基于摄动理论的弹丸落点预测精度仿真研究

The Accuracy Analysis of Projectile Point Prediction Based on Perturbation Theory

弹道修正技术中,需对弹丸飞行状态实时预测落点,通过比较目标点与预测点形成修正控制指令,传统预测模型计算复杂、预测实时性差。提出了预测精度高、预测模型简单的基于摄动理论的落点预测方法。从数学角度上分析了采用摄动理论进行弹丸落点预测的理论依据,给出了偏导数的数值解法。针对某型弹道修正榴弹,分析了偏导数选取方法。仿真结果表明,选用一阶泰勒展开获得的偏导数用于落点预测精度较高;选用小步长计算获得的偏导数用于落点预测精度较高;弹丸飞行中,选用一次线性拟合插值调用偏导数用于落点预测精度较高,为弹丸落点精度预测优化提供了科学依据。

Trajectory correction projectiles need predict the landing point real-time in practical application to produce control instruction.Traditional prediction models are complex and poor of real-time.This paper presents a kind of landing point prediction technology based on perturbation theory which has simple algorithm and high accuracy.From the mathematical point of view analyzes the theoretical basis of projectile landing point prediction based on perturbation theory.The numerical solution method of partial derivative is given.For a certain type of trajectory correction projectile,the selection method of partial derivative is analyzed.Simulation results show that,the calculation of projectile point is accuracy when select first-order Taylor expansion of partial derivative.The calculation of projectile point is accuracy when select small step length calculation of the partial derivative.The calculation of projectile point is accuracy when call the partial derivative with linear interpolation method.