A Reference Point-based Precise Relative Positioning Method Using a Single Frequency Receiver

Transcription

1 A eference Pont-baed Prece elatve Potonng Method Ung a Sngle Frequency ecever Euho Km, odd Walter, J. Davd Powell, Stanford Unverty BIOGAPHY Euho Km a Ph.D. canddate n the Aeronautc and Atronautc Department at Stanford Unverty. He receved h B.S. n Aeropace Engneerng n from Iowa State Unverty and h M.S. from Stanford Unverty n. H reearch currently focue on prece potonng ung a ngle frequency recever and flght npecton truth ytem. Dr. odd Walter receved h B. S. n phyc from enelaer Polytechnc Inttute and h Ph.D. n 993 from Stanford Unverty. He currently a Senor eearch Engneer at Stanford Unverty. He a cochar of the WAAS Integrty Performance Panel (WIPP focued on the mplementaton of WAAS and the development of later tage. Key contrbuton nclude: early prototype development provng the feablty of WAAS, gnfcant contrbuton to MOPS degn and valdaton, co-edtng of the Inttute of avgaton' book of paper about WAAS and European and Japanee counterpar, and degn of onopherc algorthm for WAAS. He wa the corecpent of the IO early achevement award. Prof. J. Davd Powell receved h B.S. degree n Mechancal Engneerng from MI and h Ph.D n Aero/Atro from Stanford n 97. He oned the Stanford Aero/Atro Department Faculty n 97 and currently an Emertu Profeor. ecent focu of reearch centered around applcaton of GPS: applcaton of the FAA WAAS for enhanced plot dplay, the ue of WAAS and new dplay to enable cloer pacng on parallel runway, and the ue of WAAS for flght npecton for conventonal navgaton ad. He ha coauthored two text book n control ytem degn. ABSAC h paper nvetgate how to take advantage of the known poton of a pont at whch a ngle frequency GPS recever located. Ung th reference pont and a ngle frequency recever, a prece relatve potonng method developed. h method partcularly uted for the applcaton whoe accuracy requremen are relaxed a tme pae. In ome crcumtance, one requre a far better accuracy than a ngle frequency recever ung tandalone GPS or WAAS provde. Further, typcal prece potonng method uch a dfferental GPS (DGPS, real tme knematc urvey (K, and prece pont potonng (PPP cannot be ued due to hardware or cot lmtaton. h dffcult tuaton can be overcome wth the new algorthm, prece relatve potonng (PP, decrbed n th paper. he PP method requre raw meauremen (e.g. peudo range, carrer phae meauremen, and ephemer from a ngle frequency recever. It alo requre a reference pont. he reference pont can be an ntal poton of a recever (or any poton durng navgaton for potproceng that can be obtaned by ung varou technque, for example, the ue of other enor. he PP ha two mode. One Iono-Free (I-F PP, the other one Carrer-Baed (C-B PP. he I-F PP gnfcantly mtgate the effect of multpath and onophere delay and cancel out uer recever clock error by ung combnaton of peudorange and carrer phae meauremen between atellte. On the other hand, C-B PP ue only carrer phae meaurement a rangng ource. herefore, the I-F PP can acheve better tablty than tandalone GPS or WAAS can provde, and the C-B PP provde prece poton oluton n a hort-tme applcaton. he PP partcularly well uted to the problem of accurate arcraft poton determnaton uch a flght npecton. Prelmnary reul how a centmeter to decmeter level of tablty n horzontal and vertcal plane. IODUCIO Prece potonng ung GPS ha been one of the mot actve reearch area n the communty of navgaton becaue there have been many applcaton that requre a hgh level of accuracy n poton. he applcaton

