Improved Adjustment Method Applied in Transformation of Laser Tracker

Items	WTLS	SCTLS
Functional model	$y + e_{y} = (A + E_{A}) ξ$	Eqs. (2) and (5)
Statistics model	$b l k d i a g (Q_{A}, Q_{y})$	$Q_{e e}$
Dimension of $Q$	$13 n \times 13 n$	$6 n \times 6 n$
Character of $Q$	Off-diagonal	Diagonal
Expression of $e$	$e = {[v e c^{T} (E_{A}) e_{y}^{T}]}^{T}$	Eq. (7)
Dimension of $e$	$13 n \times 1$	$6 n \times 1$
Repeated elements	Different	Same
Character of ${\hat{R}}_{1}$	Non-orthogonal	Orthogonal
Number of independent elements of $ξ$	12	7
Precision evaluation	None	Eq. (19)

Table 2. Average of absolute bias in simulation
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Table 2. Average of absolute bias in simulation
Method $ε (\hat{R})$ /10^-4 $ε (\hat{t}) / m m$
SCTLS 1.144 0.196
WTLS 1.776 0.315
LS 2.698 0.510

Table 3. Observations from laser tracker in Hefei Light Source

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Table 3. Observations from laser tracker in Hefei Light Source

Number	Name	Laser tracker A observation			Laser tracker B observation
Number	Name	$d$ /mm	$α$ /（ $^{\circ}$ ）	$β$ /（ $^{\circ}$ ）	$d$ /mm	$α$ /（ $^{\circ}$ ）	$β$ /（ $^{\circ}$ ）
1	P2	5130.34	-149.7184	84.7385	3679.01	-89.9996	55.3951
2	P3	1804.06	-97.0605	74.8887	3679.01	-0.0035	55.3948
3	P4	2728.38	113.2676	80.0798	3678.79	89.9947	55.3928
4	HCG07	1410.30	121.7104	174.2693	2677.13	37.3065	85.3736
5	HCG08	4836.53	173.0513	106.8160	1969.89	-164.6853	83.5931
6	HCG09	4286.10	-171.1741	109.0869	1404.26	-122.2511	81.0910
7	HCG10	1819.21	123.8746	140.3887	2334.53	59.5167	84.6475
8	HCG11	3126.54	176.5045	116.5998	317.92	137.0496	46.4115

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Tao Luo, Zhijun Qi, Wei Wang, Xiaoye He. Improved Adjustment Method Applied in Transformation of Laser Tracker[J]. Chinese Journal of Lasers, 2024, 51(2): 0204001

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