A dual quaternion algorithm of the Helmert transformation problem

Earth, Planets and Space

Table 6 3D coordinates of control points in original system and noises added (m)

Point no.	\(x^{\text{o}}\)	\(y^{\text{o}}\)	\(z^{\text{o}}\)	Noise in \(x^{\text{o}}\)	Noise in \(y^{\text{o}}\)	Noise in \(z^{\text{o}}\)	Positional error sphere
1	10.00000	30.00000	5.00000	− 0.03190	0.02380	0.01060	0.00057
2	20.00000	30.00000	12.50000	− 0.02880	− 0.02400	0.00440	0.00047
3	30.00000	30.00000	15.00000	0.01140	− 0.00040	− 0.01840	0.00016
4	10.00000	20.00000	9.50000	− 0.00800	− 0.00310	− 0.04340	0.00065
5	20.00000	20.00000	11.00000	0.01380	− 0.03210	− 0.00120	0.00041
6	30.00000	20.00000	10.00000	0.01630	0.00510	− 0.02020	0.00023
7	10.00000	10.00000	14.50000	0.01420	− 0.02110	0.01230	0.00027
8	20.00000	10.00000	4.50000	0.02580	0.02830	0.01020	0.00052
9	30.00000	10.00000	4.00000	0.01340	− 0.01610	0.03380	0.00053