Author name used in this publication: 郑作亚Author name used in this publication: 陈永奇Author name used in this publication: 卢秀山Title in Traditional Chinese: 基於模糊度中誤差的GPS信號第三民用頻率L5的選取研究Journal title in Traditional Chinese: 測繪學報2007-2008 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Chen, YQ

Lu, XS

Zheng, ZY

PolyU Institutional Repository

? 36 ?  ? 4 ? ?  ?  ?  ? Vol. 36, No. 4 2007 ? 11 ? ACTA GEODAETICA et CARTOGRAPHICA S INICA Nov. , 2007  ????: 1001-1595( 2007) 04-0383-06 ?????: P228. 4     ?????: A????????? GPS???????? L 5?????郑作亚1, 陈永奇2, 卢秀山1( 1. ?????? ???????????,?? ?? 266510; 2. ?????? ???????????,??)Study of Choosing the Third Frequency of GPS Signal Based on the StandardError of the Estimated AmbiguityZHENG Zuo-ya1 , CH EN Yong-qi2 , LU Xiu- shan1(1. College of G eo-inf ormat ion Sci ence and E ngineering , S handong Univ ersi ty of S ci ence and Technology , Qingdao 266510,China; 2. Depar tment of L and Surv eying and Geo-inf or mati cs , The H ong K ong Polyt echnic Univer si ty , H ong K ong, China)Abstract: T o achieve high precision positioning w ith Global Positioning System ( GPS) in GPS static positioning orkinematic positioning , car rier phase ambiguity integers must be successfully resolved and fixed. It is well know n tous, t he US Department of Defence ( DoD) has announced, that it would introduce a third civ il frequency identicalw ith the currently L 2 frequency, and later , after December , 2004, it w ould improve the effective and reliability ofambiguity solution. The cho ice of the third civ il frequency is discussed according to the standard er ror of ambiguityin this paper, and study of determining st andard error of ambiguity , the r elationship of signal frequency and standarderro r of ambiguity, finally, we advice the value r ange o f the third civil frequency. It offers an idea and reference forfrequency chooses of nav igation system signal as GALILEO system, t he others navig ation systems in the futur e.Key words: GPS signal; ambiguity solut ion; standard error; L 5 frequency; tr iple frequency observations?  ?:从模糊度参数标准中误差角度出发讨论信号 L 5频率的选取问题, 在双频观测资料模糊度参数估计基础上,研究三频观测资料模糊度参数估计 ,并进行模糊度参数标准中误差确定?讨论信号频率与模糊度标准中误差之间的关系,最后提出新的民用频率取值范围的建议?为今后的 GALILEO 系统?其他导航系统等信号频率选取提供一种思路和借鉴?  ????: 2006-06-30; ????: 2006-10-23????: ?? RGC????( B- Q934) ;??????????????????????????( SD060804)????: ???( 1978- ) ,?,?????,??,???? GNSS??/???????????????????????E-mail: caszzy@gmail. com???: GPS 信号;模糊度解算; 标准中误差; L 5 频率;三频观测值1  引  言??? GPS ??????????????,??????????????????????? GPS??????????,??????????????????????[ 1~ 5]??? GPS ???????,???????????? 2004? 12 ?????? GPS ??????????????(??? 2012 ?????