带初始前置角和末端攻击角约束的偏置比例导引律设计以及剩余飞行时间估计

针对导弹飞行过程中受到外部干扰导致前置角变化较大的问题，设计了满足任意初始前置角和末端攻击角度约束的偏置比例导引律，并对该导引律下系统参数的收敛性给出了证明。基于现有分段迭代求解剩余飞行时间的方法进行拓展，解决了现有分段迭代求解方法在前置角等于π/2 rad时存在奇点的问题，并用该改进方法给出了该导引律的剩余飞行时间估计。对提出的导引律和改进的分段迭代求解方法进行仿真，结果表明：该导引律能够满足任意初始前置角和末端攻击角度约束下导弹的脱靶量和末端角度要求，且在飞行末端加速度指令收敛至0；与以往研究结果相比，该导引律在前置角大于π/2 rad时能够实现对导弹的更有效控制；使用改进的分段迭代求解方法对提出的导引律进行剩余飞行时间估计，估计误差小，误差收敛快。仿真结果验证了该偏置比例导引律和剩余飞行时间估算方法的有效性。

BPNG Law with Arbitrary Initial Lead Angle and Terminal Impact Angle Constraint and Time-to-go Estimation

A biased proportional navigation guidance (BPNG) law with arbitrary initial lead angle and impact angle constraint is designed for a large change in lead angle due to external disturbance during missile flight. The convergence of system parameters under this guidance law is proved. The problem of the existence of singularity in existing piecewise iterative method is solved by expanding the existing method, and the time-to-go estimation method under this guidance law is presented. The proposed guidance law and the improved piecewise iterative method were simulated. The simulated results show that the guidance law can satisfy the requirements of miss distance and terminal impact angle of missile under the constraints of arbitrary initial lead angle and arbitrary impact angle, and the acceleration command also converges to zero at the flight terminal. Compared with previous research results,the proposed biased proportional navigation guidance law can achieve the effective control of missile when the lead angle is greater than π/2 rad. The proposed estimation method is used to estimate the time-to-go with small estimation error and fast error convergence. Simulated results demonstrate the effectiveness of the proposed guidance law and time-to-go estimation method.