2 nclude automatc arcraft landng, atttude determnaton, and autonomou control of land vehcle. Extenve tude on prece potonng drven by commercal and academc ntere have reulted n ucceful method and produc. One of the popular method eal-me Knematc (K urvey. K typcally requre two or more recever to cancel out the common error between them. It alo ue carrer phae meauremen a rangng ource ntead of code phae meauremen. herefore, a K ytem ha a reference recever, whoe locaton known, and one or more rover recever. Alo, a K ytem ha a ophtcated nteger ambguty reoluton algorthm n order to ue carrer phae meauremen a rangng ource. here are many mplementaton of ambguty reoluton. he robutne and effectvene of the algorthm are mportant factor for the performance of a product []. Wth the help of error correcton from a reference recever and the ue of carrer phae meauremen a rangng ource, current K ytem uually acheve a centmeter level of accuracy. In addton to hgh accuracy, ome K ytem have the capablty of an ntant nteger reoluton [] and of effectvely handlng cycle-lp [], whch provde robutne n varou tuaton. Due to thee advantage, K ytem are wdely ued n many applcaton. Another method Prece Pont Potonng (PPP ung a dual frequency recever [3]. Unlke K, PPP depend on external ource lke nternatonal GPS ervce (IGS n order to mtgate the varou error n code or carrer phae meauremen and orbtal error. Due to thee error correcton from external ource, PPP doe not requre multple recever but need a dual frequency recever for accurate nteger ambguty reoluton. Ung one recever perm more flexble operaton than K. However, latency or pot proceng nevtable nce the external ource are not avalable n real tme. PPP provde a dec to centmeter level of accuracy n poton doman. Although thee technque can provde a hgh level of accuracy n poton a well a a robut performance, t not poble to ue thee method n ome applcaton uch a a flght npecton truth ytem. he reaon that the FAA flght npecton truth ytem not only requre a hgh level of accuracy (up to 3cm 95% but alo near real tme proceng. In addton to that, flght npecton procedure can t afford the addtonal tme n ettng up local reference GPS recever. Due to thee requremen, K and PPP are not uted to th applcaton. herefore, n the current FAA flght truth npecton ytem, a navgaton grade IS ha been ued a a man enor wth a radar altmeter and a von enor n order to acheve the requremen. h paper preen a reference pont-baed prece relatve potonng method ung a ngle frequency recever. It motvated to enhance and reduce the cot of the current FAA flght npecton truth ytem by elmnatng the expenve IS but acheve the ame requremen wth a ngle frequency recever. In th method, t aumed that a uer able to fnd the relatve coordnate of a recever to a reference pont at one tme durng navgaton by ung other enor. he abolute poton of the reference pont alo aumed to be urveyed. In a flght npecton procedure, a threhold on a runway erve a a reference pont whch accurately urveyed. he onboard radar altmeter and von enor are ued to fnd the relatve poton of an arcraft over the threhold. Fgure llutrate the procedure of the flght npecton and poton determnaton accuracy requremen. It hould be alo noted that the flght tme very hort (le than 3 mnute wthn the tght accuracy requremen. he new method epecally developed to take advantage of the known poton of a recever at one tme and the hort operaton tme. he reference pont-baed prece relatve potonng (PP method ha two mode. One Iono-Free PP, and the other Carrer-baed PP. he Iono-Free PP provde table poton oluton wth reduced multpath noe, whch ue both code and carrer phae meauremen and cancel out the onopherc delay. On the other hand, the Carrer-baed PP provde very prece poton oluton nce t ue only carrer phae meauremen. But, the carrer-baed PP ha onopherc delay and a large ba n the meauremen. hee dfferent error charactertc of the two PP mode can be utlzed to atfy the accuracy requremen of the flght npecton truth ytem, whch wll be dcued later. h method can be mplemented n real tme or n potproceng. However, the relatve poton of a recever to a reference pont hould be known at the ntal tme for a real tme proceng. For pot-proceng, the relatve poton to a reference pont only need to be provded at one tme durng navgaton. he overall abolute poton accuracy of th method lmted to the accuracy of the other enor that ued to fnd the relatve poton to the reference pont. h paper contructed a follow. he dervaton of the I-F and C-B PP wll be hown n ecton. Alo, the error charactertc of the two mode wll be analyzed n that ecton. he reul from the tet of the two mode wth tatc data wll be hown n ecton 3. he concluon wll be followed n ecton 4.

