30 4 Vol. 30, No. 4 2012 11 PROGRESS IN ASTRONOMY Nov., 2012 1000-8349(2012)04-501-17 GNSS 1,2 2 1 ( 1. 100036 2. 200030 ) GNSS LEO GPS GNSS LEO P128 A 1 GNSS GNSS, ARP (PCO) (PCV) GNSS GNSS GNSS GNSS 4 GNSS 3 2012-03-12 2012-06-07 (11173048 10873029) (06DZ22101)
502 30 2 GPS ( ) L1 L2 LC ( ) PCV 2.1 2.1.1 GNSS GNSS PCO v = Ax b. (1) A (3) x PCO b v x = (A T PA) 1 (A T Pb), (2) P 2.1.2 1 [1] 90
4 GNSS 503 90 90 180 270 i ( x i, y i ) ARP (x 0, y 0 ) (x 1, y 1 ) (x 2, y 2 ) x 1 = x 0 x 1 + x 2 y 1 = y 0 y 1 + y 2 x 5 = x 0 + x 2 + y 1 y 5 = y 0 + y 2 x 1 x 2 = x 0 x 1 y 2 y 2 = y 0 y 1 + x 2 x 6 = x 0 + x 2 + x 1 y 6 = y 0 + y 2 + y 1 x 3 = x 0 x 1 x 2 y 3 = y 0 y 1 y 2 x 7 = x 0 x 2 y 1 y 7 = y 0 + y 2 + x 1 (3) x 4 = x 0 x 1 + y 2 y 4 = y 0 y 1 x 2 ( x i, y i ) (i =1,2,,7) (x 0, y 0, x 1, y 1, x 2, y 2 ) (1) (2) (x 1, y 1 ) (x 2, y 2 ) 1 [1] 0 2.2 30 min
504 30 2 [2] 2 [2] A B H A H B A B h A h A δh A δh B (U A ) i,j (U B ) i,j A B i = 1, 2, 3, 4 j = 1, 2 H AB = H B H A = [(U B ) 1,1 h B δh B ] [(U A ) 1,1 h A δh A ], (4) H AB = H B H A = [(U B ) 1,2 h B δh A ] [(U A ) 1,2 h A δh B ], (5) δh B δh A = 1 2 {[(U B) 1,1 (U A ) 1,1 ] [(U B ) 1,2 (U A ) 1,2 ]}. (6) h AB = δh B δh A ( U AB ) i,j = (U B ) i,j (U A ) i.j ( U AB ) i,j i A B h AB = δh B δh A = 1 2 ( 1)i 1 [( U AB ) i,1 ( U AB ) i,2 ]. (7) 4 h AB 2.3
4 GNSS 505 3 [3] 3 [3] 2.4 [4] (ARP) 15 24 h L1 L2 LC PCO
506 30 4 ARP (PCV) GNSS PCO PCV 3 GNSS 3 (PCV) 70% 3.1 [5,6] GPS GNSS GPS PCV 1994 3.2 AOAD/M T PCVs 0 [7] ( ) PCV PCV PCV 3.2.1 PCV PCV L1 L2 LC PCV [4] PCO PCV i = τ i + α 1 θ i + α 2 θ 2 i + α 3 θ 3 i + α 4 θ 4 i, (8) i θ i α i τ i
4 GNSS 507 PCV PCV PCV z 90 0 PCV(z = 90 ) = 0. (9) RMS 3.2.2 PCV 24 h GNSS [8] PCV PCV [4,8] L1 t 1 ( 1) i Φ i 1(t 1 ) =ρ i 1(t 1 ) c dt 1 + c dt i + c f L1 N i 1(1) i 1,ion(t 1 )+ i 1,trop(t 1 ) + d 1 (t 1 ) + d i (t 1 ) + PVC 1 (θ i (t 1 )), Φ i 1 t 1 ρ i 1(t 1 ) c dt 1 (GPS ) dt i (GPS ) f L1 L1 N i 1(1) L1 i 1,ion(t 1 ) L1 i 1,trop(t 1 ) L1 d 1 (t 1 ) d i (t 1 ) PCV 1 (θ i (t 1 )) L1 PCV θ i (t 1 ) i t 1 ( 2) Φ i 2(t 1 ) =ρ i 2(t 1 ) c dt 2 + c dt i + c f L1 N i 1(1) i 2,ion(t 1 )+ i 2,trop(t 1 ) + d 2 (t 1 ) + d i (t 1 ) + PVC 2 (θ i (t 1 )). (10) (11) SD SD i 1 2(t 1 ) = ρ i 1 2(t 1 ) c dt 1 2 + (10) (11) c f L1 N i 1 2(1) + d 1 2 (t 1 ) + PVC 1 2 (θ i (t 1 )). (12) dt i d i (t 1 ) ( i 1,ion (t 1) i 2,ion (t 1)) ( i 1,trop(t 1 ) i 2,trop(t 1 )) PCV PCV 1 2 (θ i (t 1 )) = α 0 + α 1 (θ i (t 1 )) + α 2 (θ i (t 1 )) 2 + α 3 (θ i (t 1 )) 3 + α 4 (θ i (t 1 )) 4. (13) ( 1) ( 2) j j