[ 6] ) ,???????????????????,????? GPS?????????????????????????, ???????????,???????????????????, ?????????????????????, ????????????????,???????????????????????, ????????????????????????????, ??????????????, ???????????????,??????? L 5 ?????????,?????????????????????????????????????????, ??????????????????,?????????: L 1, L 2 ??????????,?????????????;??? GPS ???, L 1 ????, ? L 2, L 3 ?????, ??????????????????????????????????????????,???????,??????????,?????????,?????????????; ???????, ??????????,??????????????,????????????????????????????,??????????????? GPS??????????????, ?????????????????,????????????????????????, ????????????????,???????????????2  双频观测资料的模糊度参数估计??????????????????????????????L 1= K1 U1= Q+ c#(dt- dT )- K 1d ion+  K1 b1+ ML 1+ E1L 2= K2 U2= Q+ c#(dt- dT )- K 2d ion+  K2 b2+ ML 2+ E2P 1= Q+ c#(dt - dT ) + K 1d ion+ MP1+ e1P 2= Q+ c#(dt - dT ) + K 2d ion+ MP2+ e2(1)??, c???,? 2. 997 924 58 @ 108 m#s- 1; dt ,dT ???????????; d ion??????; K 1, K 2 ????????????????, K 1/ K 2= f 22/ f 21; <1, <2, f 1, f 2, K1, K2, b1, b 2??? L 1, L 2 ???????????????;P 1, P 2 ? L 1, L 2 ??????????; ML 1,ML2, MP1, M P2??????????????????????????????????????????????????, ?????; Q?????????????; E1, E2, e1, e2 ??????????????????????????????( 1) ,?L D=f 1L 1- f 2L 2f 1- f 2= Q+ c( dt- dT )+- f 1K 1+ f 2K 2f 1- f 2d ion+ KDbD+M ( L 1+ L 2) + E( L 1+ L 2) (2)??, KD= c/ ( f 1- f 2 )????, bD= b 1- b2 ????????,??????????,??PD=f 1P 1+ f 2P 2f 1+ f 2= Q+ c(dt - dT ) +f 1K 1+ f 2K 2f 1+ f 2d ion+ M ( P1+ P 2)+e( P 1+ P2) (3)???? (2)??( 3)????????????[ 7] , M ( L 1+ L 2) ? M ( P 1+ P 2) ??????,???????? E( L 1+ L 2)? e( P1+ P2)???????, ???, ??????, ????,???????????,?????????,???????????????(2)?( 3)????????????[ 7]bD= b1- b2=1KD( LD- PD)= <1- <2-( f 1- f 2)c#f 1P 1+ f 2P 2f 1+ f 2= <1- <2- k 12( P 1+ P 2) (4)??, k 12= f 1- f 2f 1+ f 2= 17137, P 1=P 1K1, P2=P 2K2???,??????????????????,??????????????????????????,???????????????????, ?? (4)????, bD??????????????,??, ?????????(??? k 12)?????????????????????????????????????,????????? bD????,????L 1 ????????????b 1= bD+ b2- e( P1+ P 2) (5)??, b2 ??? ( 1)????????, e ( P1+P 2)?????????????(1)????L 1 ????????b1= b1- E1 (6)b1???( 1)????????, E1 ? L 1 ???????????(5)??(6)????????? Q, ? b1 ???????b^1= ( ATQ- 1A)- 1ATQ- 1 b1b 2+ bD, AT= (1, 1)(7)????,?????,?????????384 ?  ?  ?  ?                   ? 36 ???????, ?????????????????,?????? Almg ren[ 8]?????????????, ????,???????, ?????????, ???????????????????[ 12] , ????????????????????3  三频观测资料的模糊度参数估计???????????????????,?????????????????????(?: ??????????????????????????? L 3, P3, ????????)L 1= K1 U1= Q+ c#(dt- dT )- K 1d ion+  K1 b1+ ML1+ E1L 2= K2 U2= Q+ c#(dt- dT )- K 2d ion+  K2 b2+ ML2+ E2L 3= K3 U3= Q+ c#(dt- dT )- K 3d ion+  K3 b3+ ML3+ E3P 1= Q+ c#(dt - dT ) + K 1d ion+ MP1+ e1P 2= Q+ c#(dt - dT ) + K 2d ion+ MP2+ e2P 3= Q+ c#(dt - dT ) + K 3d ion+ MP3+ e3(8)??????,?????????????????????????[ 11] , ????, ????????????????????, ??????????,?????????????????????????, ??(8) , ????????????bD12= b1- b2= U1- U2- k 12( P 1+ P2) (9)bD13= b1- b3= <1- <2- k 13( P 1+ P3) (10)??, k 12= ( f 1- f ) / ( f 1+ f 2 ) , k13= ( f 1- f 3) /( f 1+ f 3)???