数值微分在设备组合弹道精度评估中的应用  

Numerical differentiation for evaluating theoretical accuracy of device combination trajectory

作　　者：何京江[1] 杨涵 郭茂耘[2] 柴毅[2] HE Jingjiang;YANG Han;GUO Maoyun;CHAI Yi(Xichang Satellite Launch Center,Xichang,Sichuan 615000,P.R.China;College of Automation,Chongqing University,Chongqing 400044,P.R.China)

机构地区：[1]西昌卫星发射中心,四川西昌615000 [2]重庆大学自动化学院,重庆400044

出　　处：《重庆大学学报》2025年第2期1-9,共9页Journal of Chongqing University

基　　金：国家自然科学基金重点项目(61633005)。

摘　　要：设备组合弹道精度评估是测量设备布站设计和设备组合弹道选优方案制定的重要基础。设备组合弹道精度评估通常采用基于误差传播原理的弹道精度评估算法,求解弹道分量关于测元的雅克比矩阵是该算法的核心。然而,对于复杂的弹道方程很难求得雅克比矩阵的解析式。为了解决复杂弹道方程的雅克比矩阵求解难题,提出基于样条数值微分的设备组合弹道精度评估算法,通过构造弹道分量数值队列,进行基于样条插值的数值微分计算出弹道分量关于测元的雅克比矩阵,计算得到设备组合弹道理论精度。最后,通过与单台设备定位方程的理论雅克比矩阵和弹道精度进行对比,验证基于数值微分的设备组合弹道精度评估算法的有效性和实用性。The theoretical accuracy evaluation of device combination trajectories is a critical foundation for device allocation design and trajectory selection.Existing models for accuracy evaluation are based on the error propagation principle,using the Jacobian matrix of the trajectory with respect to measurement elements as their core.However,obtaining the analytic expressions for the Jacobian matrix elements in complex trajectory equations is challenging.This paper proposes and designs a theoretical accuracy evaluation algorithm for device combination trajectories based on numerical differentiation.By constructing numerical sequences and calculating the Jacobian matrix using numerical differentiation with spline interpolation,the theoretical accuracy of the device combination trajectory is determined.The algorithm’s effectiveness and practicality are validated by comparing the Jacobian matrix and accuracy values of the proposed method with those derived from a single device position equation.

关 键 词：弹道精度评估模型 雅克比矩阵 样条插值 数值微分 

分 类 号：TM571.6[电气工程—电器]