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:
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- とらふみ ひでやま
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1 A1 GPS/GNSS A11 GPS GPS GPS { 29 GPS m 95% GPS GLONASS Galileo GNSS global navigation satellite system GPS GPS GPS IIR-M L2C SBAS satellite-based augmentation system WAAS MSAS 9 GPS/GNSS GPS GPS GNSS GPS/GNSS A12 GPS GPS GPS A { GPS 24
2 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: GPS 2: GPS FAA HP sitioning service GPS SPS Performance Standard /1/ 1227:6 MHz L2 P precision code; Y P PPS; precise positioning service P P 2 P L1
3 N 20 0 o W o 60 o o E, m 0 17 S 3: GPS , m 4: GPS Space Segment MHz Mcps C/A 1023 L P 1023 L P 1023 GPS space segment control segment user segment 5 GPS GPS II IIA IIR 3 GPS MCS; master control station 4 5 GPS User Segment Control Segment 5: GPS GPS interface control document L2C /2/ A13 GPS GPS GPS
4 A131 GPS GPS GPS GPS 1 1 1/100 ï= c=f 1/ m 100 khz 3km 2ô GPS f C [Hz] p(t) s t (t) =p(t) sin2ôf C t (1) p(t) sin 2ôf C t f p [Hz] +1 Ä1 BPSK=binary phase shift keying 2 p(t) f p GPS s t (t) s t (t) =D(t) p(t) sin2ôf C t (2) D(t) Ü1 50 bps p(t) Ü1 f p = 1:023 MHz N = 1023 N sin 2ôf C t f C = 1575:42 MHz 2 sin 2ôf C t D(t) p(t) D(t);p(t) f+1; Ä1g s t (t) p(t) +1 Ä1
5 PRN 1 PRN 2 自己相関 相互相関 t, μs a PN PRN (PRN1) (PRN1 vs PRN2) τ, μs b 6: PN PRN code 2 GPS N = ms GPS PRN ICD 37 PRN PRN /2/ PPN 2 p(t) GPS 1:023 MHz 300 m 6 GPS PRN a PRN1 PRN2 PRN 100 b PRN1 PRN1 PRN2 ú= 0 GPS GPS 10 Ä12 GPS GPS x; y; z 4 A132 GPS GPS
6 = 30 T L M H O W 300 = 6 #1 #2 #3 #4 #5 a 300 = 6 順番に送信 = 30 6 b この順に送信 7: 50 bps 1 7 a GPS b TLM telemetry HOW handover TLM HOW GPS GPS HOW :00: ICD /2/ 1 2 #1 3 #2 4 UTC 5 1 2
7 1: GPS (429) (449) (430) (450) (431) (451) (432) (452) (0) (433) (453) (1) (434) (454) (415) (435) (455) (416) (436) (456) (417) (437) (457) (418) (438) (458) (419) (439) (459) (420) (440) (460) (421) (441) (461) (422) (442) (462) (423) (443) (463) (424) (444) (464) (425) (445) (465) (426) (446) (466) (427) (447) (467) (428) (448) (468) n 2 n 2 SV health 0 URA 15 T GD L1 T GD GPS t oc 2 a f0 ;a f1 ;a f2 3 T GD t t Åt t = Ä à a f0 + a f1 (t Ä t oc )+a f2 (t Ä t oc ) 2 +Åt r Ä T GD g (3) Åt r Åt r = Ä 2ep ñ e A sin E (4) c 2 ñ e = 3: Ç m 3 /s 2 IODC IODC 2 3 3, 4 GPS 6 ephemeris GPS
8 2: TLM HOW WN URA 77 6 SV health 83 2MSB IODC T GD Ä31 s LSB IODC t oc 4 s a f2 Ä55 s/s a f1 Ä43 s/s a f0 Ä31 s 3: TLM HOW IODE C rs Ä5 m oån Ä43 sc/s 107 8MSB LSB M 0 Ä31 sc oc uc Ä29 rad 167 8MSB LSB e Ä oc us Ä29 rad 227 8MSB p A Ä19 m 1= LSB t oe 4 s right ascension of the ascending node; ä X inclination angle; i 0 GPS 55 argument of perigee;! semi major axis; a b b = a p 1 Ä e 2 eccentricity; e 0 î e<1 e e =0e =1 true anomaly; í epoch GPS mean anomaly M M = E Ä e sin E (5) E eccentric anomaly p 1 Ä e2 sin E cos E Ä e sin í= ; cos í= 1 Ä e cos E 1 Ä e cos E (6) t 0 M 0
