1 RTK-GPS Prinile and Pratie of RTK-GPS 11 RTK-GPS 11 RTK-GPS RTK-GPS Referene Station, Base Station User Station, Remote Station, Rover Station GPS Carrier Phase 11: RTK-GPS GPS mm Ambiguity 1 RTK-GPS RTK-GPS 1
12 (1) RTK-GPS S/N A i ia (11) (1) ia = f r ia + d i + A + N ia (11) f r ia GPS A i d i i A A N 12 NovAtel In GPS RT-2 NovAtel RT-2 1 7 1 7 11 12 13 1 2 3 4 5 6 12: 13 SA 6 m 2 5 SA SA SA SA (2) GPS A 2 i j ia, ja A 2
m 8 4 4 8 1 2 3 4 5 6 13: D ija D ija = ja ia (12) 2 ia, ja (3) A, B i ia, ib i D iab D iab = ib ia (13) 2 ia, ib GPS (4) i j A,B2 GPS i ia, ib j ja, jb DD ijab (14) (1) DD ijab = ( jb ja ) ( ib ia ) (14) = ( jb ib ) ( ja ia ) GPS SA i, j A DD ijab jb ib B i, j 2 RTK-GPS SA mm 2 3
14 3 1 1 1 2 3 1 2 3 4 5 6 14: 8 mm 4 4 = 88 mm 8 1 2 3 4 5 6 15: 15 88 mm NovAtel RT-2 DOP 4 RTK-GPS 3 Cyle sli 4 Dilution of Preision 4
13 RTK-GPS - FLOAT RTK-GPS FLOAT GPS WGS-84 World Geodeti System 1984 1984 (2), xyz ECEF Earth Centered Earth Fixed z x 2 y (14) t f DD ijab(t) = (r jb (t) r ja (t)) (r ib (t) r ia (t)) + f N ijab(t) = (r jb (t) r ib (t)) (r ja (t) r ia (t)) + f N ijab(t) (15) r GPS GPS (x i (t), y i (t), z i (t)), (x j (t), y j (t), z j (t)) xyz (x B (t), y B (t), z B (t)) (15) 1 (14) (15) 1 5 s 1 t ( 1) (16) 8 f DD 12AB(t)+(r 2A (t) r 1A (t)) = (r 2B (t) r 1B (t)) + f N 12AB(t) f DD 13AB(t)+(r 3A (t) r 1A (t)) = (r 3B (t) r 1B (t)) + f N 13AB(t) >< f DD 14AB(t)+(r 4A (t) r 1A (t)) = (r 4B (t) r 1B (t)) + f N 14AB(t) (16) >: f DD 1sAB(t)+(r sa (t) r 1A (t)) = (r sb (t) r 1B (t)) + f N 1sAB(t) t 5 5
(17) 8 f DD 12AB() + (r 2A () r 1A ()) = (r 2B () r 1B ()) + f N 12AB(t) >< >: f DD 13AB() + (r 3A () r 1A ()) = (r 3B () r 1B ()) + f N 13AB(t) f DD 14AB() + (r 4A () r 1A ()) = (r 4B () r 1B ()) + f N 14AB(t) f DD 1sAB() + (r sa () r 1A ()) = (r sb () r 1B ()) + f N 1sAB(t) (17) r GPS GPS A B (x A, y A, z A ), (x B (t), y B (t), z B (t)) i i =1; 2; 3; 111;s (x i (), y i (), z i ()) t (x i (t), y i (t), z i (t)) xyz 8 r ia () = (x A x i ()) 2 +(y A y i ()) 2 +(z A z i ()) 2 >< >: r ib () = (x B (t) x i ()) 2 +(y B (t) y i ()) 2 +(z B (t) z i ()) 2 r ia (t) = (x A x i (t)) 2 +(y A y i (t)) 2 +(z A z i (t)) 2 r ib (t) = (x B (t) x i (t)) 2 +(y B (t) y i (t)) 2 +(z B (t) z i (t)) 2 (18) r 2 t n (x B;n (t), y B;n (t), z B;n (t)) 1 B i B r 1iB;n (t) = r ib;n (t) r 1B;n (t) r 1iB;n (t) q = (x B;n (t) x i (t)) 2 +(y B;n (t) y i (t)) 2 +(z B;n (t) z i (t)) 2 q (x B;n (t) x 1 (t)) 2 +(y B;n (t) y 1 (t)) 2 +(z B;n (t) z 1 (t)) 2 (19) n = (x B; (t), y B; (t), z B; (t)) r 1iB; (t) 1 i B t 1 B i B r 1iB;n () = r ib;n () r 1B;n () r 1iB;n () q = (x B;n (t) x i ()) 2 +(y B;n (t) y i ()) 2 +(z B;n (t) z i ()) 2 q (x B;n (t) x 1 ()) 2 +(y B;n (t) y (t)) 2 +(z B;n (t) z 1 ()) 2 (11) 6