3 ± m Poton determnaton accuracy requrement ±3cm y ( k ( k ( k = ρ ( k ( k ( k ( k = r c( δtu δ λ ( k ( k ρ (.3 8km (mn 3km (5 unway eference pont Fgure : Illutraton of FAA flght npecton truth ytem accuracy requremen and procedure n vertcal plane. Dervaton of Prece elatve Potonng Equaton here are two poble prece relatve potonng oluton. One Iono-Free (I-F prece relatve potonng (PP, whch free of the onopherc delay. he other one carrer-baed (C-B prece relatve potonng, whch ue only carrer phae meauremen a rangng ource.. Iono-Free (I-F prece relatve potonng he GPS meaurement for rangng ource are code phae meauremen ( ρ and carrer phae meauremen (, whch are ( k ( k ( k ( k ( k ( k ( u ρ = r I c δt δt ρ (. ( k ( k ( k ( k ( k ( k ( k r I c( tu = δ δ λ (. the upercrpt (k ndcate the aocated atellte. ( k r the geometrc range between a uer and k th atellte. ( k ( k I and are the onopherc delay and the tropopherc delay repectvely n the range ( k meauremen. δt u the recever clock error, andδt ( k the clock error of the atellte. and ( k denote the modelng error, multpath, and unmodeled effec n code and carrer phae meauremen repectvely. λ the carrer wavelength on L, and ambguty on L of the atellte. ρ ( k the nteger he tropopherc delay can be compenated from the current hgh fdelty tropophere model [4]. Satellte clock error correcton can be computed by ung GPS ephemer data or wth WAAS data. Wth thee error correcton, equaton (.3 become y ˆ c t r c t ( k ( k ( k ( k ( k δˆ = δ u λ ( k ( k ( k ( k ρ t ( k and ( k tand for the redual error of the tropopherc delay and the atellte clock error correcton. ˆ the etmated tropopherc delay, andδ t the etmated atellte clock error. ˆ At th pont, let u degnate a reference pont, p whoe abolute poton aumed to be urveyed. ref (.4 he poton of a uer at any tme can be decrbed a the um of the poton of the reference pont and the relatve poton to the reference pont, δ p, a follow. p = p δ p (.5 uer ref the poton of a uer. p uer he geometrc range between the reference pont and a atellte, r, can be ealy computed nce the abolute poton of the reference pont known. It well known that when the baelne of the reference pont and the recever hort (~km compared to the dtance to the k th atellte, the dfference between the geometrc range ( k to the atellte from the uer, r,and the reference pont, ( k r, can be decrbed a [5] ( k ( k ( k r r = δ p (.6 ( k the lne of ght vector to k th atellte from the reference pont. h tuaton llutrated n Fgure. he onopherc delay are cancelled out by ummng the halve of the code phae meauremen and the carrer phae meauremen a follow.

4 Sat k Sat b ˆ p = δ p δ p. bp the error nδ pˆ caued by the other enor whch ued to fnd the relatve poton to the reference pont. herefore, the value of b p depend on r (k the accuracy of the other enor. nteger ambguty term. ˆ ( k, bp and the noe term. herefore, decrbed a ˆ ( k, the etmated ha offe becaue of λ ˆ ( k, can be r ( r (k ˆ = b (. λ λ (k ( recever δ p ef r ( b ( k ( p b = ( b ρ t (. Fgure : Geometry of a recever and a reference pont herefore, f ( k r ubtracted from equaton (.4, then y y r ˆ c t ( k ( k ( k ( k ( k = ˆ δ ( k ( k = δ p cδtu λ ( k ( k ( k ( k ρ t ( (.7 ( k Let u ubtract y from y n order to cancel out the recever clock error, then ( ( k ( y = y y ( k ( δ p λ ρ t = ( (.8 ( ( k ( ( denote. ( here are two unknown, δ p and, n equaton (.8 except the noe term. Snce t aumed that δ p known at one tme durng navgaton, t poble to approxmately evaluate at that partcular tme. Let u denote the etmated relatve poton to the reference pont from other enor aδ pˆ. hen, the nteger ambguty term can be approxmated a λˆ y p ( k ( = ( δ ˆ ( k ( = ( bp λ ρ t (.9 b the ba n the etmated nteger term, and t cloely related to the poton error charactertc. h ue wll be dcued n the analy of the error charactertc of the I-F and C-B prece relatve potonng oluton. ow, t poble to olve for λ ˆ ( k, from equaton (.8 a follow. y ˆ ( p δ p by ubtractng ( k ( λ = δ ρ t b (. = (.3 It eay to contruct a ytem of lnear equaton by mplementng the ame procedure for the other atellte n order to olve forδ p n the leat quare ene. But, rather than olvng the ytem of equaton mlar to equaton (., t may be better to further reduce the multpath noe by ung a Hatch flter. In th cae, the k carrer moothed peudo range, ρ t, can be ued n tead of ( k ( ρ, whch t ( ( ( k ( k ( M ( k ( t t [ ( t M M ( k ( k ( ( t ( t ] ρ = ρ ρ (.4 M the number of epoch of the meauremen k that are ued for moothng. he ue of ρ t make ( ( equaton (.3 nvald becaue the onopherc delay are not exactly cancelled out. herefore, a mall number for M derable n order for the derved equaton to be