508 30 SD j 1 2(t 1 ) =ρ j 1 2(t 1 ) c dt 1 2 + c f L1 N j 1 2(1) + d 1 2 (t 1 )+ α 0 + α 1 (θ j (t 1 )) + α 2 (θ j (t 1 )) 2 + α 3 (θ j (t 1 )) 3 + α 4 (θ j (t 1 )) 4. (14) ρ i 1 2(t 1 ) ρ j 1 2(t 1 ) t 1 1 2 i j DD1 2(t i j 1 ) = + c N f 1 2(1) i j + α 1 [(θ i (t 1 )) (θ j (t 1 ))] + α 2 [(θ i (t 1 )) 2 (θ j (t 1 )) 2 ]+ L1 α 3 [(θ i (t 1 )) 3 (θ j (t 1 )) 3 ] + α 4 [(θ i (t 1 )) 4 (θ j (t 1 )) 4 ]. (15) t 2 1 2 i j DD1 2(t i j 2 ) = + c N f 1 2(1) i j + α 1 [(θ i (t 2 )) (θ j (t 2 ))] + α 2 [(θ i (t 2 )) 2 (θ j (t 2 )) 2 ]+ L1 α 3 [(θ i (t 2 )) 3 (θ j (t 2 )) 3 ] + α 4 [(θ i (t 2 )) 4 (θ j (t 2 )) 4 ]. (16) L1 (16) (15) T D i j 1 2(t 2 1 ) = +α 1 A i j 1 (t 2 1 ) + α 2 A i j 2 (t 2 1 ) + α 3 A i j 3 (t 2 1 ) + α 4 A i j 4 (t 2 1 ), (17) A i j 1 (t 2 1 ) = [(θ i (t 2 )) (θ j (t 2 ))] [(θ i (t 1 )) (θ j (t 1 ))], (18) A i j 2 (t 2 1 ) = [(θ i (t 2 )) 2 (θ j (t 2 )) 2 ] [(θ i (t 1 )) 2 (θ j (t 1 )) 2 ], (19) A i j 3 (t 2 1 ) = [(θ i (t 2 )) 3 (θ j (t 2 )) 3 ] [(θ i (t 1 )) 3 (θ j (t 1 )) 3 ], (20) A i j 4 (t 2 1 ) = [(θ i (t 2 )) 4 (θ j (t 2 )) 4 ] [(θ i (t 1 )) 4 (θ j (t 1 )) 4 ]. (21) (17) K N 4 = TD N 1 = K N 4 α 4 1, A i j 1 (t 2 1 ) A i j 2 (t 2 1 ) A i j 3 (t 2 1 ) A i j 4 (t 2 1 ).. A i j 1 (t n (n 1) ) A i j 2 (t n (n 1) ) A i j 3 (t n (n 1) ) A i j 4 (t n (n 1)).., (22) α 4 1 = [α 1 α 2 α 3 α 4 ] T, (23) α = (K T K ) 1 (K T TD). (24)
4 GNSS 509 PCV PCV PCV PCV 1 cm [8] 1996 6 30 IGS PCVs 0 Wubbena [9,13] 3.3 20 90 Geo++ [10,11] GPS ( ) GPS, ( PCV ) ( PCV [12] ) PCVs Φ j i = ρj i (t) c dt i + c dt i + λ N j i j ion,i + j trop,i + j MP,i + dj PCV,i + ε. (25) [10,13] δ SID δ SID Φ j i = c (δsid dt i δ SID dt j ) + λ δ SID N j i δsid j ion,i + δsid j trop,i + δsid ε. (26) PCV δ SID Φ j,m i,k = λ δsid N j,m i,k + δsid ε. (27) 180 δ SID Φ j i = c (δsid dt i δ SID dt j )+λ δ SID N j i δsid j ion,i +δsid j trop,i +d(0,0),j PCV,i d(α,z),j PCV,i +δsid ε, (28)
510 30 δ SID Φ j,m i,k = λ δsid N j,m i,k d PCV PCV + δsid ε + d j,m PCV,i,k, (29) α j = α i + α z j = z i + z d PCV (α i, z i, α, z) = d PCV (α i, z i ) d PCV (α j, z j ), (30) PCV PCO PCV ANTEX ( 4.1 ) 3.4 PCV 2006 11 5 IGS 11 6 IGS GFZ TUM 10 GPS 1994 IGS PCVs AOAD/M T PCV GPS VLBI SLR GPS 15 10 9 [5,14] 15 10 9 10 cm [14] IGS 5 10 IGS 1 10 9 2 10 9 VLBI SLR [5] 90 0 PCVs PCVs PCVs 10 PCVs PCVs
4 GNSS 511 1 mm [24] PCVs PCVs PCVs IGS 2006 4 GNSS GNSS PCV [15] 4.1 PCV PCO PCV PCO 4 4 PCVs PCVs 4 z z [16] sin(z ) = R sin(z), (31) r
512 30 R r 0 90 0 14.28 ( ) z max Rmax = arcsin sin(z max ). (32) r min PCO PCV [16] φ (z ) = φ(z). (33) φ (z ) = φ(z). (34) z ( ) r φ (z ) = r(1 cos z ). (35) PCO PCV PCV PCO PCV PCO PCV PCO PCO APR [17] PCO PCV GPS PCO PCV PCO PCV raw PCV [18,19] 4.2 PCO PCV [16,20] IGS ( ) [21] PCO PCV [21] IGS PCO PCV LC ( ) w = cos 2 z(z ), PCV
