Author name used in this publication: 钟萍Author name used in this publication: 丁晓利, DING Xiao-liAuthor name used in this publication: 郑大伟Author name used in this publication: 陈武Author name used in this publication: 黄丁发Title in Traditional Chinese: 一種基于交叉證認技術的自適應小波變換及其在削減GPS多路徑誤差中的應用Journal title in Traditional Chinese: 測繪學報2007-2008 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Chen, W

Ding, XL

Huang, DF

Zheng, DW

Zhong, P

PolyU Institutional Repository

? 36 ?  ? 3 ? ?  ?  ?  ? Vol. 36, No. 3 2007 ? 8 ? ACTA GEODAETICA et CARTOGRAPHICA S INICA Aug, 2007  ????: 10011595( 2007) 03027907 ?????: P228. 4     ?????: A??????????????????????? GPS?????????钟  萍1,丁晓利1,郑大伟2,陈  武1, 黄丁发3( 1. ?????????????????, ?? ??; 2. ????? ????? ???????????, ??200030; 3. ?????? ?????,???? 610031)An Adaptive Wavelet Transform Based on Crossvalidation andIts Application to Mitigate GPS Multipath EffectsZHONG Ping1, DING Xiaoli1, ZHENG Daw ei2, CHEN Wu1, HUANG Dingfa3(1. Department of L and Surveying and GeoInf ormatics, The Hong Kong Polytechnic Univ ersity ,H ong K ong, China ; 2. Center f or Astrogeodynamics Research, Shanghai Ast ronomical Observatory, Chinese Academy of Sci ences, Shanghai 200030, China; 3. Department ofSurv eying and Mapping , Southw est Jiaotong Univ ersity , Chengdu 610031, China )Abstract: GPS multipath disturbance is a bottleneck problem that limits accuracy of Global Positioning System( GPS) positioning. A method based on the technique of crossvalidation to automatically identify wavelet signal layers is developed for separ ating noise from signals in data series, and applied to mitigate GPS multipath effects. Exper iments w ith both simulated data series and real GPS observ at ions show that the method is a pow erful signal decomposer, which can successfully separ ate noise from signals as long as the noise lev el is lower than about half of themagnitude of the signals. A multipath correction model can be derived wit h the proposed method and t he siderealdaytoday repeating property of GPS mult ipath signals can be used to remove multipath effects in subsequent days ofGPS observations, and ther efore improve the quality of the GPS results.Key words: crossvalidation; w avelet tr ansform; GPS; multipath effects?  ?:多路径效应影响是目前限制 GPS 定位精度进一步提高的瓶颈?提出用交叉证认技术自动识别小波分解的信号层,再通过小波重构实现降噪和信号提取, 并将该方法应用于 GPS 多路径误差的削减中?对模拟数据和实际 GPS 观测资料的分析表明, 该方法能合理分离不同噪声水平下资料序列中的信号和噪声; 当噪声水平小于信号振幅的一半时,能成功分离资料序列中的高频信号?同时,运用该方法得到的多路径改正模型和GPS 多路径效应的重复性, 可有效地削弱多路径效应的影响,提高 GPS 定位精度?  ????: 20060630; ????: 20070122????: ????????????????( PolyU 5148/ 04E) ; ?????????????????( 897M )????: ?  ?( 1980) ,?,?????,?????,????GPS ????????Email: p. zhong@ polyu. edu. hk???:交叉证认; 小波变换; GPS; 多路径效应1  引  言??????( GPS)???????????????????????????,????????????????,??????????????????????? GPS ????????????, ???????? (???5 km) ,??, GPS ??????????????????????; ?????????(?,???????????????,?????) ,???????????????, ?????????????????????????????????????,?????????GPS?????????[ 1]????,???????????? GPS?????????????? GPS???,??????(?????????????)??????,??????????????;????????????, ?????????????? GPS ?????????????????, ???????????????????(?)????????;????????????, ?? GPS ?????????????,? GPS?????( SNR)???, ????????(???? FIR ??[ 2]?????[ 3]?Vondrak??[ 4]?)???, ?????????????????????????????(???????)?????,????????????????????????????, ????????????????, ??????????????????????????????????, ??????????????????????????????????????,??????????????,???????????????????????????????,??????????????????,??????????????????????????????????????????????????,?????????????????????,????????, ??????????[ 5, 6]??????????????,?GPS???????????????????? GPS ??????????????,?????????????????;??,???????????? GPS ??, ??????????2  GPS多路径信号特征?????(?? 1 ??)?? GPS ???????????????? GPS ?????,??????? GPS??????, ?????????,???? GPS?????[ 1]?? 1????????????????? d ????????????????Sd= A cos  (1)?????S r= A cos ( + ) ,  (0   1) (2)??, A ??????????????; ???????, ??????????????????; ???????????? 