Analytical algorithm of weighted 3D datum transformation using the constraint of orthonormal matrix

Earth, Planets and Space

Table 4 Calculated transformation parameters and mean error

Parameters	Set 1			Set 2			Set 3
Parameters	PA	CPA	IPA	PA	CPA	IPA	PA	CPA	IPA
ΔX (m)	30.000215	30.000215	30.000215	29.997125	64.907810	29.997125	29.999564	29.884451	29.999564
ΔY (m)	30.000014	30.000014	30.000014	29.999418	−17.354508	29.999418	30.000156	31.848392	30.000156
ΔZ (m)	9.999992	9.999992	9.999992	10.000804	−1.797635	10.000804	9.999562	9.420190	9.999562
α (°)	70.998025	70.998025	70.998025	70.994443	−70.994443	70.994443	70.999494	60.478813	70.999494
β (°)	77.999873	77.999873	77.999873	77.996704	77.996704	77.996704	77.999588	43.508921	77.999588
γ (°)	73.001648	73.001648	73.001648	73.000253	73.000253	73.000253	73.000571	−89.744632	73.000571
λ	1.000012	1.000012	1.000012	1.000049	1.000049	1.000049	1.000025	1.000025	1.000025
ME (m)	0.000315	0.000315	0.000315	0.000197	0.000197	0.000197	0.000313	0.000313	0.000313
Parameters	Set 4			Set 5			Set 6
Parameters	PA	CPA	IPA	PA	CPA	IPA	PA	CPA	IPA
ΔX (m)	29.999778	29.999778	29.999778	30.000278	30.000278	30.000278	30.000000	30.000000	30.000000
ΔY (m)	30.000191	30.000191	30.000191	30.000389	30.000389	30.000389	30.000333	30.000333	30.000333
ΔZ (m)	9.999647	9.999647	9.999647	10.000083	10.000083	10.000083	10.000333	10.000333	10.000333
α (°)	71.000802	71.000802	71.000802	−45.000000	−35.145218	−54.854782	unsolved	−61.858215	−61.858215
β (°)	78.000742	78.000742	78.000742	16.444350	−24.651859	−24.651859	77.998588	77.998588	77.998588
γ (°)	72.999769	72.999769	72.999769	15.645706	6.418995	6.418995	72.998563	72.998563	72.998563
λ	1.000028	1.000028	1.000028	1.000016	1.000016	1.000016	1.000008	1.000008	1.000008
ME (m)	0.000294	0.000294	0.000294	0.000296	0.000296	0.000296	0.000407	0.000407	0.000407