( 10)????, ?? L 3 ???f 3????? L 1??? f 1??, ?????????????? k13???, ???????????????????, ??????????????????,?????????????????????(9)?(10)???(8)???????,????????????, ? A= f 1/ f 2, B=f 1/ f 3, ??????????????????????????1 1 - 1 11 1 - A2 A1 1 - B2 B1 1 1 01 1 A201 1 B20 Qc#$td ionf21K1 b1=  L 1- E1L 2+ K2 bD12- E2L 3+ K3 bD13- E3  P1- e1  P2- e2  P3- e3]1 - 1 11 - A2A1 - B2 B1 1 01 A2 01 B2 0Q+ c#$t d ionf21 K1 b1=  L 1- E1L 2+ K2 bD12- E2L 3+ K3 bD13- E3  P 1- e1  P 2- e2  P 3- e3(11)??(11)????? 6 ?????(???Q+ c#$t ????????) ,???( 11)?? 3????????????, ??????????????????,??????????(11)????????????, ???????????,???????BX= L- e (12)??,B=1 - 1 11 - A2 A1 - B2 B,  X =Q+ c#$t d ionf21 K1 b 1,L- e=  L 1L 2+ K2 bD12L 3+ K3 bD13-E1E2E3(13)????????, ??(12)??X^= ( BT B) - 1BT L (14)?????????QX^X^= R20( BTB)- 1(15)??, R20 ???????4  基于模糊度中误差的 GPS信号 L5频率的选取  ???????????????????385? 4 ?       ???? :????????? GPS ???????? L 5 ????????? GPS???????????,????????????????????,?????, ????????????????????????, ?????????????????????4. 1  ??????????????????( Q+ c#$t )????????,????????? b1??????????,??, ???( 12)?( 14) , ?????????b1 ???????R^b1=R0K1( BTB)-1233 (16)??, R0??????, ???????????? 2~ 3 mm.4. 2  ????????????????????(13)???? B???(16) ,?????R^b1=R0K1S 1S 2(17)??, S 1, S 2[ 9, 10]???S 1= 2(1+ A4+ B4- A2- B2- A2B2)S 2= 3(1+ A4+ B4) ( 1+ A2+ B2)+ 2( 1+ A+ B)(1+ A2+ B2) (1+ A3+ B3) - (1+ A+ B) 2(1+ A4+ B4)- 3(1+ A3+ B3)2- (1+ A2+ B2)3??, ??????????????????????????4. 3  ??????????? GPS??????????????????????????????????, ?????????: ¹ L 1,L 2 ??????????, ????????????; º ??????????? L 1 ????,?????? L 2, L 3??????????????????? 1 B?L 1 ?????? R^b1????F ig. 1 The relationship of B and RMS R^b1of ambiguity L 11. ???? L 1, L 2??????????,???1 575. 42 MHz? 1 227. 60 MHz, ?????? 19 cm? 24 cm,? A= f 1/ f 2 U 1. 283???????, R^b1???? B?????????? 2  f 3 ??? L 1 ?????? R^b1????Fig. 2  The relationship of frequency f 3 and RMS R^b1ofambiguity L 1? 3  K3 ? R^b1???Fig . 3  The relationship of K3 and R^b1(?: ?? SE?? Standard Error, lambda- 3???? K3)??? 1~ 3????? MATLAB ????????? B? L 1 ?????? R^b1????f 3??? L 1 ?????? R^b1???????K3? L 1?????? R^b1????????????, L 1 ?????? R^b1? B, f 3 ?? K3 ?? M ???????(?????)???, ? B= 1? f 3= f 1?, L 1 ?????? R^b1???,?171 113. 309 10(????????) , ?? B?L 1?????? R^b1????????? 4??? 4?????,? B< 1,? B> 1. 3, R^b1????,?????? f 3 ???,?????? f 3>386 ?  ?  ?  ?                   ? 36 ?1. 575 4 @ 109 ? f 3< 1. 212 @ 109; ??? GPS????????,?????????????,? BI [ 1. 051, 1. 25] , ??????????????[ 10]??, ??????????? f 3=1 176. 45 MHz,?? K3= 25. 44 cm, ?????????????? 4 ? R^b1?????? B?????Fig . 4  The B inter- zone when the good R^b1????[ 10] , ??????, R^bD13? B??????:R^bD13=RPK1| 1- B|B(18)? 5  B? f 1, f 3 ???????? R^bD13????F ig. 5 The relationship of B and RMS R^bD13of difference off 1 and f 32. ??? GPS ???, L 1 ????, ?1 575. 42 MHz,???? 19 cm, ? L 2, L 3 ????, ? R^b1???? A, B??????????? GPS?????????, ?? GPS ?????????????, ???? A??