5 reaonable. he value of M may vary wth repect to the actvty of the onophere and multpath. Wth the determned nteger ambguty term and the moothed peudo range, the I-F prece relatve potonng equaton for k number of atellte can be decrbed n a (, ( ( ( (, ˆ, y λ, (, ˆ (, ( ( (, y λ, = δ p( t (.5 ˆ ( k ( y λ t t, t Y( t H( t the ubcrpt denote the carrer-moothed meauremen. here no combnaton of the ame atellte, uch a ( (,. Varou weghtng matrx can alo be contructed for the equaton (.5. hen, the relatve poton wth repect to the reference pont can be etmated wth weghted leat quare a follow. ( ( δ pˆ t = H ( t W( t H( t H ( t W( t Y( t (.6 IF he error charactertc of δ pˆ IF wll be dcued n the later ecton.. Carrer-baed (C-B prece relatve potonng Snce the nteger ambgute,, are olved n the proce of I-F prece relatve potonng, t poble to ue only the carrer phae meauremen a rangng ource. he mlar procedure to the I-F prece relatve potonng algorthm can be appled for the C-B prece relatve potonng a follow. At frt, let u apply the tropophere and the atellte clock error correcton to the carrer phae meauremen. Alo, ( k Subtractng r from the carrer phae meauremen reul n z r ˆ c t ( k ( k ( k ( k ( k = ˆ δ ( k ( k ( k = δ p I cδtu λ ( k ( k ( k t (.7 ( k ( z = z z ( k ( ( δ p I λ = t (.8 ow, let u apply the etmated nteger term to the above equaton. hen, ( ( δ z λˆ = p I ( k ( b t (, ( ( (, ˆ, z λ, (, (, ( ( (, ˆ z λ, = δ pt ( ˆ ( k ( z λ, (.9 A ytem of lnear equaton mlar to the equaton (.9 for the other atellte can be decrbed a Z( t H( t ( t t t, = I b (. (. Of coure, there n no combnaton of the ame atellte. he relatve poton wth repect to the reference pont can be olved from ( ( δ pˆ t = H ( t W( t H( t H ( t W( t Z( t (. CB he error charactertc of δ pˆcb next ecton. wll be dcued n the.3 he error charactertc of I-F and C-B prece relatve potonng oluton I-F and C-B prece relatve potonng (PP oluton have dfferent error charactertc. hee dfferent error charactertc mply when to ue ether I-F or C-B poton oluton. Equaton (.3 how the varou error term n the meauremen for the I-F PP. Let u retate equaton (.3 a a functon of tme a follow. hen, the dfference between z ( k and ( z ( ( ( t = ρ t t ( t ( t b ( (.3

6 ( ( k ( p ( ( ( ( ( ( b ( = ( b ρ ( ( (.4 he tme, t, ndcate the elaped tme from the tme,, when the dfferenced nteger term are reolved. In, equaton (.3, k t t do not gnfcantly ( ( and ( ( change over tme [5]. herefore, b ( and (, ( actually mtgate the redual tropopherc delay ( k and the atellte clock error over hort tme (~ten of mnute. can be gnored nce t very mall ( ( compared to the other term. herefore, equaton (.3 can be approxmated over hort tme a follow. ( ( k ( t ρ ( t bp ( ρ = ρ ( t bif ( ( ( (.5 b IF the ba due to naccurate determnaton of the relatve poton to the reference pont and multpath when the nteger term are reolved. Of coure, t ( ( wll have a larger but fxed ba when tme ncreae uch that and do not effectvely mtgate ( ( ( t and ( ( ( t. he magntude of bif depend on the multpath and the accuracy of other enor whch are ued to fnd the relatve poton to the reference pont. σ can be approxmated a follow. b IF σ b σ σ ρ (.6 IF bp σ b p the rm of other enor, andσ ρ the rm range error due to multpath. herefore, the precene of the I- F PP depend on the accuracy of the other enor and multpath. he rm of t qute mall compared to ( ( the rm of the error the code phae meaurement. h manly due to the elmnated (or nearly elmnated f carrer-moothng ued onopherc delay and the reduced multpath effect. On the other hand, the equaton (. how the error term n the meauremen for the C-B PP. Let u retate the equaton (. a a functon of tme a follow. ( ( ( (, t = I t b ( t ( t t ( t Equaton (.7 can be approxmated over hort tme (~ten of mnute a follow. n (.7 ( ( k (, b CB ( ( ( ( ( ( ρ I ( t bcb p ( ( ( t I t ( b = (.8 the ba caued by naccurate determnaton ( ( k, ( t (, of the nteger ambgute. t wll be larger but fxed a tme ncreae lke. approxmated a follow. Apparently, σ b IF b 8 CB bp ρ can be σ σ σ σ σ t (.9 ( t much lager than ( k, ( t,. herefore, t hghly lkely that the meauremen for the C-B PP may have a lager ba than I-F PP. It proved n the analy that the qualty of other enor ued to fnd the relatve poton to the reference pont effec the performance of I-F PP and C-B PP nce any offe caued by the other enor wll reman a a ba n the range meaurement. b CB It clearly hown that I-F PP provde better performance the C-B PP. he man drawback of the C-B PP that the uncompenated onopherc delay and the large ba n the meauremen,, may ntroduce drftlke error n poton doman n a few ten of mnute. However, the C-B PP reul n mooth oluton nce there lttle multpath n the meauremen. Furthermore, the C-B poton oluton more prece cloer to the begnnng. h motly due to that the dfferental delay of the onophere doe not rapdly change over tme. herefore, t could be derable to ue the C-B PP oluton near the begnnng of the operaton tme and ue I-F PP later. he tranton tme to C-B PP to I-F PP can be determned from the feld tet, but t won t be dcued n th paper. It hould be noted that the C-B relatve poton oluton do not match to the urveyed relatve poton to the reference pont when the operaton tme. h caued by the remanng error term n the equaton (.8 when the tme. he offet can be computed from the C-B relatve poton oluton and the urveyed relatve poton at tme. h offet wll be calbrated for the entre C-B relatve poton oluton..4 Satellte contellaton change and cycle-lp It lkely that a new atellte come after the reoluton of the dfference nteger term,, at the ntal tme. At th tme, the accurate relatve poton from a recever to the reference pont may not be avalable. One poble

