Author name used in this publication: 陈武Title in Traditional Chinese: GPS在物理大地測量中的應用及GPS邊值問題Journal title in Traditional Chinese: 測繪學報2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Chen, W

Li, F

Yue, JL

Author name used in this publication: 陈武Title in Traditional Chinese: GPS在物理大地測量中的應用及GPS邊值問題Journal title in Traditional Chinese: 測繪學報2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishedVoR allowe

PolyU Institutional Repository

? 32 ?  ? 3 ? ?  ?  ?  ? Vol. 32, No. 3 2003 ? 8 ? ACTA GEODAET ICA et CARTOGRAPHICA SINICA Aug. , 2003  ????: 10011595( 2003) 03019806 ?????: P223     ?????: AGPS????????????GPS????李  斐1, 2,陈  武1, 岳建利2( 1. ?????? ???????????, ??; 2. ???? ?????????????,?? ?? 430079)Physical Geodesy with GPSLI Fei1, 2, CHEN Wu1, YUE Jianli2(1. Dep t . of L and Sur veying and Geoinf ormatics, Hong Kong, China; 2. National L ab . f or I nf ormation Engineering in Sur v ey ing and Mapp ing and Remote Sensing , Wuhan University , Wuhan 430079, China)Abstract: Starting from the basic pr inciple of physical g eodesy, the problems as fo llow ing are analysed: the effectcaused by GPS on the t heories and met hods of the physical g eodesy, the action of GPS in solving some difficult problems of physical geodesy and the change in function of some objects investig ated in physical geodesy . In the meant ime, the discussions in this paper refer to the application of Neumann boundary value problem, the determination ofheight system and the definition and solution of GPS boundary value problem.Key words: physical geodesy ; GPS; BVP ; disturbing gravity; hight system; GPSBVP?  ?: 针对 GPS 技术逐步用于物理大地测量的现状,从物理大地测量的基本原理及方法入手,分析了 GPS对传统物理大地测量理论及方法所产生的影响?GPS在解决物理大地测量中的一些难题所发挥的作用以及对物理大地测量的一些功能所造成的变化?重点讨论了物理大地测量边值问题的基本属性的改变?第二边值问题的应用?高程系统的确定?GPS边值问题的定义?特征及求解?最后, 对 GPS 与物理大地测量进一步结合所面临的有关问题进行了简要论述?  ????: 20020926; ????: 20021227????:?? MPF( A. 34. 37. PD51)????????????( 20010103) ;?????????????????????( 020201)????:?  ?( 1960 ) ,?,?????,??,??????,?????,????????????????????????:物理大地测量; GPS;边值问题;扰动重力;高程系统; GPS边值问题1  引  言?????????????????????????????, ??????(???)????(??)?????, ??????, ??????????? GPS ??????????,????????????????,???????????????????????????????????????, ??? GPS?????????????, ?????????????????????????????????? GPS??????, ??????????????????? GPS ???????,?????????????,?????????(?????) ,?????????????(????)???????(??????????) , ??, ????????????,???????????????(??????)????????, ? GPS ???????????????, ??????????????????????????, ???????????????????????????? GPS????????????????????,????????? GPS???????????????????,???? GPS????????????,????????????????????????, GPS???????????? Moritz?????[ 1, 2] , ????????????????????2  物理大地测量研究基本原理????, ??????????????Stokes??? Molodensky ????????????????????????????, ??,??????????????????????????,??????????g= F ( S , W ) (1)???? F ????F - 1,?????? SS = F- 1[ g ( s) , w ( s) ] (2)??(1)??(2)?, g ????????; S ?????; W ????????????(2)?,????? F - 1?????????? S ,??,???????????????????????????????????,??,????????????????????????????????????????????????:???????????????????????????????,??????????????????????????????????,??????????????, ?????????????????????????????, ???? h ???(?? 1)??????????????, ???????????????????????? h ???, ??????????????: h = H 1+ H 2, ?????????????????????????; ????,??????????(???)?????, ??????????????????????????? 1  ??????????Fig. 1 Sur faces corr esponding to heights?? 1?, S1 ??????, S 3 ????????, ? S 2 ???????(????)?????????? Stokes???, ???????????????,???? H ,???1??H 1= H ;???????? S 2, ???????????????,??????????? S 1 ?????,???????? N ,? H 2= N?????????????????????? g ??????????? T ? Laplace ??????????????? Stokes????[ 1]N =R4 gS ( ) d (3)??, ????????????; R ???????; g ????????????; S ( )? Stokes?????, ? 1????? h ??h= H 1+ H 2= H + N (4)?Molodensky ???, ????? S 2 ???????????????????,?????( S 2 ?????????? S 1 ???????)??????, ?? S 2 ?????? S 1?????,?????????? H * ???,S2 ????????,? S 2 ????????????? ??? 