32 2 Vol. 32, No. 2 2014 5 PROGRESS IN ASTRONOMY May, 2014 doi: 10.3969/j.issn.1000-8349.2014.02.08 65 m 1 2 3 1,4 1 1 (1. 200030 2. 200072 3. 201203 4. 100049) 65 m ( ) 3 mm ITRF2008 X 2 826 708.604 5 0.42 Y = 4 679 237.054 2 m ± 0.45 mm, Z 3 274 667.531 4 2013 6 29 UTC0h f = (2.95 ± 3.26) mm VLBI 0.43 VLBI GPS P228.6 A 1 (VLBI) ( ) 2013-09-18 2014-02-12 (11178024, 11373060 U1331205) ( ) (06DZ22101) 863 (2012AA121603) jll@shao.ac.cn
2 65 m 247 IVS ( VLBI ) IERS ( ) ITRF ( ) [1 3] (3D) VLBI ( ) VLBI [4] VLBI VLBI (LCN) LCN ( ) GPS 3D LCN 3D LCN VLBI LCN (Az-El) ( ) ( ) ( ) LCN LCN ( ) LCN VLBI [5] LCN LCN LCN GPS 3D VLBI ( ) [6 8] T ( GPS ) LCN 3D ( ) T
248 32 VLBI 65 m 2012 10 S/X L C K Ka 2013 65 m 2013 6 7 LCN 2 1 LCN 1 A1 A4 G5 GPS 65 m 65 m A1 A2 65 m A3 A4 A2 A4 TM30 TS30 0.5 as 0.6 mm+1 ppm GPS ASHTECH UZ-12 Trimble 5700 2013 6 23 7 7 LCN GPS 7 7 30 60 90 120 7 8 150 180 240 270 300 330 0 7 9 150 7 10 20 30 40 50 60 70 80 88 7 13 120 188 120
2 65 m 249 15 30 40 50 60 70 80 88 188 8 18 28 38 48 58 68 78 88 3 LCN LCN LCN GPS 3D LCN 3D LCN ( ) 3D 3.1 LCN 1 A1 A4 A1 A1 A2 x z xyz LCN LCN 1 σ x / 0.7 as 1.9 as 0.01 mm 1 x/m y/m z/m σ x /mm σ y /mm σ z /mm A1 0.000 0 0.000 0 0.000 0 / / / A2 155.957 2 0.000 0 0.006 6 0.02 / 0.07 A3 129.844 1 117.641 8 0.004 4 0.02 0.02 0.07 A4 34.215 7 94.713 9 0.000 4 0.03 0.02 0.07 G5 LCN GPS 6 km 25 m IGS SHAO GAMIT ITRF2008 [1] LCN 3D XY Z 2 σ X GPS 2013 6 29 UTC0h SHAO ITRF2008 ( 2 831 733.766 9 4 675 665.852 9 3 275 369.329 4) m 1 2 LCN 3D ( ) 2008 7 25 m [9,10] 3D 7
250 32 2 GPS X/m Y /m Z/m σ X /mm σ Y /mm σ Z /mm A1 2 826 729.534 4 679 262.767 3 274 544.855 0.4 0.4 0.4 A2 2 826 653.989 4 679 217.667 3 274 673.627 0.4 0.4 0.4 A3 2 826 755.409 4 679 152.789 3 274 678.772 0.4 0.4 0.4 A4 2 826 784.426 4 679 194.559 3 274 594.605 0.4 0.4 0.4 1 2 LCN xyz 3D XY Z 3 σ 2 3D A1 A1 A1 (U 0 ) xyz XY Z X x Y = R TOP T + (1 + D)R x(r 1 )R y (R 2 )R z (R 3 ) y + Z z 0 0, (1) T = [T 1, T 2, T 3 ] T 3D T D R x (R 1 ) R 1 R TOP A1 3D 3 3 S E N W U A1 Case 1 Case 4 R SEU = R y (π/2 ϕ)r z (λ) λ = 121.136 06 ϕ = 30.921 1 R ENU R NWU R WSU R SEU R z (π/2) R z (π) R z (3π/2) wrms LCN (0, 0, 0) T m (0, 0, 1) T m (1) 3D WGS84 1 m 3 H Case 1 Case 2 H = 1 m Case 3 Case 4 H = 1 m 1 LCN 4 1.1 cm 4 1 1 Case 3 NWU 3 A1 Case 4 R 3 π/2 ( NWU) WSU Case 3 Case 1 (SE) 1 ( NW) (1 + D) 1 1 LCN xy 4 z U 0