7 opton to deal wth a new atellte to ue δ ˆp ntead of δ pˆ n order to obtan a new. he effect of ung δ ˆp that the new more lkely to have a larger ba than other dfferenced nteger term. It alo may caue a udden ump n the poton doman, whch not derable for the purpoe of prece potonng. One trck to avod the udden ump to compute poton wth and wthout a new atellte at th partcular epoch. he dfference between the two poton oluton defned to be a calbraton factor. he poton oluton wth the new atellte n the future wll be calbrated to the calbraton factor. It alo poble that a atellte dappear durng the navgaton perod. Uually, a udden ump n poton doman alo oberved when a atellte dappear. What need to be done n th cae to re-compute the poton at the prevou epoch wth and wthout the lot atellte and compute the calbraton factor. hen, the calbraton factor wll be appled to the future poton oluton. Another poble tuaton a cycle-lp. A cycle-lpped atellte can be treated lke a atellte that dappear and come back mmedately. It hould be noted that th mple calbraton technque partcularly ueful for a hort tme operaton becaue the ump ac lke a ba n hort tme. he overue of th calbraton technque for a long tme may degrade the performance of the I-F PP and C-B PP. Fgure 3: Horzontal poton error n Eat and orth of I-F PP and C-B PP 3. ESULS he propoed algorthm are proceed wth tatc recever data. he data were taken wth a ovatel antenna at Stanford Unverty n March, 5. he reference pont et to be the poton of the antenna whoe poton accurately (better than a few centmeter urveyed. he amplng rate of the data wa econd, and econd of carrer-moothng ued for the I-F PP. he I-F PP and the C-B PP performance for the mnute of operaton tme are compared. hen, I-F PP proceed for hour operaton tme, and t compared wth the tandalone GPS. 3. Comparon of the performance of I-F PP and C- B PP for mnute operaton tme he I-F PP and the C-B PP algorthm are proceed wth 4 data e of mnute operaton. Alo, tandalone GPS poton oluton are proceed for thee te. Fgure 3 and 4 how the horzontal and vertcal poton error. Fgure 4: Vertcal poton error of I-F PP and C-B PP he poton oluton from tandalone GPS are calbrated to the poton of the reference pont at the ntal tme n order to compare the tablte of tandalone GPS and PP algorthm. he I-F PP provde noer poton oluton than C-B PP but t more table than C-B PP over tme. I-F PP oluton are le noy than the calbrated GPS poton. he dtnct error charactertc of C-B PP that the poton error qute mall near to the begnnng and become larger a tme pae, whch expected from the ecton.3. Overall, C-B PP provde the bet performance among the three poton oluton over mnute of operaton tme. he number of atellte reman the ame, and no cycle-lp are oberved for each operaton. 3. he performance of I-F prece relatve potonng for hour operaton tme he reul n horzontal and vertcal of the I-F PP and tandalone GPS wth data e of hour operaton tme are hown n Fgure (5 and (6. he number of atellte hown n Fgure (7, and no cycle-lp oberved.

