Pont Real-Tme Knematc Postonng Y. Gao, M. Abdel-Salam, K. Chen and A. Wojcechowsk Department of Geomatcs Engneerng 5 Unversty Drve N.W., Calgary, Alberta, Canada TN N4 Abstract. Autonomous pont postonng was the orgnal am of GPS. However, due to errors caused by satellte ephemerdes, satellte clock correctons, onosphere, osphere, multpath and nose, the accuracy of autonomous pont postonng cannot be better than a couple of meters, even after Selectve Avalablty (SA) was turned off. Nowadays, wth the emergence of Pont Real- Tme Knematc (P-RTK) postonng, a lot of attenton s agan focused on standalone postonng. Ths method arose from the avalablty of precse ephemers and satellte clock correctons. The concept behnd ths method s to make use of un-dfferenced code and carrer phase observatons along wth precse correctons to get the best accuracy out of GPS. The concepts, challenges, processng steps and results of the P-RTK system are presented n ths paper. Currently at the Unversty of Calgary, a software system has been developed that acheves centmeter to decmeter level accuracy wth a sngle GPS recever. All components of P-RTK have been ncorporated n ths software, whch s portable and user-frendly, contanng many graphcal nterface tools for analyzng data. Keywords: GPS, Precse Pont Postonng, RTK Introducton Current carrer phase RTK postonng at centmeter level accuracy requres the combnaton of observatons from a mnmum of two GPS recevers. At least one of these serves as the base staton wth known coordnates, and the others serve as rover statons whose poston coordnates are to be determned relatve to the base staton(s). Drawbacks of ths approach nclude the practcal constrants mposed by the requrement that smultaneous observatons need to be made at the rover and base statons, and that the rover staton should be n the vcnty of the base staton(s), typcally up to klometers. The requrements for the deployment of base staton(s) and the spatally lmted operatng range of the rover statons have ncreased the operatonal cost and logstcal complexty n the feld. As such, the full adopton of RTK technology has been lmted n many applcatons. Ths paper descrbes the concept of Pont Real- Tme Knematc Postonng (P-RTK). Ths new RTK postonng approach s based on undfferenced carrer phase data usng a sngle GPS recever asssted by precse orbt and clock correctons. Snce P-RTK has no requrement for the deployment of base staton(s), t s a global RTK approach capable of provdng greater soluton consstency wth ncreased operatonal flexblty. P-RTK wll not only enrch the postonng optons avalable to users, but also provde better tme transfer capabltes and ad meteorologcal dscplnes. The remander of the paper s organzed nto fve sectons. The P-RTK method s frst descrbed n Secton. Varous models for un-dfferenced carrer phase data processng are presented n Secton. Challenges n pont RTK are explored n Secton 4. Numercal results are presented n Secton 5 to assess the potental of the method and to dentfy problems that need to be solved n the future. Fnally, several concludng remarks are gven n Secton. Concept of Pont RTK Postonng Conventonal Standard Pont Postonng (SPP) that was ntally desgned for GPS s subject to the nfluence of all error sources. Major error sources nclude those ntroduced by broadcast orbts and clocks, as well as atmospherc effects. Snce SPP s only able to provde poston solutons wth an accuracy level of several meters, t s not sutable as a postonng method for geodetc and surveyng applcatons that requre a postonng accuracy of several centmeters. However, the stuaton has changed wth the advent of precse orbt and clock correcton products wth centmeter level accuracy, snce the two errors assocated wth broadcast orbts and clocks can be sgnfcantly reduced. Once orbt and clock errors are removed from GPS observatons, much hgher postonng accuracy can be expected even when a sngle GPS recever s used. The