1 ?, H 2= ???????????????????????????????????[ 1]?????? Molodensky???[ 2]????????????= R4 ( g+ G 1) S ( )d (5)??, g ???????; G 1 ?????????,? 1????? h ??h= H 1+ H 2= H* +  (6)????????????????????????, ? 1?? S 2 ?????????199? 3 ?          ?  ??: GPS ???????????? GPS ?????????(???)?????????????,??????????? 1??????????????????????????????? 1  Stokes???Molodensky???????Tab. 1 Main characters of Stokes and Molodensky s theoryS tokes?? Molodensky ?????? h= H + N h= H * + ???? ????? ???????? ??????: H ??????: H *???? ?? Laplace ???? ????? Fredholm ???????? ?????????? ??????????????? Stokes?? Molodensky?????? ??????????? ??????????3  GPS后的物理大地测量??????????, GPS ?????????????????????????, ??????? h ?????????????????????????, ????? 1?????,?????,???????????????,???????????????????????????????????????g= F [ S ( h ) , w ( h ) ]?S ( h) = F- 1[ g( h) , w ( h ) ] (7)??, S ?????????????; g ? w???????????, ?????? F - 1?????????????( 7)??(2)???????????????? S ,?????? h??????????3. 1  ?????????????GPS??????, ???????, ???????????????? h ,???????????????????????????:?(7)????? h ( H 1, H 2)??????(H 1, H 2 ???????????????????????????????)???????????????????    ?????????????,??????????,???????????????, ???????????????????,?W = F 1( S , g)? f ( T ) = F1( S , g) (8)??, S ???????????????????; f ( T )?????? T ??????????????????????????,??????????????; F1 ?????????????( 7)??(8) ,? GPS ??????????????????????3. 2  ?????????????????GPS????????????????????????????????????????????????????????????????????,???????????????????????, ?????????????????????[ 2] , ??????????????????, ?????????????????????????????????????[ 1]???, ?? GPS ?????????????(?????????????????????)?????,???????????????? ???????????, ?????????? g = g - ???????, GPS ?????????????,?????,??????????????????, ???????????????????????,?????????????,???????????????? GPS ????????????????????????,????????????????????????????????????????????????????????????(????????????????) , ???? g ?????T ?????: g = Tn , ?????,????????, ????????? T ?Laplace????????,?T = 0Tn | s= - g(9)??????????? Hotine??[ 4]T ( r , )= R4gH ( r , )d (10)??, H ( r , )?Hotine?,?????200 ?  ?  ?  ?                   ? 32 ?   H ( r , )= 2Rl- lnl + R- r cos r ( l - cos ) (11)???????H ( r , )= n= 02n+ 1n + 1Rn+ 1rn+ 1 Pn ( cos ) (12)?(10)??( 12)?, Pn ? n ? Legendre ??; ????; r ??????; l ???????????????? Stokes???, ???????? N ?,???(10)??(12) ,?? r R ?,????N =R4gS( )d=R4g n = 0 2n + 1n+ 1 Pn ( cos ) d (13)?Molodensky ???, ????? g ????????, ??????????? ????(???????)= R4 gH ( ) d+ n = 0 R4 gnH ( )d(14)??, gn ?? g ???????????, ?( 13)??(14)???????g ????????N ???????( 3)??(5) , ????????, ?????????????????????????: ???????? Hotine???????????????????????????:Hot ine???? Stokes??, ???????????,?????????[ 5]? ??????g ????????????????????,????????,???????????????????????4  GPS与高程系统???????????: ?? GPS ?????????????????????????,??, ?????????????????????,???????????????????????????,??????????????????????????????????(?)?????????????????? GPS???????????????,?????????????????(?)??????? ????????:1. ????????????????,????????????????????????,????????????, ?????,??????????????????????????????[ 6]?2. ?? GPS ??, (?)??????????????????,????????????????????,????????????????????????????????????????????,????,??????????????, ???????,?????????????3. GPS??????,????????????????? GPS ??, ???????GPS??????, ??????????????????????(?)????????,??????,??,????????????????????? GPS?(???) ,????????, ???????????????????,?? GPS??, ???(?)????????,??????,????(?)??????????????????? GPS ??????????????, ?(?)??????????????????,???????????????,??????????????????????????????????????????????,?????????????????????,????????,????? GPS ???????(????)???,?????????,???? GPS ??????????????? N ?????,????? H ????H * ??H = hGPS- N , H* = hGPS-  ( 15)?( 15)?????????,?? GPS?????????(?)????????????, GPS???????????????5  GPS边值问题5. 1  ???? GPS??????:????????????, ?????????????, ??(?)