GPS 21 6 10 GPS(Global Positioning System) GPS GPS 1 GPS 24 28 GPS GPS 4 1970 I 1978 1985 10 1989 II 1994 ( 1991 ) 1
1: GPS 1.1 GPS GPS c = 2.99792458 10 8 m/sec (1) ( ) GPS 1.1.1 GPS GPS t t [sec] t r [sec] r[m] c[m/sec] r = c(t r t t ) (2) GPS (N ) i GPS r i [m] GPS (x, y, z) i GPS (x i, y i, z i ) r 2 i = (x i x) 2 + (y i y) 2 + (z i z) 2 (3) 2
r 1 1 3 r 3 r 2 2 2: r 2 1 = (x 1 x) 2 + (y 1 y) 2 + (z 1 z) 2 r 2 2 = (x 2 x) 2 + (y 2 y) 2 + (z 2 z) 2 r 2 N = (x N x) 2 + (y N y) 2 + (z N z) 2 (4) (x, y, z) 2 3
1.1.2 GPS i GPS r i [m] δ[sec] (pseudo-range) r i[m] r i = r i + cδ (5) (r 1 cδ) 2 = (x 1 x) 2 + (y 1 y) 2 + (z 1 z) 2 (r 2 cδ) 2 = (x 2 x) 2 + (y 2 y) 2 + (z 2 z) 2 (r N cδ) 2 = (x N x) 2 + (y N y) 2 + (z N z) 2 (6) (x, y, z, δ) 4 4 4 GPS GPS 1.2 GPS m 10 n sec (10 8 sec 1 1 ) 10 12 (1 1 3 1 ) 1 =86400 sec) 8.64 10 4 sec 10 12 = 8.64 10 8 sec (7) 8.64 10 8 sec 3 10 8 m/sec = 25.9m (8) 4
m 2 ( ) GPS 10 12 10 13 2 E 1, E 2 ν [3] ν = (E 2 E 1 )/h (9) h (Planck) (Heisenberg) t E [3] t E h (10) 9) E = h ν ν = (2π t) 1 (11) t 1 5
2.1 1 (1/2) L S = 1/2 J J = L + 1/2, L 1/2 L 0 0 LS I I = 0 I = 1/2, 3/2, 5/2,... I = 1, 2, 3,... I S = 1/2 F F = I + 1/2 F = I /2 2 2 1. 2. (10 18 [sec] 1 ) 3. 1 6
2 ν Cs = 9, 192, 631, 770Hz (12) 2.2 (Cs) 133 Cs (6S ) 133 Cs I = 7/2 6S F = 4, 3 100 ( ) 2 (Ramsey) [4] 2 t 1 2 2.3 (Rb) 87 Rb (5S ) ν 87Rb = 6, 834, 682, 612.8Hz (13) 87 Rb I = 3/2 5S F = 2, 1 2 [4] (5S 5P ) 3 2 2 1967 7
87 Rb 5S F = 2, 1 F = 1 5P F = 1 5P 5P F = 2, 1 F = 1 F = 2 F = 2 3 F = 1 F = 2 F = 1 F = 2 [4] 5P 5S F=2 F=1 3: 3 (Ne, Ar, Kr, N 2 ) Rb 1 8
3 ( )[5] 3.1 GPS GPS 4.45 10 10 UTC( ) 1. ( ) GPS GPS 2. (2 ) U/c 2 = 5.27 10 10 (14) GPS (3.874 km/sec) GPS (v/c) 2 /2 = 8.4 10 11 (15) ECI(Earth-Centered Inertial system) v dτ dt dτ ( 1 + U c 2 v2 2c 2 ) dt (16) GPS (16) 3.2 GPS GPS 2 [2] 9
3.2.1 (Sagnac) ECEF (Earth-Centered Earth-Fixed) GPS ( 70 m sec) m 3.2.2 GPS (16) 0.0015 ±10 m GPS TOPEX/Poseidon 3 1995 [2] GPS 4 4.1 GPS 16 3 NASA (Center National d Etudes Spatiales: CNES) 10
4.2 50 1000 km D iono [m] D iono = 40.3N e f 2, (17) f N e 2 1 50 % 4.3 GPS GPS 4.4 GPS GPS GPS 11
