设备组合弹道理论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。设备组合弹道理论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的求解难题，本文提出了基于数值微分的设备组合弹道理论精度评估算法，通过构造弹道分量数值队列，并对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，进而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理论精度进行对比,验证了本文提出的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 theory accuracy evaluation of device combination orbit is the important base of device allocation design and selection of device combination trajectory. The Jacobian matrix of orbit about measuring element is the kernel of the theory accuracy evaluation model of orbit based on error propagation principle. However, it is hard to get the elements’ analytic expression of the Jacobian matrix of complex orbit equation. The theory accuracy evaluation algorithm of device combination trajectory based on numerical differentiation is raised and designed in the paper. By means of constructing numerical queue and calculating Jacobian matrix by numerical differentiation based on spline interpolation, and then the theory accuracy of device combination orbit is obtained. At the last part of the paper, the algorithm is verified to be effective and practical by compared itsJacobian matrix and accuracy value with single position equation’s.

TM571.6

国家自然科学基金重点项目（61633005）：基于大数据的航天发射系统安全性实时评估方法