞行时间的计算方法

为了给比例导引法提供尽可能精确的剩余飞行时间,基于导弹-目标相对运动模型,研究了剩余飞行时间的计算方法。建立了以导弹前置角收敛到0为准则的剩余飞行时间计算模型。对于比例系数为3时的特殊情形,利用解析方法得到了该计算模型的一阶解和二阶解,通过仿真分析对解的精度进行了评估; 利用多项式拟合方法得到比例系数为其他值时剩余飞行时间的近似解,仿真分析表明多项式次数为5时拟合精度较好; 将研究的剩余飞行时间算法应用于拦截不同类型目标的比例导引过程,结果表明,该算法用于比例导引拦截匀速目标具有良好效果,在导弹速度足够大时也可有效拦截匀加速目标。

Study on Time-to-go Algorithm in Proportional Navigation Guidance

In order to provide an accurate time-to-go to the proportional navigation guidance, the calculation method of time-to-go was studied based on the missile-target relative motion model. The time-to-go caculation model was established according to the criterion of the missle's leading angle converging to zero. For the special case that the navigation gain was three,the first and second order solutions of the model were obtained by using the analytical method,and the accuracy of these solutions were evaluated by simulation analysis. The approximate solution of time-to-go for the other navigation gain was obtained by using the polynomial fitting method. The simulation results show that the fifth order polynomial fitting has better precision. The time-to-go algorithm was applied to intercepting different types of tagets with proportion navigation guidance. The results show that the algorithm can effectively intercept the constant speed target and the constant acceleration target,as long as the missile's velecity is large enough.