8 umber of Satellte 9 8 Fgure 5: Horzontal Error n data e for hour operaton Data Set Fgure 7: he number of atellte n data e for hour operaton.5 Eat orth MS(m.5 Fgure 6: Vertcal Error n data e for hour operaton Data et Fgure 8: MS of I-F PP n data e for hour operaton It clearly hown n fgure (5 and (6 that the I-F PP provde gnfcantly better tablty than tandalone GPS over hour operaton tme. he poton error mot of tme are le than m both n horzontal and vertcal. he mean, varance, and root-mean-quare (MS value for the potonng error of tandalone GPS and I-F PP n fgure (5 and (6 are hown n fgure (8, (9, (, (, ( and (3. MS(m.5 Eat orth Data et Fgure 9: MS of tandalone GPS n data e for hour operaton

9 .5 Eat orth.5 Eat orth Mean(m Varance(m Data et Fgure : Mean of I-F PP n data e for hour operaton Data et Fgure 3: Varance of tandalone GPS n data e for hour operaton Mean(m Varance(m Eat orth Data et Fgure : Mean of tandalone GPS n data e for hour operaton.5.5 Eat orth Data et Fgure : Varance of I-F PP n data e for hour operaton COCLUSIO In th paper, a reference pont-baed prece relatve potonng method developed. It aumed that a uer can be equpped wth only a ngle frequency recever but can ue other enor n order to fnd the relatve dtance to a reference pont at leat one tme durng navgaton. he abolute poton of the reference pont aumed to be known to a uer. In order to make the mot of the known poton of a recever to the reference pont, the two algorthm, I-F PP and C-B PP, are developed. he dervaton of the two method and the analy of ther expected error charactertc are dcued. hen, the two prece relatve potonng method are teted wth the tatc data. he reul of the te how that the performance of C-B PP, mot of the tme, better than I-F PP for mnute of operaton. Epecally, C-B PP upercede I-F PP near the begnnng wth le than 3cm poton error n horzontal and le than 5cm n vertcal for a few mnute of operaton. I-F PP provde better tablty than tandalone GPS for hour of operaton. he atellte contellaton change do not gnfcantly degrade the performance of I-F PP for the operaton tme. he rm of I-F PP for hour of operaton le than 5cm n horzontal and le than m n vertcal. hee poton error do not take nto account the offe caued by other enor when determnng the relatve poton of a recever to the reference pont. herefore, the overall accuracy of th method the um of the accuracy of the PP and the accuracy of the other enor. Snce thee reul are obtaned from the te ung the tatc data, a dynamc uer may have lghtly dfferent reul. h epecally true that f the hort baelne aumpton between a recever and a reference pont doe not hold. It alo expected that the arborne uer may have better reul nce multpath uually le n the ar

10 than on the ground. Uer n an urban canyon wll have wore reul due to the evere multpath. It promng that the combnaton of I-F PP and C-B PP can replace the expenve navgaton grade IS n the current flght npecton ytem wth a ngle frequency recever. ACKOWLEDGMES he author gratefully acknowledge the upport of FAA flght npecton dvon (AV EFEECES. Y. Yang,.. Sharpe,.. Hatch, avcom echnology, Inc., A Fat Ambguty eoluton echnque for K Embedded wthn a GPS ecever Proc. IO GPS, Portland, Oregon, Sept.. Donghyun Km and chard B. Langley, Intantaneou real-tme cycle-lp correcton for qualty control of GPS carrer-phae meauremen, avgaton: J. Int. avgaton, Vol. 49, o. 4, wnter Gao, Y. and X. Shen (. A ew Method Of Carrer Phae Baed Prece Pont Potonng, avgaton: Journal of the Inttute of avgaton, Vol. 49, o.. 4. Colln, J.P.,.B. Langley & J. LaMance (996, Lmtng factor n tropopherc propagaton delay error modellng for GPS arborne navgaton. 5nd U.S. Inttute of avgaton Annual Meetng, Cambrdge, MA, 9- Jun., Pratap Mra and Per Enge, GLOBAL POSIIOIIG SYSEM: Sgnal, Meauremen, and Performance, Ganga- Jamuna Pre,.