改进最小二乘算法在天文定位中的应用

doi:10.12305/j.issn.1001-506X.2021.06.24

摘要/Abstract

摘要：

运用数字天顶仪进行天文定位时，需采用最小二乘算法建立电荷耦合元件图像坐标系和天球切平面坐标系之间的映射关系。针对最小二乘算法只考虑了观测量中的误差，没有顾及系数矩阵中的误差和数据中可能存在的粗大误差问题，为了提高数字天顶仪进行天文定位时的解算精度，将最小二乘算法与总体最小二乘算法进行有效结合构成了混合最小二乘算法，该算法能够同时顾及坐标转换中系数矩阵和观测量中的误差。为了消除识别恒星数据中可能存在的粗大误差对天文解算的影响，对所提算法进行了稳健加权，并结合星等设置合理的权阵。数据分析的结果证明，稳健加权混合最小二乘算法在进行天文解算时具有较高的精度。

关键词: 数字天顶仪, 坐标转换, 混合最小二乘, 稳健加权

Abstract:

It is necessary to use the least square algorithm to establish the mapping relationship between the charge-coupled device (CCD) image coordinate system and the celestial tangent plane coordinate system when using the digital zenith camera for astronomical positioning. The least squares algorithm only considers the errors in the observation, but does not consider the errors in the coefficient matrix and the possible gross errors in the data. In order to improve the accuracy of the digital zenith camera in astronomical positioning, the least squares algorithm and the total least squares algorithm are effectively combined to form a mixed least squares algorithm, which can take into account the errors of the coefficient matrix and observation in coordinate transformation. In order to eliminate the influence of the possible gross errors in star recognition data on astronomical solution, the proposed algorithm is weighted robustly, and a reasonable weight matrix is set combined with magnitude. The results of data analysis show that the robust weighted mixed least squares algorithm has high accuracy in astronomical solution.

Key words: digital zenith camera, shift between coordinates, mixed least squares, robust weighting

中图分类号:

P232

黄坤阳, 刘先一, 张志利. 改进最小二乘算法在天文定位中的应用[J]. 系统工程与电子技术, 2021, 43(6): 1659-1663.

Kunyang HUANG, Xianyi LIU, Zhili ZHANG. Application of improved least squares algorithm in astronomy positioning[J]. Systems Engineering and Electronics, 2021, 43(6): 1659-1663.

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序号	x	y	u	v
1	1.0	3.0	25.0	25.0
2	1.8	4.0	29.0	36.4
3	2.0	1.5	8.0	25.5
4	2.0	3.0	20.0	33.0
5	2.2	1.7	8.6	28.1
6	2.5	2.0	9.5	32.0
7	3.0	1.5	3.0	33.5

序号	x	y	u	v
1	1.01	3.02	24.8	24.8
2	1.82	4.10	29.2	36.38
3	2.11	1.52	7.80	25.48
4	2.80	3.02	20.02	32.98
5	2.25	1.71	8.58	28.23
6	2.47	1.98	9.47	32.04
7	2.97	1.51	2.92	32.90

算法	$\hat a $	$\hat b $	$\hat c $₁	$\hat c $₂
最小二乘	4.214 1	7.768 3	5.263 1	3.127 9
总体最小二乘	4.773 5	6.928 9	8.913 0	3.799 5
混合最小二乘	4.475 3	8.249 7	4.679 2	1.437 6
稳健加权混合最小二乘	4.910 7	7.828 4	6.653 6	1.317 5

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