1  GPS ????????F ig. 1  Schematic repr esentat ion of GPS multipathphenomenon  ?? 1?????,??????????AB ?BC ??,??? 2d cos ???????????????????= 4d cos  (3)??, ????????, ????????????, ?????????????????????S = Sd+ S r= R cos ( + ) (4)??, ??????? R ????????? ??????[ 1]R= A (1+ 2cos + 2) 1/ 2 (5)= arctan ( sin 1+ cos ) (6)???(6)?????,???????? ?????,?? / = 0 ???????????? = 1, =  / 2,?,???? / 4?????(?? L 1??, ??????????4. 8 cm)???,???????????????? GPS??,??????????????????????? f ?????? ?????????(3)??,??? 2??f =12ddt = 2dsin ddt (7)??(7)?????,????????????? GPS ????????, ???????????????, ??????????????????????????[ 7] , ??, ?????????,?????????????????????????? GPS ???????????????,? GPS ???????????????,???????????????[ 1, 8]??????? GPS???,???????????????????????[ 9, 10]280 ?  ?  ?  ?                   ? 36 ?(????????) ,??????????????????????????????,??????? GPS?????????????????,?????????????????????,?? GPS????????3  小波滤波????????????????????????????????????????,?????????(???)???(??)???????(??)????????? f????????[ 11]W f ( a, b ) = f , a, b=R f ( t ) 1| a |  ( t - ba)dt (8)??,  ( t )????; a ? b ??????????, a, b  R ?a 0;  ( t )?  ( t )??????????????????:f =1C  RRf ,  a, b  a, b( t ) dadba2 (9)??,?? C  ???????????????????????????????,????? Mallat???????????????????????????????????,????????????????????????????????,??????????????????????????????????,?????????????????????????,???????????????????????[ 12]???,?????????[ 5, 6]??????????????4  交叉证认法?????????????????????????????????????????????????????????????????:???,???????( x i , y i ) , i= 1, 2, ,N ?????:???( x 1, 2m- 1, y 1, 2m- 1)????( x 2, 2m , y2, 2m) , m= 1, 2, , N1(N ????, N 1=N / 2; N ????, N 1= (N - 1) / 2)???????????, ???????????,??????(????? N 2) ,? N 2<< N 1????,?????? K ?????, ????? k ???????f , ?????????????????C ( k , P ) =1N 2 N2i = 1[ y 2, i - f ( x 2, i ) ] 2 (10)??, P ?????????????; ( x 2, i ,y2, i) , i = 1, 2, , N 2 ????????;f ( x 2, i )???????????? f ? x 2, i??????????, ?? k1 ( k 1 = 1, 2, , K + 1) ?k 2( k 2= k 1, k 1+ 1, , K + 1)????????????, ????????, ? 1 ? K ?????????????, ? K + 1??????????????????? k 1 ? k 2 ??????? M ????????Pj , j = 1, 2, , M ,???( 10)?? M ???????? C ( k1, 2,P j ) ,?????????C ( k 1, 2, P ) =1M Mj = 1 C ( k 1, 2, P j ) (11)??C ( k 1, 2, P )????? k1, 2, ? k 1? k 2 ??????????????????????,????????? K + 1??????,??????????? k 1+ 1? k 2+1?????????????????????????????????????????,???????????????,??,?????????, ????????????????????????????????1???, ?????????????????,????????????????,??????????????????????, ?????????????????????, ???????????70%???????????????;??,???????????????????????,??????????????????????,????????? N 2 ??????N 1 ? 20% ,??????? M = 20?5  模拟试验与分析????????u t= sin (2t / 2 400)+ sin (2t / 300)+0. 6sin (2t / 60)+ et (12)??,???? u t ???????????et ?281? 3 ?    ?  ??: ??????????????????????? GPS ???????????????????????????,?????????? 2 400 s, 300 s? 60 s???????????????????? 1 s, ???? 4 000??????????????????[ 13] ,?????????????????Meyer????????? 2????? e t??????N (0, 1. 0)?,???????????????, s ???????; a8 ?????????; d 8~ d 1????????????????????????????, ???????????????? s= a8+ d 8+ d7+ + d 1?? 2 ???????????? N ( 0, 1. 0)??????Fig . 2  Wavelet decomposition o f simulated data series at noise level N ( 0, 1. 0)  ?? 2?????,?????????????????????,???????????????????????????????????,? 3 ????????????????????????????????????????? d 5~ d8????? a8(???d 5~ a8?,??)?(a) ??????( b) ????? N( 0, 1. 0)???????( c) ???? 1 ?????? d 5~ d 8 ????? a8 ?????( d) ??????????????(e) ???????????????????? 3 ??????????????????????Fig. 3 T est r esults of ident ifying waveletdecomposed signallayers wit h the crossvalidation method? 1?????????????????????????, ??????????????????????????????????????1??: 0. 016 7 Hz(??????? 60 s)??d 5? d 6???, 0. 003 3 Hz(??? 300 s)??d 7? d 8 ???; ?????????????[ 3]??,???? a8 ?????????[ 0,282 ?  ?  ?  ?                   ? 36 ?0. 002 0] Hz,???????? 0. 000 4 Hz(??? 2 400 s)?? a8???????? d 5~ d8? a8??????, ?????????????????1 ??Meyer???????????(??? 