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

Earth, Planets and Space

Table 3 Simulative true coordinates of control points in system A

Point number	Set 1 (m)			Set 2 (m)			Set 3 (m)
Point number	X	Y	Z	X	Y	Z	X	Y	Z
1	52.116	7.239	14.222	52.116	7.239	14.222	94.294	37.450	17.742
2	58.807	9.608	24.512	58.807	9.608	24.512	103.013	41.272	28.201
3	61.443	9.072	34.463	61.443	9.072	34.463	111.732	45.093	38.659
4	49.949	17.746	16.493				76.310	36.628	18.693
5	51.773	16.629	26.376				85.029	40.450	29.151
6	51.570	14.060	36.090				93.748	44.271	39.610
7	48.187	28.543	18.797				58.325	35.806	19.643
8	40.683	20.745	27.902				67.044	39.627	30.102
9	40.886	18.466	37.650				75.763	43.449	40.560
Point number	Set 4(m)			Set 5 (m)			Set 6 (m)
Point number	X	Y	Z	X	Y	Z	X	Y	Z
1	60.227	13.048	14.899	44.537	25.929	18.493	30.608	28.012	19.782
2	60.835	11.060	24.681	59.073	21.858	26.985	31.216	26.023	29.563
3	61.443	9.072	34.463	73.610	17.787	35.478	31.824	24.035	39.345
4	54.410	20.941	16.865	88.146	13.716	43.971
5	55.017	18.953	26.647	102.683	9.645	52.463
6	55.625	16.965	36.429	117.219	5.573	60.956
7	48.592	28.834	18.831	131.756	1.502	69.449
8	49.200	26.846	28.613	146.292	−2.569	77.941
9	49.808	24.857	38.394	160.829	−6.640	86.434