method that derves hgh precson postonng solutons by processng un-dfferenced carrer phase observatons from a sngle GPS recever asssted wth precse orbt and clock correctons s called Precse Pont Postonng (PPP) (Zumberge et al., 7; Kouba and Heroux, ; Gao and Shen, ). The word precse s used here to dstngush t from the conventonal SPP method. PPP has receved ncreased attenton n the past several years wthn the GPS communty due to ts great operatonal flexblty and accuracy promse. Furthermore, f ambguty resoluton of undfferenced carrer phase observatons becomes feasble, the PPP method wll be ready to support the development of new RTK systems usng a sngle recever, wthout the need for base staton(s). Ths s P-RTK, whch s dscussed n ths paper. PPP reles on the use of precse orbt and clock correctons. To date, there are many organzatons, ncludng the Internatonal GPS servce (IGS), Natural Resources Canada (NRCan) and Jet Propulson Laboratory (JPL), whch offer precse data n both post-msson and real-tme modes. IGS currently provdes precse satellte orbt and clock correcton data wth dfferent precsons and latences: predcted correctons wth accuraces of 5cm and 5ns, avalable twce daly, rapd correctons wth accuraces of 5cm and.ns, wth a latency of 7 hours, and fnal correctons wth accuraces of less than 5cm and.ns, and wth a latency of days (IGS, ). JPL and NRCan provde real-tme satellte orbt and clock correctons over the Internet for testng purposes. Observaton Models n Pont RTK The observaton equatons for code and carrer phase measurements on the L frequency ( =, ) are shown n Equatons () and (). P( dt dt ) orb on / L mult / P ( ) + ε ( P( ) L Φ( dt dt ) orb don / L + λ N + λ ( φr ( t, φ s ( t, ) mult / Φ ( + ε ( Φ( ) () () where: P ( s the measured pseudorange on L (m); Φ ( s the measured carrer phase on L (m); ρ s the true geometrc range (m); c s the speed of lght (m/s); dt s the satellte clock error (s); dt s the recever clock error (s); d orb s the satellte orbtal error (m); d s the ospherc delay (m); d / s the onospherc delay on L (m); on L λ s the wavelength on L (m); N s the nteger phase ambguty on L (cycle); φ r ( t, s the ntal phase of the recever oscllator; φ s ( t, s the ntal phase of the satellte oscllator; d s the multpath effect n the measured mult / P( pseudorange on L (m); d Φ s the multpath effect n the measured mult / ( carrer phase on L (m) and ε (.) s the measurement nose (m). Note that the ntal phase of the recever and satellte oscllators s commonly gnored n conventonal double-dfference RTK systems based on carrer phase. If t s combned wth the nteger phase components nto a sngle term, Equaton () can be rewrtten as: Φ( dt dt ) where N + λ N orb mult / Φ( d + ε ( Φ( ) s no longer an nteger term. on / L () In order to mtgate the onospherc effect, whch s the largest error source n GPS postonng after SA was turned off, onosphere-free combnatons are usually formed n dual-frequency recevers and have the followng expressons: P Φ IF IF = [ f ( L) f P( L) dt dt ) = [ f P mult / P( L+ L ) Φ orb ( L) f Φ( L) dt dt ) mult / Φ ] /[ f + ε ( P( L + L)) orb ] /[ f ( ) ( L+ L + ε ( Φ L + L)) f cf + ] f ] N f cf f (4) N (5)
