Grid Model for High-accuracy Coordinate Transformation of China Geodetic Coordinate System 2000

doi:10.11947/j.JGGS.2019.0103

Abstract

Abstract:

After implementing CGCS2000, establishing grid models for high-accuracy coordinate transformation which are mainly used to transform border lines and coordinate grids of topographic maps becomes an important issue in mapping applications. Consequently, a grid model for high-accuracy coordinate transformation of CGCS2000 is proposed. Specifically, we firstly analyze a minimum curvature equation of coordinate transformation, which possesses the characteristics of both the global and local smoothness, achieving better consistency with the consecutive smoothness for the coordinate transformation of map’s linear feature. Then an iterative calculation method of grid nodes and an approach for establishing regional grid models based on collocation by two-step minimization are proposed. Meanwhile, a data structure of grid model is constructed. Finally we give the optimized grid interval and transformation accuracy in China corresponding to the proposed grid model. Using 48433 points of 2000 National Geodetic Control Network of China, we take the proposed model into practice by constructing grid models for coordinate transformation from BJS54 and XAS80 to CGCS2000, and the external positional accuracies for both models are 0.26m and 0.03m respectively.

Key words: CGCS2000; coordinate transformation; minimum curvature method; grid model; data structure; collocation

Zhiping LU,Ziqing WEI,Jun LI,Chong GUO. Grid Model for High-accuracy Coordinate Transformation of China Geodetic Coordinate System 2000[J]. Journal of Geodesy and Geoinformation Science, 2019, 2(1): 17-25.

Figures/Tables 6

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Coordinate transfor- mation	Grid interval	Mean value		Mean square error		Maximum value \|v\|		\|v\|<0.1m		\|v\|<0.05m
Coordinate transfor- mation	Grid interval	Component B	Component L	Component B	Component L	Component B	Component L	Component B	Component L	Component B	Component L
BJS54 → CGCS 2000	3'×3'	0.000	-0.000	0.011	0.010	0.039	0.038	100%	100%	100%	100%
	2.5'×2.5'	0.000	-0.000	0.009	0.008	0.035	0.041	100%	100%	100%	100%
	1.5'×1.5'	-0.000	0.000	0.004	0.004	0.016	0.014	100%	100%	100%	100%
	1.2'×1.2'	-0.000	-0.000	0.004	0.003	0.028	0.015	100%	100%	100%	100%
XAS80 → CGCS 2000	3'×3'	-0.000	0.000	0.001	0.001	0.004	0.004	100%	100%	100%	100%
	2.5'×2.5'	0.000	0.000	0.001	0.001	0.005	0.003	100%	100%	100%	100%
	1.5'×1.5'	0.000	0.000	0.003	0.002	0.009	0.006	100%	100%	100%	100%
	1.2'×1.2'	0.000	0.000	0.003	0.003	0.012	0.010	100%	100%	100%	100%

Coordinate transfor- mation	Grid interval	Mean value		Standard error		Maximum value \|v\|		\|v\|<0.1m		\|v\|<0.05m
Coordinate transfor- mation	Grid interval	Component B	Component L	Component B	Component L	Component B	Component L	Component B	Component L	Component B	Component L
BJS54 → CGCS 2000	3'×3'	-0.014	0.000	0.061	0.053	0.197	0.159	90.2%	92.7%	73.2%	73.2%
	2.5'×2.5'	-0.012	0.002	0.059	0.053	0.168	0.156	92.7%	92.7%	68.3%	75.6%
	1.5'×1.5'	-0.026	-0.013	0.076	0.073	0.206	0.200	73.2%	58.5%	51.2%	56.1%
	1.2'×1.2'	-0.039	-0.020	0.135	0.117	0.397	0.343	56.1%	70.7%	31.7%	48.7%
XAS80 → CGCS 2000	3'×3'	0.001	0.003	0.008	0.007	0.034	0.034	100%	100%	100%	100%
	2.5'×2.5'	-0.001	0.005	0.014	0.012	0.049	0.047	100%	100%	100%	100%
	1.5'×1.5'	-0.003	0.006	0.031	0.024	0.076	0.066	100%	100%	92.7%	95.1%
	1.2'×1.2'	-0.004	0.005	0.034	0.026	0.071	0.068	100%	100%	90.2%	95.1%

Coordinate transformation	Grid interval	Number of common points	Mean square error/m
Coordinate transformation	Grid interval	Number of common points	Component B	Component L
BJS54→ CGCS2000	2.5'×2.5'	48433	0.062	0.071
XAS80→ CGCS2000	2.5'×2.5'	48433	0.006	0.012

Coordinate transformation	Grid interval	Number of common points	Number of points for external check	Mean square error/m		Point position error/m
Coordinate transformation	Grid interval	Number of common points	Number of points for external check	Component B	Component L	Point position error/m
BJS54→CGCS2000	2.5'×2.5'	48433	484	0.124	0.227	0.259
XAS80→CGCS2000	2.5'×2.5'	48433	484	0.017	0.022	0.028

Calculation	Mean value		Standard error		Maximum value \|v\|
Calculation	Component B	Component L	Component B	Component L	Component B	Component L
Tentative calculation 1	-0.122	-0.093	0.059	0.029	0.283	0.146
Tentative calculation 2	-0.045	-0.029	0.049	0.027	0.176	0.068