9 4: TLM HOW oc ic Ä29 rad 77 8MSB LSB ä 0 Ä31 sc oc is Ä29 rad 137 8MSB LSB i 0 Ä31 sc oc rc Ä5 m 197 8MSB LSB! Ä31 sc ä _ ä0 Ä43 sc/s _i i 0 Ä43 sc/s M(t) = r ñe a 3 (t Ä t 0)+M 0 (7) M(t) =M 0 +2ô s a T =2ô 3 (8) ñ e GPS km T = =23 56 GPS 1 4 GPS 3:874 km/s GPS t t oe M M = M 0 +(n 0 +Ån) Å(t Ä t oe ) (9) í 5 E E 0 = M 10 E i+1 = E i + e sin E i (10) 6 í ECEF û û= í+! (11) C u r i u û 6 4 r 7 5 = 6 4 A(1 Ä e cos E) 7 5 i i 0 + _i (t Ä t oe ) 2 3 C uc C us " # C rc C rs 7 cos 2û 5 (12) sin 2û C ic C is ECEF ä = ä 0 +( ä _ Ä ä _ e ) Å(t Ä t oe ) Ä ä _ e t oe (13) x cos ä Ä sin ä cos i " # 6 4 y 7 5 = 6 4 sin ä cos ä cos i 7 r cos u 5 r sin u z 0 sini _ä e =7: Ç 10 Ä5 (14) rad/s GPS IODE IODC sc=semi-circle; 1 sc = ô rad 3: km GPS
10 X Z 降交点 P 近地点 Y Ω ω i 昇交点 a y M M a F 2 虚焦点 O r E θ F 1 b 地球 C x P 近地点 t oa b 8: 70 ms GPS 3km GPS GPS Sagnac 100 km GPS ã 0 ã 3 ;å 0 å 3 8 GPS [s] 8 >< F Ç 5 Ç 10 Ä9 + AMP ê ëi T iono (t L )= Ç 1 Ä x2 2 >: + jxj < 1:57 x4 ; 24 5 Ç 10 Ä9 F; jxj ï1:57 (15) 9 15 x
11 5: TLM HOW SV ID e 91 8 t oa Ä21 12 s éi Ä19 sc ä _ ä0 Ä38 sc/s SV p health A Ä11 m 1= ä 0 Ä23 sc ! Ä23 sc M 0 Ä23 sc MSB a f a f1 Ä38 s/s 290 3LSB a f0 Ä20 s 6: TLM HOW SV ID ID = ã 0 Ä30 s 77 8 ã 1 Ä27 s/sc ã 2 Ä24 s/sc ã 3 Ä24 s/sc å å 1 14 s s/sc å 2 16 s/sc å 3 16 s/sc o A 1 UTC Ä50 s/s MSB LSB A 0 o UTC Ä30 s t ot 12 s WN t UTC 0 weeks Åt LS 0 s WN LSF 0 weeks DN Åt LSF 0 0 days s x = 2ô(t L Ä 14 Ç 3600) PER (16) t L pierce point GPS t t L =12Ç3600 ï i + t 14 5ns AMP ã 0 ã ( 3 ) 3X i AMP =max 0; ã i û m (17) i=0 û m [rad] PER å 0 å 3 ( ) 3X i PER =max 20 Ç 3600; å i û m (18) i=0 F
12 , D iono ns AMP PER/ , t h 9: 35 EL 35 GPS F =1+16(0:53 Ä EL) 3 (19) û m 0:00137 = Ä 0:022 (20) EL +0:11 û i0 = û u + cos AZ 8 >< û i0 ; jû i0 jî0:416 û i = 0:416; û i0 > 0:416 (21) >: Ä0:416; û i0 < Ä0:416 ï i = sin AZ ï u + cos û i (22) û m = û i +0:064 cos(ï i Ä 1:617) (23) AZ û u ;ï u û i ;ï i semi-circle A133 i r i [m] ö i [m] é[s] pseudo-range r i = ö i + cé= ö i + s ö i (x; y; z) i (x i ;y i ;z i ) ö i = p (x i Ä x) 2 +(y i Ä y) 2 +(z i Ä z) 2 (24) [m] x 8 r 1 = p (x 1 Ä x) 2 +(y 1 Ä y) 2 +(z 1 Ä z) 2 + s >< r 2 = p (x 2 Ä x) 2 +(y 2 Ä y) 2 +(z 2 Ä z) 2 + s >: r N = p (x N Ä x) 2 +(y N Ä y) 2 +(z N Ä z) 2 + s (25) x; y; z; s é x; y; z 4 1 s = cé s 5 1 x; y; z 2 s 25
