基于伴随同化方法的空间飞行器轨道估计  

Trajectory Estimation of the Aircraft in a Double-Satellite Passive Positioning System with the Adjoint Method

作　　者：靳光震[1] 高艳秋[1] 曹安州[1] 吕咸青[1] 

机构地区：[1]中国海洋大学物理海洋实验室,山东青岛266100

出　　处：《数学的实践与认识》2013年第14期177-186,共10页Mathematics in Practice and Theory

基　　金：自然科学基金(41076006;41206001);江苏省自然科学基金(BK2012315)

摘　　要：基于空间几何原理提出了一个双星无源定位方案,方案中包括两个观测坐标系和一个基础坐标系.每个观测坐标系中分别存在一条由观测卫星发出指向目标飞行器的射线,考虑到实际观测中存在各种误差,任意两颗观测卫星对目标飞行器的定位方向一般不在同一个平面内(即为异面直线),假定两条异面直线的公垂线段的中点(相交的情况下为交点)是目标飞行器所在的位置,而公垂线段的长度表征两颗卫星的观测误差.利用空间飞行器的观测数据计算了飞行器在基础坐标系中的位置坐标并进行了误差估计.利用一个基于伴随同化方法的数值模型估计了空间飞行器主动段的轨道.正向模型用来模拟飞行器的运动过程,伴随模型用来优化参数.通过同化空间飞行器在基础坐标系下的观测数据得到了空间飞行器的轨道.设计了数值实验以检验该模型的合理性,实验结果表明了双星无源定位系统的正确性,通过同化卫星对飞行器的观测数据,该伴随同化模型可以对空间飞行器的轨道进行成功估计.A double-satellite passive positioning system is constructed based on the theory of space geometry. In this system, two observation coordinate systems and a fundamental coordinate system exist. In each observation coordinate system, there exists a ray from the observation satellite to the aircraft. One difficulty lies that these two rays may not intersect due to the existence of different kinds of errors. Under this situation, this work assumes that the middle point of common perpendicular between two rays is the actual position of aircraft. Based on the theory of space geometry, the coordinates of the aircraft in the fundamental coordinate system can be determined and the error of observation can be estimated. A dynamic model with the adjoint method is developed to estimate the trajectory of the aircraft during the process of rocket propulsion. The forward model is used to simulate the motion of the aircraft and the adjoint model is used to optimize parameters. By assimilating observed coordinates, which are the coordinates of the aircraft in the fundamental coordi- nate system based on observation, the trajectory of the aircraft is obtained. A numerical experiment is designed to validate the reasonability of this model. Simulation results show rationality of the double-satellite passive positioning system and indicate that by assimilating several observed coordinates, the trajectory of the aircraft can be obtained with the adjoint model.

关 键 词：双星无源定位 轨道估计 数值模型 伴随同化 

分 类 号：V412.41[航空宇航科学与技术—航空宇航推进理论与工程]