快速仅测角相对导航初始相对轨道确定方法

doi:10.12305/j.issn.1001-506X.2021.04.24

摘要/Abstract

摘要：

针对线性化的测量模型和相对运动模型会导致仅测角相对导航星间距离不可观测的问题, 提出一种快速仅测角相对导航初始相对轨道确定(initial relative orbit determination, IROD)方法。首先, 采用相对轨道根数(relative orbit elements, ROE)建立非线性相对运动模型, 该模型可以将星间距离和相对轨道形状进行解耦。然后, 在线性理论获得的共线性解附近系统地改变星间距离大小, 并执行一系列最小二乘拟合, 随后采用二分法或牛顿迭代法快速在全局范围内找到最小拟合残差的最优解。最后, 通过搭建的半物理仿真平台对该方法在4种轨道场景中的性能进行仿真测试, 验证了所提方法的有效性。

关键词: 仅测角相对导航, 初始相对轨道确定, 二分法, 牛顿迭代法, 最小二乘拟合

Abstract:

For the problem of unobservable inter-satellite distance of angles-only relative navigation caused by the linear measurement model and relative motion model, a fast initial relative orbit determination (IROD) method of angles-only relative navigation is proposed. Firstly, the relative orbit elements (ROE) is used to establish a nonlinear relative motion model, which can decouple the inter-satellite distance and the relative orbital shape. Then, the inter-satellite distance near the collinear solution obtained by linear theory is changed, systematically, and a series of least-square fitting is performed, and then the dichotomy or Newton iteration method is used to find the optimal solution of the minimum fitting residual quickly in the global range. Finally, a semi-physical simulation platform is built to test the performances of the method in 4 orbital scenarios, and the effectiveness of the proposed method is verified.

Key words: angles-only relative navigation, initial relative orbit determination (IROD), dichotomy method, Newton iteration method, least-square fitting

中图分类号:

V249.32

杜荣华, 张翔, 廖文和. 快速仅测角相对导航初始相对轨道确定方法[J]. 系统工程与电子技术, 2021, 43(4): 1057-1068.

Ronghua DU, Xiang ZHANG, Wenhe LIAO. Fast initial relative orbit determination method of angles-only relative navigation[J]. Systems Engineering and Electronics, 2021, 43(4): 1057-1068.

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参数	变量	仿真值
空间目标初始轨道根数	(a, e, i, Ω, ω, M)	(6 878.137 km, 0, 40°, 120°, 0°, 50°)
初始ROE (场景1)	(aδa, aδe_x, aδe_y, aδi_x, aδi_y, aδλ)	(0, 0.5, 0, -0.5, 0, -30)km
初始ROE (场景2)	(aδa, aδe_x, aδe_y, aδi_x, aδi_y, aδλ)	(-0.15, 0.3, 0, -0.3, 0, -20)km
初始ROE (场景3)	(aδa, aδe_x, aδe_y, aδi_x, aδi_y, aδλ)	(0, 0, -0.2, 0, 0.2, -5)km
初始ROE (场景4)	(aδa, aδe_x, aδe_y, aδi_x, aδi_y, aδλ)	(0, 0, 0, 0, 0, -0.5)km
相机测量误差标准差	σ_α=σ_ε	18″
相机测量偏差标准差	σ_{b, α}=σ_{b, ε}	5″
姿态测量误差标准差	(σ_{att, off-axis}, σ_{att, roll})	(6, 40)″

轨道场景	方法	用时/s
场景1	批量搜索法	13.74
	二分法	2.32
	牛顿迭代法	0.65
场景2	批量搜索法	14.78
	二分法	3.13
	牛顿迭代法	0.82
场景3	批量搜索法	13.51
	二分法	2.16
	牛顿迭代法	0.53
场景4	批量搜索法	23.22
	二分法	4.14
	牛顿迭代法	1.03

轨道场景	百分比误差P_x/%
轨道场景	批量搜索法	二分法	牛顿迭代法
场景1	7.07	7.03	5.87
场景2	6.55	5.45	5.35
场景3	5.20	3.80	3.80
场景4	35.8	34.0	32.4

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