N (16) (17) - B n (t) f DD 12AB() + r 12A () f DD 13AB() + r 13A () f DD 14AB() + r 14A () f B DD 1sAB() + r 1sA () n (t) = f DD 12AB(t)+r 12A (t) f DD 13AB(t)+r 13A (t) f DD 14AB(t)+r 14A (t) B @ f DD 1sAB(t)+r 1sA (t) r 12B;n () + 1 f N 12AB;n(t) r 13B;n () + f N 13AB;n(t) r 14B;n () + f N 14AB;n(t) r 1sB;n () + f N 1sAB;n(t) r 12B;n (t)+ (111) f N 12AB;n(t) r 13B;n (t)+ f N 13AB;n(t) r 14B;n (t)+ f N 14AB;n(t) r 1sB;n (t)+ C A f N 1sAB;n(t) (x B;n (t), y B;n (t), z B;n (t)) 1x B;n (t), 1y B;n (t), 1z B;n (t) (112) 8 x B;n+1 (t) = x B;n (t)+1x B;n (t) >< y B;n+1 (t) = y B;n (t)+1y B;n (t) (112) >: z B;n+1 (t) = z B;n (t)+1z B;n (t) N 1iAB;n (t) 1N 1iAB;n (t) (113) 8 N 12AB;n+1 (t) = N 12AB;n (t)+1n 12AB;n (t) >< >: N 13AB;n+1 (t) = N 13AB;n (t)+1n 13AB;n (t) N 14AB;n+1 (t) = N 14AB;n (t)+1n 14AB;n (t) N 1sAB;n+1 (t) = N 1sAB;n (t)+1n 1sAB;n (t) (113) N 1iAB; (t) (19), (11) xyz @r 1sB;n() @x B;n (), @r 1sB;n() @y B;n (), @r 1sB;n() @z B;n (), @r 1sB;n(t) @x B;n (t), @r 1sB;n(t) @y B;n (t), @r 1sB;n(t) @z B;n (t) 7
8 i;n () = @r 1iB;n() @x B;n () = x B;n (t) x 1 () (xb;n (t) x 1 ()) 2 +(y B;n (t) y 1 ()) 2 +(z B;n (t) z 1 ()) 2 x B;n (t) x i () (xb;n (t) x i ()) 2 +(y B;n (t) y i ()) 2 +(z B;n (t) z i ()) 2 i;n () = @r 1iB;n() @y B;n () = y B;n (t) y 1 () (xb;n (t) x 1 ()) 2 +(y B;n (t) y 1 ()) 2 +(z B;n (t) z 1 ()) 2 y B;n (t) y i () (xb;n (t) x i ()) 2 +(y B;n (t) y i ()) 2 +(z B;n (t) z i ()) 2 >< >: i;n () = @r 1iB;n() @z B;n () = z B;n (t) z 1 () (xb;n (t) x 1 ()) 2 +(y B;n (t) y 1 ()) 2 +(z B;n (t) z 1 ()) 2 z B;n (t) z i () (xb;n (t) x i ()) 2 +(y B;n (t) y i ()) 2 +(z B;n (t) z i ()) 2 i;n (t) = @r 1iB;n(t) @x B;n (t) = x B;n (t) x 1 (t) (xb;n (t) x 1 (t)) 2 +(y B;n (t) y 1 (t)) 2 +(z B;n (t) z 1 (t)) 2 x B;n (t) x i (t) (xb;n (t) x i (t)) 2 +(y B;n (t) y i (t)) 2 +(z B;n (t) z i (t)) 2 i;n (t) = @r 1iB;n(t) @y B;n (t) = y B;n (t) y 1 (t) (xb;n (t) x 1 (t)) 2 +(y B;n (t) y 1 (t)) 2 +(z B;n (t) z 1 (t)) 2 y B;n (t) y i (t) (xb;n (t) x i (t)) 2 +(y B;n (t) y i (t)) 2 +(z B;n (t) z i (t)) 2 i;n (t) = @r 1iB;n(t) @z B;n (t) = z B;n (t) z 1 (t) (xb;n (t) x 1 (t)) 2 +(y B;n (t) y 1 (t)) 2 +(z B;n (t) z 1 (t)) 2 z B;n (t) z i (t) (xb;n (t) x i (t)) 2 +(y B;n (t) y i (t)) 2 +(z B;n (t) z i (t)) 2 (114) x, y, z 8
