直角坐标系统中的观测误差相关函数解析分析

Theoretical analysis of correlation function concerning errors of observation in Cartesian coordinate system

在火控系统中,目标坐标的测量是在球坐标系中进行的,而解相遇问题是在直角坐标系统中进行的,为了设计出火控系统最优滤波器,需要获得直角坐标系中观测误差的相关函数。利用随机变量的特征函数和欧拉公式,首先推导了完整的直角坐标系统中的观测误差的相关函数,在此基础上根据实际条件依次进行了4步合理简化。最后,通过实例计算,分析了相应的简化可能造成的滤波精度损失,为实际的火控系统设计提供了依据。

In the fire control system,the measurement of target is made in the polar coordinate system,while the analysis and solvement of the target movement are carried out in the Cartesian coordinate system.Thus,the optimal filter for fire control can be designed after obtaining the correlation function concerning errors of observation in the Cartesian coordinate system.The complete correlation functions were deduced by means of the characteristic function of the stochastic variables and the Eular formular.Based on the functions,four steps of simplification were performed for the feasibility in practical cases.The loss of the filtering accuracy in the simplifications was simulated and evaluated,which provides a theoretical basis for practical design of the fire control system.