GPS GPS(Global Positioning System) GPS GPS 1 GPS GPS GPS I II 1994 ( 1991 ) 1
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1 GPS GPS(Global Positioning System) GPS GPS 1 GPS GPS GPS I II 1994 ( 1991 ) 1
2 1: GPS 1.1 GPS GPS c = m/sec (1) ( ) GPS 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
3 r 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
4 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) GPS GPS 1.2 GPS m 10 n sec (10 8 sec 1 1 ) ( ) 1 =86400 sec) sec = sec (7) sec m/sec = 25.9m (8) 4
5 m 2 ( ) GPS 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
6 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 / (10 18 [sec] 1 )
7 2 ν Cs = 9, 192, 631, 770Hz (12) 2.2 (Cs) 133 Cs (6S ) 133 Cs I = 7/2 6S F = 4, ( ) 2 (Ramsey) [4] 2 t (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 )
8 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
9 3 ( )[5] 3.1 GPS GPS UTC( ) 1. ( ) GPS GPS 2. (2 ) U/c 2 = (14) GPS (3.874 km/sec) GPS (v/c) 2 /2 = (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
10 3.2.1 (Sagnac) ECEF (Earth-Centered Earth-Fixed) GPS ( 70 m sec) m GPS (16) ±10 m GPS TOPEX/Poseidon [2] GPS GPS 16 3 NASA (Center National d Etudes Spatiales: CNES) 10
11 km D iono [m] D iono = 40.3N e f 2, (17) f N e % 4.3 GPS GPS 4.4 GPS GPS GPS 11
12 5 GPS GPS 5.1 (space segment) GPS ) 55 26,562 km( 20,200 km) ( 0.01 ) GPS 1989 GPS II,IIA 2 (Cs) ( ) 2 (Rb) GPS IIR 3 (Rb) MHz 154 ( GHz L1 ) 120 ( 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
13 GPS (USNO: US Navy Observatory) GPS 20 n sec [2] 5.3 (user segment) 3 3 GPS 4 GPS 4 GPS GPS GPS P ( ) C/A ( ) GPS GHz(L1 ) GHz (L2 ) 2 2 L1 50% (PSK:Phase Shift Keying) GPS P ( 6 16m, L1,L2 ) C/A ( m L1 ) (SA:Selective Availability) SA 13
14 SA C/A 5 20m [6] SA SA DGPS ( ) SA C/A Mbps; 1msec P Mbps; DGPS(Differential GPS) GPS GPS GPS C/A ( km ) m GPS(Differential GPS) DGPS SA GPS ( ) 10 km 2 mm GPS 1/100 GPS GPS [1] 2 14
15 GPS 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
16 ,510 km GLONASS Galileo(EU) Galileo (EU) (ESA: European Space Agency) Galileo GIOVE-A Galileo GPS GLONASS Galileo ,000 km( 23,616 km) GPS 5 20 m Galileo m 4 m Galileo M Hz(E5 ) M Hz(E6 ) M Hz(L1 ) 3 (Open Service, OS) M Hz(E5 ) M Hz(L1 ) 4 m 8 m 16
17 (encrypted Commercial Service, CS) (1 m ) M Hz(E5 ) M Hz(E6 ) M Hz(L1 ) 3 3 RTK) TCAR(Three-Carrier Ambiguity Resolution) Galileo EU Galileo Galileo Galileo Galileo Galileo
18 ( 0.1 ) GPS L1 L2 E6 L GPS DGPS GPS GPS GPS (SBAS) WAAS SBAS( GPS ) EGNOS SBAS MSAS SBAS 6 (MTSAT-1R) (MTSAT-2)
19 [1] ( ISBN: ) [2] GPS [3] J.J.Sakurai, [4] ( ISBN: ) [5] Neil Ashby, Relativity in the Global Positioning System, Living Rev. Relativity 6, (2003), 1. [Online article] [6] GPS ( ISBN: ) 19
GPS 1 2 GPS 29 GPS II IIA IIR 3 2 km GPS GPS 3 ID GPS 4 GPS GPS X Y GPS 1575:42 MHz L1 C/A coarse/acquisition code C/A SPS; standard po- 1:
A1 GPS/GNSS sakai@enrigojp A11 GPS GPS GPS { 29 GPS 6 10 13 m 95% GPS GLONASS Galileo GNSS global navigation satellite system GPS GPS GPS 2005 9 IIR-M L2C SBAS satellite-based augmentation system WAAS
Tokyo University of Marine Science and Technology Laboratory of Satellite Navigation Engineering Tokyo University of Marine Science and Technology GNS
GNSS DGPSSBAS MSAS SBAS/MSAS MSAS LEX GPS 4 7.5 26,561km 121158 2 55 L1=1,575.42MHz (10.23MHz154) L2=1,227.6MHz (10.23MHz120) C/A Code (1.023MHz : 1023 chips)l1 P(Y) codel1l2 3 GPS P(Y) P(Y) C/A M P(Y)
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005 GPS 107 000 GPS (Global Positioning System) GPS GPS GPS GPS GPS 1 GPS GPS 3 GPS GPS 1GPS GPS GPS 1 1.1 GPS.1.1 GPS.1. GPS 3.1.3 9.1.4 11.1.5 13. 14..1 14.. 14..3 15..4 17 1) 17 ) 17 3) 18..5 19.4 GPS
最 新 測 量 学 ( 第 3 版 ) サンプルページ この 本 の 定 価 判 型 などは, 以 下 の URL からご 覧 いただけます. このサンプルページの 内 容 は, 第 3 版 1 刷 発 行 時 の
最 新 測 量 学 ( 第 3 版 ) サンプルページ この 本 の 定 価 判 型 などは, 以 下 の URL からご 覧 いただけます. http://www.morikita.co.jp/books/mid/047143 このサンプルページの 内 容 は, 第 3 版 1 刷 発 行 時 のものです. 3 10 GIS 3 1 2 GPS GPS GNSS GNSS 23 3 3 2015
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図 -2 測位方式の概念図 RTK-GPS: Real Time Kinematic GPS 2 図 D-GPS RTK-GPS cm 1ms GPS CDMA 巻 8 号情報処理 2002 年 8 月 - 2 -
1 RTK-GPS 柳原 徳久 (株)日立製作所 n-yanagi@gm.merl.hitachi.co.jp 初本慎太郎 (株)日立産機システム hatsumoto-shintarou@ice.hitachi.co.jp 日本ではカーナビゲーションが広く普及しており 新車への装着率は約 30 に達している カーナビの位置検 出には GPS Global Positioning System が用いられていることはよく知られている
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.5 GPS の誤差 1NInst:0-31 ( ) 測定値が真値に対して一定方向に偏っている誤差 ( 計測によって修正 ( 校正 ) できる ) ( ) 測定値がはっきりしない原因によって真値の付近でばらつく誤差 ( 修正 ( 補正 ) できない. 数回の観測の平均など ) ( ) 計器の表示の読み違えなどによる誤差 ( 計測者の技量等にも依存する. 間違えに気づいたときは再計測する ) 誤差の要因
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