13 送信源 #3 R 3 -s r 3 送信源 #1 r 1 -s r 1 ユーザ r 2 -s r 2 送信源 #2 År i Åx; Åy; Åz;Ås 5 Åx; Åy; Åz;Ås x 1 = x 0 +Åx; y 1 = y 0 +Åy; z 1 = z 0 +Åz; s 1 = s 0 +Ås 10: 1 x; y; z; s x 0 ;y 0 ;z 0 ;s 0 2 x 0 ;y 0 ;z 0 ;s 0 8 r1= p 0 (x 1 Ä x 0 ) 2 +(y 1 Ä y 0 ) 2 +(z 1 Ä z 0 ) 2 + s 0 >< r2= p 0 (x 2 Ä x 0 ) 2 +(y 2 Ä y 0 ) 2 +(z 2 Ä z 0 ) 2 + s 0 >: rn 0 =p (x N Ä x 0 ) 2 +(y N Ä y 0 ) 2 +(z N Ä z 0 ) 2 + s 0 (26) 3 r i År i = r i Ä ri 0 4 x 0 ;y 0 ;z 0 ;s 0 r i x; y; z; s 8 >< i i i = Ä(x i Ä x 0 )=r 0 i ; = Ä(y i Ä y 0 )=r 0 i ; = Ä(z i Ä z 0 )=r 0 i ; = 1 x 0 ;y 0 ;z 0 ;s 0 Åx; Åy; Åz; Ås År 1 Åx Åy Åz Ås År 2 Åx Åy Åz Ås (27) År N Åx Åy Åz Ås 6 x 1 ;y 1 ;z 1 ;s 1 2Åx; Åy; Åz; Ås x 0 = y 0 = z 0 = s 0 =0 4 Åx =[ÅxÅyÅzÅs ] T ; År = [År 1 År 2 ÅÅÅÅr N ] T 4 G Åx =År (28) G G = = N 1 2 Ä(x 1 Äx) r 1 Ä(x 2 Äx) r 2 Ä(x N Äx) r 1 2 Ä(y 1 Äy) r 1 Ä(y 2 Äy) r 2 Ä(y N Äy) r Ä(z 1 Äz) r 1 1 Ä(z 2 Äz) r 2 1 Ä(z N Äz) r N (29) GPS 28 4 G 4 4 G Åx = G Ä1 År (30)
14 5 G 5 Åx =(G T G) Ä1 G T År (31) /3/ /4/ N>4 N =5 r 1 ;r 2 ; ÅÅÅ; r N GPS W W = 2 3 w 1 0 ÅÅÅ 0 0 w ÅÅÅ w N =õ 1 0 ÅÅÅ =õ 2 0 = 6 (32) ÅÅÅ 1=õ N õ i r i P i w i =1 Åx =(G T WG) Ä1 G T W År (33) Åx N =4 33 A14 GPS 2 km GPS DOP A141 GPS GPS GPS m 10 m 11 broadcast ephemeris precise ephemeris 1:5 m 2 3 IGS
15 m 高度 km h 密度 0 気温 K 300 密度 kg/m : 気温 熱圏流星中間圏成層圏 1000 対流圏 1 12: 人工衛星 電離層オーロラ international GPS service 5cm /5/ GPS A142 GPS 10 Ä13 1 = Ä8 3m A X GPS 100 km E Es F F1 F2 GPS GPS ns ionospheric delay D iono [m] D iono = 40:3 Z Ndl= 40:3 cf 2 TEC (34) cf2 f L1 1575:42 MHz N [m Ä3 ] R Ndl TEC total electron content [m Ä2 ] 13 2
16 20 A144 m h 13: D iono (90 é ) EL D iono (90 é ) D iono (EL)= r ê ë (35) 2 R 1 Ä e cos EL R e+h iono H iono [m] 350 km m GPS A m 34 2 L1 L2 2 L1 PR L1 L2 PR L2 PR L1 Ä PR L2 Z ûí 40:3 Ndl=(PR L1 Ä PR L2 ) Ä 40:3 ì cf 2 L1 cf 2 L2 (36) TEC 2 atmospheric delay tropospheric delay refractive index 1 1:0003 Hopåeld n [m] D tropo (h; 90 é )=H n í 0 Ä 1 1 Ä h ì 5 (37) 5 H /6/ n 0 h H 43 km n í /7, 8/ n =1+ 77:6 P d T +3:73 Ç P ì 105 w Ç 10 Ä6 T 2 (38) P d [hpa] P w [hpa] T [K] P d = 1000 hpa;p w = 10 hpa;t = 300 K n =1:0003 GPS 37 D tropo (h; 90 é )=2:47 Ä 1 Ä 2:3 Ç 10 Ä5 h Å 5 (39)
17 EL D tropo (h; EL) = 2:47 Ä 1 Ä 2:3 Ç 10 Ä5 h Å 5 (40) sin EL + 0: :5 m GPS GPS A145 GPS GPS GPS GPS 14 multipath i ii 測距誤差, m マルチパス波 ユーザ 直接波 マルチパス波 2 GPS 衛星 14: 衛星仰角, deg 15: ii GPS choke ring A146 GPS
18 8: GPS 13 m 95%; 36 m 95%; 22 m 95%; 77 m 95%; GPS SPS Performance Standard /1/ thermal noise 0:5 m A147 GPS m 5m 7 /9/ 2 95% 7 5:3 m 5:1 m DOP = Ç HDOP = Ç VDOP HDOP =2:0 VDOP =2:5 10:2 m 12:8 m 95% 2 GPS L1 GPS Global Positioning System Standard Positioning Service Performance Standard /1/ 8 95% A elevation mask angle 5 15