4 GNSS 513 ( raw PCV) GFZ TUM [19] 14 6 ( Neill 3 h ) 15 PCV (0 14 1 ) raw PCV PCO PCVs PCV PCV raw PCV [16] [16] 14 z =0 PCV raw (z ) = 0. (36) PCV raw (z = 0 ) = 0. (37) raw PCV PCV PCO PCV PCV [18,19] PCV PCO z PCV raw (z ) = PCV(z ) + z (1 cos z ). (38) PCV z [PCV raw (z ) a i z (1 cos z )] 2 = min (j = 1, 2,, 14). (39) j a i PCV raw (z ) i PCV PCV PCO PCV PCO PCV PCO PCV PCV PCV 5 [16] PCV PCV PCV [16,21] PCV (1) GNSS (2) PCV ( ) PCV n max n PCV(α, z) = (a nm cos mα + b nm sin mα)p nm (cos z), (40) n=0 m=0
514 30 5 PCV Block IIR PCV [16] PCV(α, z) α z p nm a nm b nm n m PCV n m a nm b nm n m( n max = m max = 8) a nm b nm PCV x y z 4.3 LEO GPS LEO GPS 500 1000 km 17 14 GPS LEO GPS GPS LEO LEO GPS igs08.atx [22] GPS PCO PCV 14 GPS [23] 14 LEO GPS PCVs LEO PCVs 5 5 LEO LC GPS PCV [24]
4 GNSS 515 (Φ orb Φ model ) = PCV true (e) PCV model (e) = PCV(e), (41) e LEO GPS LEO GPS 14 PCV igs08.atx PCV 2 3 mm GPS PCV 1 mm LEO PCV igs08.atx 14 PCV LEO GPS LEO [23] LEO GPS 5 GNSS 3 PCVs PCVs PCV PCV GPS 14 LEO GPS 500 1300 km 17 SVN714 L2 [20] PCV [20,25] R714 PCV PCV [26] PCV PCVs GNSS ( GPS ) GPS [1],., 2000, (12): 15 [2]., 2000, 2(3): 23 [3] Bányai L. Journal of Geodesy, 2005, 79(4): 222 [4] Mader G L. GPS Solutions, 1999, 1: 55 [5] Rothacher M, Schaer S, Mervart L, et al. SPECIAL TOPICS AND NEW DIRECTIONS, Gendt G, Dick G, eds. Germany GFZ 1995 205
516 30 [6] Rothacher M. GPS Solutions, 2001, 4(4): 55 [7] Rothacher M, Mader G. Estimation and validation of IGS absolute antenna phase center variations, http://www.aiub.unibe.ch/download/igs 01.txt, 1996 [8] Daniel N A, Andrew R, Barbara A O, et al. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, 2005, 54(5): 1820 [9] Schmitz M, Wubbena G, Boettcher G, et al. GPS Solutions, 2002, 6: 18 [10]., 2010, (3): 7 [11] Dach R, Schmid R, Schmitz M, et al. GPS Solutions, 2011, 15: 49 [12] Akrour B, SanterreR, Geiger A. GPS world, 2005, 16(2): 49 [13] Wubbena G, Menge F, Schmitz M, et al. Proc Int Tech Meet ION GPS-96, Kansas City, Missouri, 1996: 1205 [14] Zhu Y, Massmann H, Yu Y,et al. J Geod, 2003, 76(11): 668 [15] Mader G L, Czopek F M. GPS World, 2002, 13(5): 40 [16] Schmid R, Rothacher M. Journal of Geodesy, 2003, 77(7): 440 [17] Rothacher M, Schaer S, Mervart L, et al. IGS Workshop, Germany:GFZ Potsdam, 1995: 205 [18] Ge M, Gendt G, Meindl M. eds. Bern: Proceedings of the IGS Workshop and Symposium 2004, 2005 [19] Schmid R, Steigenberger P, Gendt G, et al. J Geod, 2007, 81: 781 [20] Dilssner F, Springer T, Flohrer C, et al. Journal of Geodesy, 2010, 84(8): 467 [21] Dach