A n (t) 2;n () 2;n () 2;n () 111 f 3;n () 3;n () 3;n () f 4;n () 4;n () 4;n () f s;n () s;n () s;n () 111 111 f A n (t) = 2;n (t) 2;n (t) 2;n (t) 111 f 3;n (t) 3;n (t) 3;n (t) f 4;n (t) 4;n (t) 4;n (t) f B @ s;n (t) s;n (t) s;n (t) 111 111 f 1 C A (115) 1 1x B;n (t) 1y B;n (t) 1z B;n (t) A n (t) T A n (t) 1 1 1N 12AB;n (t) A n (t) T B n (t) = 1N 13AB;n (t) (116) 1N 14AB;n (t) B @ C A 1N 1sAB;n (t) (16) (116) 1x B;n :1 m, 1y B;n :1 m, 1z B;n :1 m 1 xyz (x B, y B, z B ), 14 FLOAT FLOAT 16 (a) (b) 9
92 : 12,233 km 9 88 86 84 1 2 3 4 5 6 394 : 42,435 km 392 39 388 386 1 2 3 4 5 6 (a) (b) 16: 17 2 σ 12 1 8 6 4 2 1 2 3 4 km 17: FLOAT 1
(16) 3 xyz DOP RTK-GPS FIX 15 RTK-GPS - FIX RTK-GPS FIX (14) t (117) f DD ijab(t) = (r jb (t) r ja (t)) (r ib (t) r ia (t)) + f N ijab (117) = (r jb (t) r ib (t)) (r ja (t) r ia (t)) + f N ijab FLOAT FLOAT (x i (t), y i (t), z i (t)), (x j (t), y j (t), z j (t)) xyz (x B (t), y B (t), z B (t)) (15) (14) (15) 1 s 1 t(1) (118) 8 f (DD 12AB(t) N 12AB )+(r 2A (t) r 1A (t)) = r 2B (t) r 1B (t) f >< (DD 13AB(t) N 13AB )+(r 3A (t) r 1A (t)) = r 3B (t) r 1B (t) f (DD 14AB(t) N 14AB )+(r 4A (t) r 1A (t)) = r 4B (t) r 1B (t) (118) >: f (DD 1sAB(t) N 1sAB )+(r sa (t) r 1A (t)) = r sb (t) r 1B (t) FLOAT t n (x B;n (t), y B;n (t), z B;n (t)) 1 B s B r 1sB;n (t) =r sb;n (t) r 1B;n (t) (19) (16) (118) - 11
B n (t) B n (t) = B @ f (DD 12AB(t) N 12AB;n )+r 12A (t) f (DD 13AB(t) N 13AB;n )+r 13A (t) f (DD 14AB(t) N 14AB;n )+r 14A (t) f (DD 1sAB(t) N 1sAB;n )+r 1sA (t) r 12B;n (t) r 13B;n (t) r 14B;n (t) r 1sB;n (t) 1 C A (119) (x B;n (t), y B;n (t), z B;n (t)) 1x B;n (t), 1y B;n (t), 1z B;n (t) (112) (19) xyz @r 1sB;n(t) @x B;n (t), @r 1sB;n(t) @y B;n (t), @r 1sB;n(t) @z B;n (t) 8 s;n (t) = @r 1sB;n(t) @x B;n (t) = x B;n (t) x 1 (t) (xb;n (t) x 1 (t)) 2 +(y B;n (t) y 1 (t)) 2 +(z B;n (t) z 1 (t)) 2 x B;n (t) x s (t) (xb;n (t) x s (t)) 2 +(y B;n (t) y s (t)) 2 +(z B;n (t) z s (t)) 2 >< >: s;n (t) = @r 1sB;n(t) @y B;n (t) = y B;n (t) y 1 (t) (xb;n (t) x 1 (t)) 2 +(y B;n (t) y 1 (t)) 2 +(z B;n (t) z 1 (t)) 2 y B;n (t) y s (t) (xb;n (t) x s (t)) 2 +(y B;n (t) y s (t)) 2 +(z B;n (t) z s (t)) 2 s;n (t) = @r 1sB;n(t) @z B;n (t) = z B;n (t) z 1 (t) (xb;n (t) x 1 (t)) 2 +(y B;n (t) y 1 (t)) 2 +(z B;n (t) z 1 (t)) 2 z B;n (t) z s (t) (xb;n (t) x s (t)) 2 +(y B;n (t) y s (t)) 2 +(z B;n (t) z s (t)) 2 (12) A n (t) 2;n (t) 2;n (t) 2;n (t) 1: 3;n (t) 3;n (t) 3;n (t) 1: A n (t) = 4;n (t) 4;n (t) 4;n (t) 1: B @ s;n (t) s;n (t) s;n (t) 1: 1 C A (121) 12