Applyng correctons from precse orbt and clock products to Equatons (4) and (5) results n the followng equatons: P Φ IF = ρ cdt ) mult / P( L+ L ) IF + ε ( P( L + L)) = ρ cdt mult / Φ cf + N f cf f N ( ) + ε ( Φ( L + L)) L+ L () (7) Based on Equatons () and (7), the unknowns to be estmated nclude the poston coordnates, recever clock offset, osphere and a combned ambguty term. The above model has been used n the observaton model for PPP processng by Zumberg et al (7) and Kouba and Heroux (). The nteger property of the ambguty cannot be exploted based on Equatons () and (7). Gao and Shen () have proposed a new code combnaton to replace Equaton () as follows: P IF, L =.5[ P( + Φ = ρ cdt +.5d mult / P( where = and. ( ] +.5λ N +.5ε ( P( + Φ( ) (8) Note that Equaton (8) s stll an onospherefree observable. A combnaton formed from Equatons (7) and (8) yelds an alternatve observaton model for PPP. Dfferent from the model based on Equatons () and (7), the new model s capable of estmatng the ambgutes assocated wth L and L frequences separately. Ths makes t possble to explot the nteger propertes of both L and L ambgutes, whch s essental for real-tme knematc postonng. To facltate hgh precson poston determnaton usng P-RTK, a number of unconventonal error correctons have to be appled, ncludng correctons for earth tdes, satellte antenna offsets and phase wnd up. These correctons are commonly gnored n conventonal RTK postonng because they can be canceled out by the carrer phase double-dfferencng procedure that s mplemented between satelltes and recevers. 4 Challenges n Pont RTK There are three major challenges assocated wth P-RTK: error mtgaton, carrer phase ambguty convergence, and ambguty resoluton. The onosphere s a conventonal error that causes the largest absolute error n GPS observatons. Due to ts dspersve nature, sgnals from satelltes suffer dfferent delays on L and L. As such, they can be mtgated through standard onosphere-free code and carrer phase combnatons. The osphere cannot be mtgated n ths manner due to ts non-dspersve nature. However, t can be modeled or estmated along wth other parameters. Unconventonal error sources must also be taken nto consderaton n order to mplement a P- RTK system. Many of these errors have been gnored n the past because they are rrelevant, neglgble, or are canceled out through dfferencng. However, n the case of un-dfferenced code and carrer phase observatons some of these errors do not cancel out and ther szes are relatvely large, nfluencng the accuracy of the method. These unconventonal errors may be related to the un-dfferenced observatons, the precse data or the standard GPS errors. Satellte antenna phase center, earth tde and ocean loadng are examples of errors related to precse data. The satellte antenna phase center correcton s necessary for Block II/IIA satelltes because the phase centers and centers of mass of these satelltes do not concde. Earth tde and ocean loadng models are necessary because errors assocated wth them can reach several decmeters. Smlarly, a satellte phase wndup correcton s necessary snce the error can reach half a cycle. In most cases, carrer phase ambgutes are consdered as float terms, often requrng long convergence tmes rangng from several tens of mnutes to several hours. Snce convergence s a crucal ssue for real-tme applcatons, long convergence tmes may prevent P-RTK from fulfllng the operatonal requrements of such applcatons. As such, fast ambguty convergence methods and algorthms should be developed. Integer ambgutes must be resolved to fully realze the accuracy of carrer phase observatons. If nteger values of the carrer phase ambgutes can be determned on-the-fly (OTF) over short tme ntervals, the P-RTK method wll be able to support real-tme knematc postonng at centmeter level accuracy. Currently, ths accuracy level s only feasble usng double-dfference RTK systems.