R, Hugentobler U, Fridez P, et al. Bernese GPS Software, version 5.0, University of Berne: Astronomical Institute, 2007: 355 [22] ftp://garner.ucsd.edu/pub/gamit/tables/igs08.atx, 2012 [23] Jaggi A, Dach R, Bock H, et al. Combining terrestrial and LEO data to extend the GPS satellite antenna patterns to nadir angles beyond 14, http://www.iapg.bv.tum.de/mitarbeiter/, 2011 [24] Montenbruck O, Garcia-Fernandez M, Yoon Y, et al. GPS Solutions, 2009, 13(1): 23 [25] ftp://garner.ucsd.edu/pub/gamit/tables/antmod.dat, 2012 [26] Schmitz M, Wubbena G, Boettcher G. GPS Solutions, 2002, 6: 18 Research on Calibration Methods of GNSS Antenna Phase Center Offsets and Variations LI Xiao-bo 1,2, WANG Xiao-ya 2, REN Jin-wei 1 (1. Institute of Earthquake Science China Earthquake Administration, Beijing 100036, China; 2. Shanghai Astronomical Observatory, Chinese Academy of sciences, Shanghai 200030, China) Abstract: GNSS measurement, including pseudo-range and carrier phase observation, is the distance between phase center of satellite antenna and phase center of receiver antenna. Satellite mass center and receiver antenna reference point (ARP) are used as reference in GNSS data processing. Consequently, the antenna phase center correction should be considered in GNSS data processing. GNSS antenna phase center correction including mean phase center offset with respect to the ARP or the mass of satellite, i.e. PCO, and the variation to the mean phase center with respect to the satellite elevation and azimuth angle, i.e. PCV. In general, the same type
4 GNSS 517 of antennas have similar PCO and PCV. This paper summarizes the methods of calibrating GNSS antenna phase center offsets and variations. In addition, the calibration of on-orbit GNSS satellite antenna phase center variation is described. PCVs are highly correlated with PCOs, the so-called daily raw PCVs are normally estimated together with other parameters including site coordinates, site-specific troposphere parameters, orbit parameters and Earth rotation parameters etc. Afterwards, the raw PCV estimates are separated into PCOs and PCVs under the assumption that PCV is the flattest by the least-square fit. The calibration of the on-orbit GPS satellite antenna PCV by LEO observations is described as well. It extends the maximum nadir angle up to 17 by establishing the un-differential carrier phase residuals. Key words: GNSS; calibration; antenna phase center offset; antenna phase center variation; LEO.......................................................................................... 2013 2013 2 5 8 11 40 160 2013 CN 31-1340/P 4-819