2 65 m 251 3 xyz XY Z Case 1 Case 2 Case 3 Case 4 SEU ENU NWU WSU U 0 /m 6 372 483.339 20 T ± σ T /mm 0.54±0.30 2.48±0.30 0.53±0.30 2.48±0.30 2.48±0.30 0.54±0.30 2.48±0.30 0.53±0.30 2.62±0.36 2.62±0.36 0.77±0.36 0.77±0.36 D ± σ D 2.000 000 5 2.000 000 5 0.000 000 5 0.000 000 5 0.000 002 4 0.000 002 4 0.000 002 4 0.000 002 4 0.000 137 0 3.138 579 4 0.000 010 0 0.002 999 2 R i ± σ Ri 0.000 003 8 0.000 003 0 0.000 003 8 0.000 003 1 (i = 1, 2, 3) 0.003 013 3 3.141 729 7 0.002 999 2 0.000 010 0 /rad 0.000 003 0 0.000 003 8 0.000 003 1 0.000 003 8 0.268 271 7 1.839 067 6 0.268 271 3 1.302 525 0 0.000 002 4 0.000 002 4 0.000 002 4 0.000 002 3 R TOP R SEU R ENU R NWU R WSU wrms/mm 2.13 2.13 1.26 1.26 H/m 1.000 00 1.000 00 1.000 00 1.000 00 Case 1 H = 1 m Case 2 3 3 1 NWU ENU (1 + D) 1 Case 1 H = 1 m LCN 4 Case 1 Case 2 Case 3 Case 4 Case 3 LCN 3D R 1 R 2 R 3 0.53 0.30 T = 2.48 ± 0.30 mm, D = (0.5 ± 2.4) 10 6, 0.77 0.36 0.000 010 0 0.000 003 8 = 0.002 999 2 ± 0.000 003 1 rad, U 0 = 6 372 483.339 20 m, 0.268 271 3 0.000 002 4 0.265 701 081 93 0.855 941 858 15 0.443 583 668 02 R TOP = 0.439 831 672 92 0.517 072 079 57 0.734 291 879 31. (2) 0.857 875 885 28 0.000 000 000 00 0.513 856 950 38 4 3 mm
252 32 4 X/m Y /m Z/m A1 0.0005 0.0025 0.0008 A2 0.0016 0.0009 0.0005 A3 0.0003 0.0002 0.0010 A4 0.0019 0.0014 0.0012 3.2 LCN A1 A4 LCN ( ) LCN LCN LCN LCN 2013 7 7 8 11 4 (v 20130707) 9 13 120 150 188 4 (h 20130713 120 h 20130709 150 h 20130713 188) LCN 5 wrms 0.5 as 0.2 km (LCN ) 0.5 mm 0.1 mm 5 /as /as /mm v 20130707 0.40 0.18 0.05 11 / h 20130713 120 0.28 0.15 0.00 8 120 h 20130709 150 0.30 0.02 0.04 10 150 h 20130713 188 0.19 0.27 0.05 9 188 [11 14] 1/4 [15] ( )
2 65 m 253 (x c, y c, z c ) σ (xc,y c,z c) n(n x, n y, n z ) 6 2 v 20130707 h 20130709 150 6 (x c, y c, z c )/m σ (xc,yc,z c)/mm n(n x, n y, n z ) v 20130707 118.867 3 27.889 6 55.839 2 0.03 0.03 0.00 0.000 06 0.000 12 1.000 00 118.867 4 27.889 0 45.182 3 0.03 0.03 0.00 0.000 01 0.000 09 1.000 00 118.866 7 27.888 4 21.680 2 0.02 0.03 0.00 0.000 02 0.000 05 1.000 00 118.866 6 27.888 6 4.842 4 0.02 0.02 0.00 0.000 01 0.000 02 1.000 00 h 20130713 120 113.016 4 21.978 2 35.241 7 0.58 0.57 0.13 0.703 35 0.710 85 0.000 05 115.969 2 24.963 3 35.241 1 0.57 0.56 0.13 0.703 39 0.710 81 0.000 04 121.991 0 31.047 4 35.240 9 0.50 0.49 0.15 0.703 34 0.710 85 0.000 02 124.939 7 34.025 3 35.240 1 0.40 0.40 0.11 0.703 37 0.710 82 0.000 03 h 20130709 150 117.323 8 19.740 3 35.239 9 0.35 0.07 0.09 0.185 50 0.982 65 0.000 05 118.098 7 23.842 2 35.239 3 0.49 0.09 0.09 0.185 58 0.982 63 0.000 08 119.692 1 32.263 9 35.239 1 0.37 0.07 0.07 0.185 65 0.982 62 0.000 06 120.464 7 36.369 9 35.239 8 0.39 0.07 0.12 0.185 67 0.982 61 0.000 09 h 20130713 188 122.148 8 20.246 3 35.240 6 0.83 0.36 0.31 0.395 54 0.918 45 0.000 01 120.487 7 24.106 2 35.241 2 0.60 0.26 0.20 0.395 60 0.918 42 0.000 04 117.104 1 31.961 7 35.240 5 0.52 0.23 0.19 0.395 50 0.918 47 0.000 06 115.445 4 35.815 6 35.241 4 0.56 0.24 0.21 0.395 58 0.918 43 0.000 07 2 (a) v 20130707 (b) h 20130709 150