????????????GPS????????????, ????201? 3 ?          ?  ??: GPS ???????????? GPS ?????????:1. ???????????????????????, ?????????????????????? GPS ?????????????????????????, ???????( 1)??????????????????????,????????????????,? GPS ??????????????????2. ?? 3???, GPS?????, ??????????????3. ?? 4???,??GPS????????????,??,???????????(?)???????????????????????, GPS ???????, ?????????(?)??????4. ????????????????????????????,????????,????????????????????????,????? GPS ??????????????????, ????????????????????,??????????, GPS?????????????????????????:????????,??????????;???????????,????????5. 2  GPS????? Neumann???????????????, ????????????,??????????? Neumann??????????????????????????????, ???????????????????, ??????????????????????,???????????????,?????( 9)????????????????? GPS?????, ????????????,??????????,???????????????, ???( 9)?????????????, GPS???????? Neumann????,??????????????????, ????????????, ??????????????????????????,??? Molodensky ?????????????,??????? Neumann?????????5. 3  GPS??????????, Moritz ? 2000 ??? Molodensky??????,??? GPS ???????, ???????????????????????,?? GPS ?????????????( 14)?????????????????,?? GPS????????????????????, ???????????????????? T ???????????T =S l dS (16)??, ???????????; S ?????,???????????????????????????[ 1] ,??(16)??????,??Th = - 2cos +S  h ( 1l ) dS (17)??, ????????????????Th = - g, ??, GPS ???????????2cos + S  h ( 1l )dS = - g (18)??, ?????????, ???????g ??????????T ( )???(18)????????, ?????? Fredholm ?????????? S ?????, ????????????????????????????,???? Moritz??????? g ???? Molodensky ??????????????[ 1] ,????2cos - ( r 2- r 2p2l - 12l ) r 2rp sec d= g(19)??, l ?????????????; r ?????????; rp ????P ???; d????????(19)? Molodensky ?????????????, ??????????????????????????????????????????????[ 1] ,?h- hpl? sec ????????????,??????????,?202 ?  ?  ?  ?                   ? 32 ???(18)???????T = R 2 l sec d R2 0l 0d+ R 2 1l 0d(20)??0= 12[g- 18 gH ( ) d]1= 12[g1- 18 g 1H ( )d]g 1= R 2 h - hPl 30 0d??,????? Molodensky ????????,???????????T =R4 g- ( h- hp ) gh H ( )d (21)??, h???????? Bruns??? VeningMeinesz??, ??(21)????????????????( 21)? Moritz?? Molodensky ?????????????????6  结论与问题GPS?????, ??????????????????, ???????????????,??,?????????????????????????????:1. GPS????????????????2. ?? GPS ??, ????????????????????????3. ? GPS????(?)????????????, ???????????????????4. GPS???????????????????, ???????,?????, ????????? Molodensky ????????,?? GPS ????????, ?????????????????????????????????????,?? GPS????????????????, GPS ???????????????????, ??????????????????, ??????????????????, GPS ?????????,??? GPS ??????????, ???????????????, ??????????????, ???????????????????????, ?????????????????????, GSP ???????????????????, ???????,?????????????????,???????????, GPS?????????????????????????????????????????,???????????????????????, ?????????????????????????????,????????????????? GPS ????????????????????????,????????????, ???????????????, ????????????????????????????, ???????????????????参考文献:[ 1]  HEISKANEN W A, MORITZ H. Physical Geodesy[ M ] . San Francisco and London: W H Freeman Co,1967.[ 2]  MORITZ H. Advanced Physical Geodesy [ M ] . Beijing : Publishing House o f Surveying and Mapping,1982. ( in Chinese)[ 3]  L I Fei. Analysis and Cor rections to Er rors Caused byG ravity Anomaly in Gravit y Inversion [ J] . Acta Geodaetica et Car to graphica Sinca, 2001, 30 ( 3) : 220225. ( in Chinese)[ 4]  HU Mingcheng, LU Fu. Moden Geodesy [ M ] . Beijing: Publishing House of Surv ey ing and Mapping,1992.[ 5]  PETR V , ZHANG Changyou, LARS E S. A Comparison of Stokes and Hotine s Approaches to Geo id Computation[ J] . Manuscripta Geodaetica, 1992, 17: 2935.[ 6]  ZHANG Chijun. On Some Problems of Pr ecise Geoid, [ J] . Crustal Deformation and Earthquake, 1997,17( 1) : 3438. ( in Chinese)203? 3 ?          ?  ??: GPS ???????????? GPS ????

GPS在物理大地测量中的应用及GPS边值问题

Abstract

Similar works

Full text

Available Versions

PolyU Institutional Repository