考虑扰动引力影响的弹道助推段误差传播解析计算方法

Analytical expression of error propagation along powered phase trajectory of missile by disturbing gravity

针对地球扰动引力对弹道导弹惯性导航精度影响日益突出这一问题,研究了沿弹道扰动引力的多项式拟合方法,并基于线性系统理论和弹道摄动思想推导了用于求解扰动引力对弹道助推段状态影响的完整解析表达式。同时考虑扰动引力影响与导弹视加速度之间的耦合特性,将扰动引力引起的视加速度偏差视为扰动引力影响的附加补偿项,并进行迭代修正。仿真结果表明:扰动引力拟合残差小于3×10^(-7)m/s^2,考虑耦合项修正的弹道误差传播解析模型计算残差减小为原有方法的1/3,计算时间仅为直接采用弹道积分求差法的1/10。

Regarding the influence to the inertial navigation system of missile by disturbing gravity was focused,a polynomial fitting method was used to express disturbing gravity along the trajectory,and an analytical expression for calculating the deviation from the nominal value without considering disturbing gravity was deduced based on the linear system theory and the perturbation theory. Moreover,the coupling property between disturbing gravity and apparent acceleration was considered. The apparent acceleration deviation caused by disturbing gravity was regarded as an additional term of disturbing gravity,and was corrected by iterative method. The simulation results show that the error of disturbing gravity fitting method is less than 3 × 10^（-7） m/s^2,and the residual error of the analytical formula considering the compensation of the apparent acceleration deviation is about 1/3 of the original method,and the computation time is only 1/10 of the numerical integration method.