5 GPS GPS 5.1 (space segment) 24 28 GPS 60 6 1 4 5 ) 55 26,562 km( 20,200 km) ( 0.01 ) 11 58 GPS 1989 GPS II,IIA 2 (Cs) ( ) 2 (Rb) 4 1997 GPS IIR 3 (Rb) 5 10 12 10 13 10.23MHz 154 (1.57542 GHz L1 ) 120 (1.2276 GHz L2 ) 2 [1] 5.2 (control segment) GPS 5 (monitor station: Ascension Island, Colorado Springs, Diego Garcia, Kwajalein, Hawaii) 1 (master control station: Colorado Springs Schriever ) 3 (Ascension Island, Diego Garcia and Kwajalein) (2006 ) 1 GPS 4 II,IIA 5 IIR Rb 2 Cs 1 Cs Rb 3 12
GPS (USNO: US Navy Observatory) 50 1 2003 GPS 20 n sec [2] 5.3 (user segment) 3 3 GPS 4 GPS 4 GPS GPS GPS 6 6.1 P ( ) C/A ( ) GPS 1.57542 GHz(L1 ) 1.2276 GHz (L2 ) 2 2 L1 50% (PSK:Phase Shift Keying) GPS P ( 6 16m, L1,L2 ) C/A ( 40 100m L1 ) (SA:Selective Availability) 2000 5 2 SA 13
SA C/A 5 20m [6] SA SA DGPS ( ) SA C/A 1.023 Mbps; 1msec P 10.23 Mbps; 1 6.2 6.2.1 DGPS(Differential GPS) GPS GPS GPS C/A (100-200 km ) m GPS(Differential GPS) DGPS SA 6.2.2 GPS ( ) 10 km 2 mm GPS 1/100 GPS GPS 2 2 2 [1] 2 14
GPS 30 1 6.2.3 RTK GPS(Real Time Kinematic GPS) RTK GPS(Real Time Kinematic GPS) RTK GPS 10 km 7 GPS GPS 7.1 GLONASS GLONASS (Global Navigation Satellite System) GPS GPS (CDMA) GLONASS (FDMA) 15
64.5 25,510 km 3 8 24 1990 24 2004 12 4 GLONASS 2008-2010 7.2 Galileo(EU) Galileo (EU) (ESA: European Space Agency) Galileo 2000 4 2005-20012 GIOVE-A 2005 12 28 2006 2012 4 Galileo GPS GLONASS Galileo 3 30 3 56 30,000 km( 23,616 km) GPS 5 20 m Galileo m 4 m Galileo 1164 1214 M Hz(E5 ) 1260 1300 M Hz(E6 ) 1563 1591 M Hz(L1 ) 3 (Open Service, OS) 1164 1214 M Hz(E5 ) 1563 1591 M Hz(L1 ) 4 m 8 m 16
(encrypted Commercial Service, CS) (1 m ) 1164 1214 M Hz(E5 ) 1260 1300 M Hz(E6 ) 1563 1591 M Hz(L1 ) 3 3 RTK) TCAR(Three-Carrier Ambiguity Resolution) 7.2.1 2003 10 30 Galileo EU 2004 7 Galileo 2005 6 3 Galileo 2005 9 7 Galileo 2005 11 Galileo 2006 1 12 Galileo 7.3 2000 2003 7.4 1 17
( 0.1 ) GPS L1 L2 E6 L5 6 7.5 GPS DGPS GPS GPS GPS (SBAS) 7.5.1 WAAS SBAS( GPS ) 2003 7 7.5.2 EGNOS SBAS 2005 7 7.5.3 MSAS SBAS 6 (MTSAT-1R) 2005 2 7 (MTSAT-2) 2006 2 2007 3 2007 9 27 18
[1] ( ISBN:4-339-01221-1) [2] GPS 2003 6 18 [3] J.J.Sakurai, [4] ( ISBN:4-88552-085-1) [5] Neil Ashby, Relativity in the Global Positioning System, Living Rev. Relativity 6, (2003), 1. [Online article] http://relativity.livingreviews.org/articles/lrr-2003-1/index.html [6] GPS ( ISBN:4-501-32260-8) 19