19 7: m m m (200) (200) (205) (206) 51 (205) (205) HDOP =2:0 102 (411) VDOP =2:5 128 (514) Global Positioning System: Theory and Applications /9/ A133 A149 DOP År x; y; z; s s Åx 28 G Åx =År (41) G Åx Åx = G Ä1 År (42) e 43 Åx = G Ä1 e (43) e 43 Åx Åx =(G T G) Ä1 G T e (44) Åx =(G T WG) Ä1 G T W e (45) covariance N a =[a 1 a 2 ÅÅÅa N ] covariance matrix cov(a) 2 3 õa 2 1a 1 õa 2 1a 2 ÅÅÅ õa 2 1a N õa 2 2a 1 õa 2 2a 2 õ 2 a 2a N cov(a) = 6 4 (46) 7 5 õa 2 N a 1 õa 2 N a 2 ÅÅÅ õa 2 N a N N Ç Nõ ai a j a i a j E [ Å] a; b õ ab = E [(a Ä E [ a ])(b Ä E [ b ]) ]
20 a i a j i = j õ ai a i a i 43 Åx cov(åx) =G Ä1 cov(e)(g Ä1 ) T (47) e õ 2 cov(e) =õ 2 II cov(åx) =G Ä1 (õ 2 I)(G Ä1 ) T = õ 2 C (48) cov(åx) 2 Åx 3 õxx 2 õxy 2 õxz 2 õxs 2 õyx 2 õyy 2 õyz 2 õ 2 ys cov(åx) = 6 4 õzx 2 õzy 2 õzz 2 õzs õsx 2 õsy 2 õsz 2 õss 2 (49) x; y; z; s i ii i õ õ 2 ii C =(G T G) Ä1 GDOP = 1 q õxx õ 2 + õyy 2 + õzz 2 + õss 2 q = C C C C2 44 PDOP = 1 q õxx õ 2 + õ2 yy + õ2 zz q = C C C2 33 HDOP = 1 q õxx õ 2 + õyy 2 (50) q = C C2 22 VDOP = 1 õp õ 2 zz = jc 33 j TDOP = 1 õp õ 2 ss = jc 44 j PDOP P=position õ x ;õ y ;õ z HDOP H=horizontal õ x ;õ y VDOP V=vertical õ z TDOP T=time C = (G T G) Ä1 GPS DOP Ç HDOP = Ç VDOP = õ PR =10m HDOP =2;VDOP =2:5 20 m 25 m TDOP =1:5 15 m c 45 ns HDOP VDOP G 48 cov(åx) =(G T WG) Ä1 (51) DOP 50 A15 GPS GPS A151 GDOP G=geometric GPS
21 ri 1 (r0 i Ä ö0 i ) 擬似距離を測定 擬似距離を測定 r 1 i Ä (r0 i Ä ö0 i ) 基準局と同じ測定誤差 測定誤差 = ö 1 i + é i +Å 1 + ó 1 i Ä (é i +Å 0 + ó 0 i ) = ö 1 i +(Å 1 Ä Å 0 )+(ó 1 i Ä ó 0 i ) 移動局 基準局から誤差情報を送信して移動局側での測定誤差を補正する 基準局 16: GPS GPS GPS GPS GPS DGPS; diãerential GPS GPS i ri 0 ö 0 i ri 0 = ö 0 i + é i +Å 0 + ói 0 (52) é i i Å 0 ó i 0 ö 0 i ri 0 Äö0 i = é i +Å 0 +ói 0 ri 1 = ö 1 i + é i +Å 1 + ói 1 (53) ö 1 i é i GPS Å;ó GPS GPS km
22 9: DGPS A152 A131 GPS 19:03 cm 19:03 cm GPS 1/ :03 cm N GPS kinematic GPS 10 GPS GPS static GPS static surveying RTK-GPS GPS GPS realtime kinematic GPS; RTK-GPS GPS CDGPS; carrier-phase diãerential GPS GPS DGPS code DGPS GPS DGPS
23 PN carrier smoothing RTK-GPS GPS A153 RTK GPS 10 km 10 km 3 RTK 100 km /10/ RTK RTK VRS virtual reference station RTK GEONET A154 integrity availability continuity 4 GPS N N>4 = (54) PDOP < 6 PDOP < 6 = (55) HDOP < 3 5
24 N>5 HDOP < 3 = (56) alert limit =1Ä (57) 95% A155 GPS augmentation system GPS GPS DGPS RTCM-104 ICAO international
