GNSS pseudo trigonometric leveling method

doi:10.11947/j.AGCS.2025.20250020

Abstract

Abstract:

A GNSS pseudo trigonometric leveling method is proposed to address the issue of low accuracy in traditional total station trigonometric leveling. This method requires the deployment of a certain number of auxiliary points around the measurement station, the establishment of a zenith direction (opposite direction of vertical line) baseline vector using a precision level and GNSS receiver, and the replacement of the traditional total station line of sight with the GNSS baseline vector. The zenith distance of the target point is obtained through the vector dot product formula, and then the trigonometric leveling measurement value between two points is obtained. GNSS pseudo trigonometric leveling does not require two-point visibility and is not affected by atmospheric refraction, making it particularly suitable for long-distance elevation transmission across obstacles such as rivers, lakes, and valleys. A comparative experiment was conducted on a 3.8 km leveling route using precision leveling measurement and GNSS pseudo trigonometric leveling round-trip measurement. The experimental results showed that the difference between the two methods was less than the second-order leveling detection limit of 11.7 mm.

Key words: pseudo trigonometric leveling, GNSS static measurement, leveling, atmospheric vertical refraction

CLC Number:

P216

Jianzhang LI, Haowen YAN, Weifang YANG, Xiaoning SU. GNSS pseudo trigonometric leveling method[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(7): 1170-1177.

Figures/Tables 7

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点号	纬度	经度	大地高/m
E	36°07′44.359 04″N	103°43′34.945 72″E	16 59.894 90
K0D1	36°07′46.008 40″N	103°43′32.565 63″E	1 659.999 00
K0D2	36°07′45.503 66″N	103°43′35.870 95″E	1 660.485 90
K0D3	36°07′43.282 04″N	103°43′38.833 00″E	1 660.631 00
K0D4	36°07′41.589 45″N	103°43′36.472 20″E	1 659.497 90
K0D5	36°07′42.348 62″N	103°43′32.256 22″E	1 658.404 20
F	36°09′31.171 04″N	103°43′11.497 58″E	1 754.421 20
K0H1	36°09′30.509 53″N	103°43′08.706 11″E	1 753.236 89
K0H2	36°09′32.485 81″N	103°43′09.251 00″E	1 754.929 80
K0H3	36°09′35.220 34″N	103°43′12.667 73″E	1 757.545 80
K0H4	36°09′33.847 61″N	103°43′15.185 55″E	1 757.535 67
K0H5	36°09′30.131 09″N	103°43′13.794 09″E	1 754.902 51

测段号	高差	测段号	高差
E-K0D1	0.105 10	F-K0H1	－1.183 10
E-K0D2	0.590 20	F-K0H2	0.509 60
E-K0D3	0.732 30	F-K0H3	3.123 90
E-K0D4	－0.397 70	F-K0H4	3.112 00
E-K0D5	－1.488 90	F-K0H5	0.479 50

基线名	ΔX	ΔY	ΔZ
E-K0D1	64.943 30	－15.013 16	41.087 32
E-K0D2	－17.435 90	－25.590 33	28.388 39
E-K0D3	－98.931 02	－3.952 88	－26.891 12
E-K0D4	－48.879 61	39.894 30	－68.977 13
E-K0D5	56.689 40	51.457 18	－50.053 20
F-K0H1	64.947 50	28.242 25	－16.467 29
F-K0H2	60.239 00	－9.913 80	32.727 79
F-K0H3	－10.950 47	－78.497 92	100.798 64
F-K0H4	－78.027 48	－69.167 95	66.629 02
F-K0H5	－60.266 59	4.761 39	－25.885 99

序号	水准线路长/km	GNSS伪三角高程测量高差/m				精密水准测量高差/m	较差/mm	二等水准测量限差/mm
序号	水准线路长/km	往测	反测	平均	中误差	精密水准测量高差/m	较差/mm	二等水准测量限差/mm
1	2.5	65.935 3	－66.819 6	66.377 5	0.004 2	66.381 0	－3.5	9.4
2	2.5	65.933 1	－66.817 4	66.375 3	0.003 6	66.381 0	－5.7	9.4
3	3.8	95.329 1	－97.082 9	96.206 0	0.004 1	96.210 6	－4.6	11.7
4	3.8	95.335 0	－97.089 0	96.212 0	0.003 9	96.210 6	1.4	11.7