[ 0. 5, 1. 5]???, ??? 1 ??? R^b1?????, ?? 6, ?? 6 ????? B????[ 1. 0, 1. 5]?? 6 ? BI [ 1. 0, 1. 5]??? R^b1???Fig. 6  T he relationship of B and R^b1w hen B between 1. 0and 1. 5???( 17)?????, ??? A I [ 0. 5,1. 5] , BI [ 1. 0, 1. 5]???????, A, B? R^b1????? 7, 8, 9???? 7 A, B?Rb^1???(???- 37. 5, ?? 30b)F ig. 7 The relat ionship of A, B and R^b1? 8  A, B? R^b1???(??? 172. 5, ?? 30b)F ig. 8 The relat ionship of A, B and R^b1??, ? 7 ? MATLAB ????? ( ???387? 4 ?       ???? :????????? GPS ???????? L 5 ?????- 37. 5,?? 30b)? A, B? R^b1??? 3 ????,????? R^b1? 100?????, ????/?????0,????????? 90b, 45b, 45b??8, 9???(??? 172. 5,?? 30b)?(???- 12. 5,?? 30b)? A, B? R^b1??? 3?????? 9 A, B? R^b1???(???- 12. 5, ?? 30b)F ig. 9 The relat ionship of A, B and R^b15  结  论?????????????????????, ???????????????????????,??????????????,??????????????????? L 5???????, ?????????????????????????????????????????, ??????????????????, ?????????: ¹ L 1, L 2 ??????????, ?????????????,??:? B< 1,? B> 1. 3, R^b1????,????? f 3???,?????? f 3> 1. 575 4 @109 MHz? f 3< 1. 212 @ 109 MHz; ??? GPS????????,?????????????,? BI [ 1. 05, 1. 25] ,?????????????????????? f 3= 1 176. 45 MHz, ??K3= 25. 44 cm ????; º ??? GPS ???,L 1????, ? L 2, L 3?????,??????????????????,??: ???? A= 1, B= 1??( A- 1) / B= 1( A\1)????????????????????????????????? GALILEO ??????????????????????????参考文献:[ 1]  HATCH R. Instantaneous Ambiguity Resolut ion[ A] . Proceed-ings of IAG Symposium 107 on Kinematic Systems inGeodesy, S urveying, and Remote sensing [ C ] . New York:S pringer-Verlag, 1990. 299-308.[ 2]  FRE I E, BEUTLER G. Rapid S tatic Posit ion ing Based on theFast Ambiguity Resolut ion Approach: The Alternat ive to Kine-mat ic Posit ioning [ A] . Proceedings of the 2nd Internat ionalSymposium on Precise Posit ioning w ith GPS[ C ] . 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Study and Software Implementation of GPSData Pre-processing and Onboard GPS Kinematic Orbit Deter-minat ion [ D] . Shanghai: Shanghai Astronomical Observatory,Chinese Academy of S ciences, 2005. ( ???. GPS ???????? GPS?????????????[ D] .??: ??????????, 2005. )[8 ]  ALM GREN K. A New Method for GPS Phase AmbiguityResolut ion On-T he-Fly [ D] . Stockholm: Royal Inst itute ofTechnology, 1998.[ 9]  HOREMUZ M, SJOBERG L E. Rapid GPS Ambiguity Reso-lut ion for Short and Long Baselines [ J] . Journal of Geodesy,2002, 381-391.[ 10]  S JOBERG L E. T riple Frequency GPS for Precise Positioning[ A] . Geodesy ) ) ) T he Challenge of the T hird Millennium[ C] . [ s. l. ] : [ s. n. ] , 2003. 141-144.[11 ]  SJOBERG L E. Unbiased and Biased Estimation of GPSPhase Ambiguities from Dual Frequency Phase and CodeObservables[ J ] . Journal of Geodesy, 1999, 73: 118-124.[12]  XU Guo- chang. GPS Theory, Algorithms an d Applicat ions[ M ] . 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基于模糊度中误差的GPS信号第三民用频率l5的选取研究

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