254 32 v 20130707 7 wrt p wrt c ( ) ( ) 1 mm 7 v 20130707 mm 1 2 3 4 wrt p wrt c wrt p wrt c wrt p wrt c wrt p wrt c 0.8 0.2 1.3 1.9 0.8 0.7 1.0 0.7 0.5 0.6 1.2 0.3 1.2 0.1 0.2 0.2 0.4 1.2 0.3 1.1 0.9 0.0 0.7 0.1 0.7 0.4 1.5 0.1 1.0 0.0 0.3 0.4 0.5 0.1 1.0 0.2 1.1 0.1 0.2 0.4 1.8 0.3 0.0 0.8 0.6 0.5 0.5 0.1 1.1 0.3 0.4 1.1 1.1 0.2 0.2 0.9 1.3 0.5 0.3 2.4 0.2 0.9 1.4 0.5 0.6 0.5 0.2 1.2 0.8 0.1 0.7 0.4 0.1 0.5 0.1 0.5 0.4 0.5 0.3 0.2 0.8 0.0 0.8 0.5 0.2 0.5 0.0 0.8 6 ( ) [15] 6 n z x y LCN v 1 v 2 { v1 = (118.866 07 27.890 86 55.839 17) T m ± (0.03 0.03 0.00) T mm v 2 = (118.867 43 27.887 22 4.842 36) T m ± (0.02 0.02 0.00) T mm. (3) h 20130709 150 LCN h 1 h 2 { h1 = (117.324 57 19.740 16 35.238 87) T m ± (0.34 0.11 0.09) T mm h 2 = (120.465 55 36.369 75 35.240 04) T m ± (0.37 0.12 0.12) T mm. (4) (3) (4) w ( )f { w = (118.866 62 27.889 39 35.239 44) T m ± (0.02 0.02 0.00) T mm. (5) f = (2.79 ± 0.25) mm
2 65 m 255 LCN x 118.866 6 0.03 y = 27.889 4 m ± 0.03 mm. z 35.240 1 0.00 (1) (2) ITRF2008 3D X 2 826 708.604 5 0.42 Y = 4 679 237.054 2 m ± 0.45 mm. Z 3 274 667.531 4 0.43 WGS84 l p h l E121 08 09.121 p = N31 05 31.031. h 49.142 m GPS 2013 6 29 UTC0h 120 150 188 3 f f = (2.95 ± 3.26) mm. (6) 3 mm 4 LCN GPS 1 2 as 0.01 mm GPS LCN 0.5 mm GPS 3 mm( 4) 0.5 as LCN 0.5 mm 0.1 mm 1 mm 65 m ITRF2008 1 mm 3 mm LCN 3D
256 32 65 m 3D 65 m 1 mm A A1 x y z xyz a a â ( ) a = [x, y, z] a = a[cos α cos δ, sin α cos δ, sin δ] R x (R 1 ) x R 1 A2 xyz a = a[cos α cos δ, sin α cos δ, sin δ] â z a xy x xyz R R R = R z (0)R y (π/2 δ)r z (α) R = R T = R z ( α)r y (δ π/2)r z (0). (a1) A3 r i i = 1, 2,, n (a1) z z w x y (x i, y i ) i = 1, 2,, n (x w, y w ) r w 2(x w x i )dx w + 2(y w y i )dy w 2r w dr w = rw 2 (x i x w ) 2 (y i y w ) 2. (a2) c = (x w, y w, z w ) c = (x c, y c, z c ) A4 3D r 1 r 2 r 3
2 65 m 257 (r 2 r 1 ) (r 3 r 2 ) n = (n x, n y, n z ) n z x y (x w, y w ) z z w1 z w2 (x w, y w, z w1 ) (x w, y w, z w2 ) a 1 = (x 1, y 1, z 1 ) a 2 = (x 2, y 2, z 2 ) A5 AB CD A(x a, y a, z a ) B(x b, y b, z b ) C(x c, y c, z c ) D(x d, y d, z d ) AB M(x m, y m, z m ) CD N(x n, y n, z n ) AM = pab CN = qcd x m = p(x b x a ) + x a y m = p(y b y a ) + y a, z m = p(z b z a ) + z a x n = q(x d