An (t) T A n (t) 1 1 A n (t) T B n (t) = B @ 1x B;n (t) 1y B;n (t) 1z B;n (t) 1T ime B;n (t) 1 C A (122) (122) FLOAT 1x B;n :1 m, 1y B;n :1 m, 1z B;n :1 m 1 16 KGPS/RTK-GPS 2 7 5 2 7 5 2drms = 27 m (m) 1 1 (m) 1 1 2 2 2 1 1 2 (m) (a-1) 2 1 1 2 (m) (b-1) 6 598 7 6 598 7 σ = 169 m (m) 596 594 (m) 596 594 592 592 59 1 2 3 4 5 6 59 1 2 3 4 5 6 (a-2) (b-2) (a) FLOAT (b) FIX 18: KGPS FLOAT FIX 18 (a), (b) FLOAT FIX 13
FLOAT FIX FLOAT RTK-GPS 6 ZBL 2 m 19(a), (b) GPS Trimble Navigation 4SSi Trimble 4SSi ZBL 2 m ZBL + (m) 3 2 1 1 2 : 85 FIX : 1 2drms = 116 m 3 : 2 m : 77 4 FIX : 998 2drms = 88 m 5 5 4 3 2 1 1 2 3 (m) (m) 5928 : σ = 84 m 5926 5924 5922 2 m: σ = 614 m 592 1 2 3 4 5 6 ( ) (a) (b) 19: RTK-GPS ZBL 2 m 11 FIX 3,6 / FIX 2drms mm Trimble 4SSi 11: RTK-GPS ZBL FIX 2drms ZBL 85 1 116 m 84 m 2 m 77 998 88 m 614 m 6 Zero base line ZBL 14
17 RTK-GPS RTK-GPS 11 RTK-GPS 2 1(x 1, y 1, z 1 ), 2(x 2, y 2, z 2 ) 2 (x, y, z) r F (x; y; z) = (x x 1 ) 2 +(y y 1 ) 2 +(z z 1 ) 2 (x x2 ) 2 +(y y 2 ) 2 +(z z 2 ) 2 r = (123) 2 2 Hyerboloid (3) 11: 18 RTK-GPS RTK-GPS MCA Multi-hannel Aess 15
RTK-GPS RTCM SC-14 7 21 18 21 (4) RTCM RTK-GPS RTK-GPS ION GPS-96 CMR 8 (5) RTK-GPS (1) RTCM SC-14 Ver21 DGPS SC-14 Ver21 RTK-GPS Tye18 21 GPS RTK-GPS RTCM RTK-GPS RTCM RTK-GPS Tye18, 19 RTK-GPS DGPS Tye1 Tye3 RTCM RTK-GPS DGPS 12 Tye18 Tye19 21 1 3 Ver 3 12: RTCM Tye18 (words) (bits) 4 2+1+4 4 = 19 19 3 = 57 5 2+1+4 5 = 23 23 3 = 69 6 2+1+4 6 = 27 27 3 = 81 7 2+1+4 7 = 31 31 3 = 93 8 2+1+4 8 = 35 35 3 = 1,5 9 2+1+4 9 = 39 39 3 = 1,17 1 2+1+4 1 = 43 43 3 = 1,29 11 2+1+4 11 = 47 47 3 = 1,41 12 2+1+4 12 = 51 51 3 = 1,53 (2) Trimble Navigation CMR RTCM RTK-GPS Tye18 21 9,6 bs RTK-GPS 1996 9 ION GPS-96 Trimble Navigation Co,Ltd RTK-GPS CMR 7 Radio Tehnial Commission for Maritime Servies Seial Committee No14 14 8 Comat measurement reord 16
RTCM RTK-GPS 2,4 bs RTK-GPS CMR Tye1 ECEF Kinemati RTK-GPS GPS RTK-GPS (5) 4SSi 3 25 RTCM RTK-GPS Tye3, 18, 19, 59 39 kbit/ 1 CMR 1/4 1 kbit/ 1 CMR RTCM RTK-GPS 17
(1) - -,, 1989 11 15 (2) GPS, (3),, 44 3 15 (4) Radio Tehnial Commission for Maritime Servies Seial Committee No14, ' RTCM Reommended Standards for Dierential Navstar GPS Servie Version 21 ', RTCM Paer194-93/SC14- STD, Washington,DC, JANUARY 3 (1994) (5) DrNiholas, CTalbot, 'Comat Data Transmission Standard for High-Preision GPS', PRO- CEEDING OF THE 9TH INTERNATIONAL TECHNICAL MEETING OF THE SATELLITE DIVISION OF THE INSTITUTE OF NAVIGATION ION GPS-96 PART 1 OF 2, 861-871