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

Abstract

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

CLC Number:

P232

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.

Figures/Tables 4

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References 33

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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

算法	δ值
最小二乘	2.486 6
总体最小二乘	12.922 1
混合最小二乘	2.398 5
稳健加权混合最小二乘	0.934 0

Application of improved least squares algorithm in astronomy positioning

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