1 Hz)Tab. 1  Central frequencies of Meyer wavelet for data serieswith sampling rate of 1 Hz?? d1 d2 d3 d4??/ Hz 0. 331 7 0. 165 8 0. 082 9 0. 041 5?? d5 d6 d7 d8??/ Hz 0. 020 7 0. 010 4 0. 005 2 0. 002 6??, ???????????????????????,? 2?????( 12)????????????????????????????? 2 ?????????????????????????????????? RMS?Tab. 2  Signal layers selected with the crossvalidationmethod and RMS values of differences betweensimulated and f iltered data series at differentnoise levels????/ cm 0. 4 1. 0 1. 4??? d5~ a8 d5~ a8 d5~ a8???? RM S/ cm 0. 100 0. 262 0. 364????/ cm 1. 8 2. 4 3. 0??? d7~ a8 d8~ a8 d8~ a8???? RM S/ cm 0. 476 0. 520 0. 535?? 2?????, ?????????????????????????, ???????????????????????,??2?????????????(???????) :???????? 1. 4 cm, ????????( 2. 6 cm)????, ????????????????;?????????? 1. 8 cm ?,??? 60 s??????????????????,?? 2?????,?????????????? RMS ?????, ????????????????, ??????????????????????????6  GPS多路径效应的削减????????????????????, ????????????????????2004?3? 10??12?,??? SR530??? GPS????AT502???????? 86 m????????????, ??????10 Hz,???????? 15??? GPS ???,???????;??????????,???? GPS ???????????????????????, ?????????????????(?? 4??)????????????????????????????????????????,????????? 0. 1 mm??????????????, ???????????????? 0. 06 Hz? 40 mm; ??????????? 0. 1 Hz, ??? 40 mm ?? 20 mm, ??20 mm?? 10 mm???????? 45 min ??????????? 4  ????????????????????Fig. 4 Motion simulation table and layout of reference androver stations for the experimentGPS?????????????,????????????????, ?????????????????????????????????????, ????????????;??????????????? X , Y ?H ??????????????????, ?????? 5, 6? 7??????, X ? Y ??????????????( UT M )?????????;? H ???????????????????????, ??????????????????????,????????????????????????, ????????????????????????????????????????????????????????????????????????????? RMS???? 3???? 3?????, ????????????????????????,????????????????????????????283? 3 ?    ?  ??: ??????????????????????? GPS ??????????(?? 5, 6? 7)???????????????????, ???????????????????,????????????? RMS??????????????????????????????? 5 ????????????????        ? 6  ??????????????????????( X ??) ??????( Y ??)Fig . 5 F iltered and differ ence series o f the X       Fig . 6  Filtered and difference ser ies of the Y direcdirect ion, with the simulated motions removed tion, wit h the simulated motions removed  ? 7 ??????????????????????( H )??F ig. 7  Filtered and difference ser ies of t he H direction, w iththe simulated motions removed  ?????, ???????????????????, ???????????????????? 0. 548? 0. 807??, ?????????????????????[ 14]??? 0. 22 ????( 99%?????)????????????????????????, ??????????????????????????,????? 5, 6? 7???????????????????????, ???????? RMS ????????? 20%~ 40%?7  结论与建议???? GPS ???????????????,???????????????????, ????????????????????,??????????????????? 3  ?????????????????????? RMSTab. 3  Signal layers of wavelet decomposition with crossvalidation method and RMS of noise seriesDayX Y H??? RMS/ cm ??? RMS / cm ??? RMS / cm1 d6~ a8 0. 122 d 7~ a8 0. 216 d7~ a8 0. 4622 d5~ a8 0. 120 d 5~ a8 0. 236 d6~ a8 0. 4933 d5~ a8 0. 122 d 5~ a8 0. 228 d6~ a8 0. 509284 ?  ?  ?  ?                   ? 36 ??????? GPS ????????????:???????????????, ?????????????????????; ???????????????,???????????????????????, ????????????????,????????????????, ??????????????,? GPS ???????? 20% ~ 40%???????????????????,????????????????????????????, ???????????????????, ????????????????????, ???????????????,????????????(??????)?,???????????????????????????????: 本文第一作者感谢香港理工大学奖学金的资助.参考文献:[ 1]  LEICK A. GPS Satellit e Surveying ( 3rd edn) [ M ] . Hoboken:John Wiley & Sons, Inc. , 2004.[ 2]  GE L, HAN S, RIZOS C. Multipath Mit igat ion of ContinuousGPS Measurements Using an Adapt ive Filter [ J ] . GPS Solut ion, 2000, 4( 2) : 1930.[ 3]  HUNG D F, DING X L, CHEN Y Q, et al . Wavelet FiltersBased Separat ion of GPS Multipath Effect s and EngineeringSt ructural Vibrat ions [ J ] . 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一种基于交叉证认技术的自适应小波变换及其在削减GPS多路径误差中的应用

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