x c ) + x c y n = q(y d y c ) + y c. (a3) z n = q(z d z c ) + z c MN AB = 0 MN CD = 0 { q = (ab ce)/(cd aa) p = (bd ae)/(cd aa), (a4) a = CD AB b = AC AB c = AB AB d = CD CD e = AC CD (a4) (a3) A6 (1) (2) z z z z w (3) z w x y (x w, y w ) (4) (x w, y w, z w ) [1] Altamimi Z, Collilieux X, Métivier L. J Geod, 2011, 85: 457 [2] Dawson J, Sarti P, Johnston G, et al. J Geodesy, 2007, 81: 433 [3] Sarti P, Sillard P, Vittuari L. J Geodesy, 2004, 78: 210 [4] Sarti P, Abbondanza C, Petrov L, et al. J Geodesy, 2011, 85: 1 [5] Sovers O J, Fanselow J L. Rev. Mod. Phys., 1998, 70: 1393 [6] Losler M. J Appl Geodesy, 2008, 2: 233 [7] Losler M. J Surv Eng, 2009, 135: 131 [8] Li Jinling, Zhang Jinwei, Guo Li. Sci China-Phy Mech Astron, 2013, DOI: 10.1007/s11433-013-5171-9
258 32 [9],,., 2010, 35: 1387 [10],,., 2010, 35: 76 [11],., 2006, 27: 90 [12],,., 1998, 18: 78 [13],,., 2004, 25: 604 [14],., 2008, 28: 92 [15],,., 2010, 35: 69 Local Survey of Shanghai Tianma 65-m Radio Telescope LI Jin-ling 1, XIONG Fu-wen 2, YU Cheng-lei 3, ZHANG Jin-wei 1,4, GUO Li 1, FAN Qing-yuan 1 (1. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China; 2. Shanghai Institute of Geological Survey, Shanghai 200072, China; 3. Shanghai Technical Center of Leica Geosystems, Shanghai 201203, China; 100049, China) 4. University of the Chinese Academy of Sciences, Beijing Abstract: A geodetic local survey was implemented at the newly constructed Shanghai Tianma 65-m radio telescope. The geocentric three-dimensional coordinates of the reference point of this telescope in the precision of millimeters (formal error) were determined, and the axis-offset was shown not significant on the precision level of 3 mm. Specifically, the coordinates of the reference point in ITRF2008 are as follows, X 2 826 708.604 5 0.42 Y = 4 679 237.054 2 m ± 0.45 mm. Z 3 274 667.531 4 The reference epoch is taken as UTC 0h, 29 June 2013. The axis-offset f is determined as the following, f = (2.95 ± 3.26) mm. The outcome provides important reference to the subsequent activities of antenna maintenance and scientific application, including the establishment of precise antenna orientation model, orientation guidance, fringe searching in data cross-correlation, analysis and application studies of VLBI observations. It is also important archive data for monitoring possible subsidence and lateral displacement of antenna foundation as well as deformation of antenna tracking-rail and structure. 0.43 Key words: VLBI; GPS; reference point; axis-offset; local survey