25 civil aviation organization GNSS SARPs; standards and recommended practices /11/ GNSS GPS ICAO GNSS 3 SBAS satellite-based augmentation system GPS GBAS ground-based augmentation system GPS ABAS aircraft-based augmentation system GPS RAIM receiver autonomous integrity monitoring GPS AAIM aircraft autonomous integrity monitoring ABAS GPS SBAS WAAS wide area augmentation system EG- NOS European geostationary navigation overlay service MSAS MTSAT satellitebased augmentation system /12, 13/ WAAS EGNOS MSAS MTSAT multi-functional transport satellite FAA WAAS MSAS 3 9 EGNOS SBAS iii iii GPS L1 1575:42 MHz GPS GBAS SBAS GBAS VHF GBAS A16 GPS II/IIA IIR IIR-M GPS L2 L5 RTK-GPS IIR-M M
26 modiåed 2008 F L2 ARNS L5 GPS GPS III III III GPS GPS Modernization JPO joint program oéce III L1C L1C JPO DGPS khz GPS ITU /15/ GPS GLONASS GLONASS GPS L GPS GPS CDMA FDMA frequency division multiple access GLONASS EU Galileo ICAO GPS SBAS EGNOS EGNOS GNSS-1 GNSS-2 Galileo Galileo Galileo GPS GLONASS A155 GPS ICAO SBAS MSAS ETS-VIII i ii iii /16, 17/ GPS GPS A17 GPS/GNSS /3/
27 GPS 30 MSAS GPS IIR-M 2005 Galileo GPS/GNSS /1/ Global Positioning System Standard Positioning Service Performance Standard, DOD, Oct /2/ Navstar GPS Space Segment / Navigation User Interfaces, Interface Control Document, ICD-GPS-200, rev C, Jan /3/ : GPS 2003 /4/ : GPS 2007 /5/ IGS /6/ Spilker, J J Jr: \Chapter 13: Tropospheric Eãects on GPS," Global Positioning System: Theory and Applications, vol I, pp 517{546, AIAA, 1996 /7/ : 1999 /8/ 2000 /9/ Parkinson, B W: \Chapter 11: GPS Error Analysis," Global Positioning System: Theory and Applications, vol I, pp 469{483, AIAA, 1996 /10/ \VRS RTK-GPS " GPS 2002 pp 145{190 Nov 2002 /11/ International Standards and Recommended Practices, Aeronautical Telecommunications, Annex 10 to the Convention on International Civil Aviation, vol I, ICAO, Nov 2002 /12/ : \ MSAS " GPS 2002 pp 81{85 Nov 2002 /13/ \ MSAS" GPS/GNSS pp 59{63 Nov 2005 /14/ RTCM Recommended Standard for Diãerential GNSS, Version 22, RTCM SC-104, Paper /SC104-STD, Jan 1998 /15/ Technical Characteristics of Diãerential Transmissions for GNSS from Maritime Radio Beacons in the Frequency Band 2835{ 315 KHz in Region 1 and 285{325 KHz in Regions 2 and 3, ITU-R M823-1, 1996 /16/ : \QZSS " GPS/GNSS 2004 pp 75{ 110 Nov 2004 /17/ \QZSS " GPS/GNSS pp Nov 2006 /1/ GPS 2001 SA ICD /2/ GPS GPS GPS GPS GPS IGS International GNSS Service GNSS IGS RINEX 30 GEONET km 30
28 RINEX GPS GPS 11 GPS/GNSS GPS/ CGSIC Civil GPS Service Interface Committee GPS GPS GPS GPS ION GNSS ION Institute of Navigation 9 GPS 2002 ION GPS 2003 ION GPS/GNSS ION GNSS CD-ROM CGSIC ION NTM ION National Technical Meeting ION 1 ION GNSS Annual Meeting 6 CD-ROM
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