New onospherc-free observaton combnaton models are necessary because the conventonal model, whch forms onospherc-free code and carrer phase combnatons, does not allow for the explotaton of the nteger property of the ambgutes. Estmaton of nteger ambgutes s dffcult due to the exstence of non-zero ntal phase offsets assocated wth the satellte and recever oscllators and the level of resdual errors that may exst n the system due to precse data and nose. Non-zero ntal phase offsets are constant bases assocated wth the tme and geometry of recever-satellte lock, and are constant durng an observed cycle slp free satellte arc (Gabor, ; Teunssen, 7). 5 Numercal Results and Analyss A software package called P has been developed at the Unversty of Calgary for precse pont postonng. The software can be used to assess the performance of dfferent data processng models as well as the nfluence of dfferent error sources on postonng results. Processng can be done n post-msson or n real-tme, and the program can be run n ether statc or knematc mode. Two pont postonng modes are avalable: Sngle Pont Postonng (SPP), whch only makes use of code measurements, and Precse Pont Postonng (PPP), whch makes use of both code and phase measurements, as well as precse satellte orbt and clock correctons. Processng n real-tme requres real-tme correctons. Currently, the developers of the software can obtan GPS C data, whch are realtme GPS wde-area correctons avalable from Natural Resources Canada (NRCan). GPS C provdes enhanced real-tme postonng by applyng correctons to user GPS recever observatons (GPS C ICD, ). 5. Statc Results Shown n Fgures and are statc data processng results usng fnal precse orbt and clock correctons from IGS, wth accuraces of 5cm and.ns, respectvely. A one-day s data set collected on February 5,, at the IGS staton ALGO was used wth a samplng nterval of s. Precse satellte coordnates were avalable every 5mn, and precse clock correctons every 5mn. Due to the dscrepancy n the samplng nterval between the GPS observatons and the precse data, the precse orbt and clock correctons were nterpolated to s, equvalent to the samplng nterval of the GPS observatons. It should be noted that ths may degrade the accuracy of the satellte orbt, and n partcular the satellte clock correctons. Postonng accuracy statstcs are gven n Table. The results ndcate that the poston soluton converges to cm n mn wth a bas below cm. North (m) East (m) Up (m) - - - 584 54 5 58 48 Fg. Clock (m) ZTD (m) -75-8 -85.4.. Poston Error Usng IGS Fnal Products 584 54 5 58 48 Fg. Satelltes Usng IGS Fnal Products Table. Statc Postonng Accuracy Statstcs Usng IGS Fnal Products Mean (m).. -. RMS (m).5.5. STD (m).5.4.8 5. Knematc Results In ths secton, the same IGS data set was processed n knematc mode. In addton, a twohour data set ( Hz) was processed n knematc
mode usng real tme GPS C correctons. GPS C.5 ephemers and satellte clock correctons are accurate at the level of -5cm and -ns, respectvely (GPS C ICD, ). -.5 As mentoned above n Secton 5., precse.5 data had to be nterpolated to s to be consstent wth the samplng nterval of the GPS observatons. As such, two solutons usng IGS fnal products are -.5 presented. Results of the frst soluton, usng clock correctons nterpolated at s, are shown n Fgures.5 and 4, wth statstcs n Table. Results of the second soluton, usng the orgnal 5mn clock correctons, are shown n Fgures 5 and, wth statstcs n Table. Fg. 5 Poston Error Usng Orgnal IGS Fnal Products North(m) East(m) Up(m) -.5 584 54 5 58 48 North (m) East (m) Up (m) - - - 584 54 5 58 48 Fg. Clock (m) ZTD (m) -75-8 -85.4.. Poston Error Usng IGS Fnal Products Interpolated at s 584 54 5 58 48 Fg. 4 Satelltes Usng IGS Fnal Products Interpolated at s Table. Knematc Postonng Accuracy Statstcs Usng IGS Fnal Products Interpolated at s Mean (m).4. -. RMS (m).54..8 STD (m).5.. Clock (m) ZTD (m) -75-8 -85.4.. Fg. 584 54 5 58 48 Satelltes Usng Orgnal IGS Fnal Products Table. Knematc Postonng Accuracy Statstcs Usng Orgnal IGS Fnal Products Mean (m).4. -. RMS (m)... STD (m)...5 Comparng Fgure and Table wth Fgure 5 and Table shows the degradaton of results after an nterpolaton of clock correctons from 5mn to s. Wthout nterpolaton the results converge very quckly, as shown n Fgure 5. After convergence, the bas s less than cm, and the errors are below 5cm. The results reflect the accuracy of IGS fnal products. When usng clock correctons nterpolated to s, convergence occurs after about 5mn, wth about 5cm horzontal accuracy and cm vertcal accuracy. Along wth staton coordnate parameters, estmaton of the osphere and recever clock offsets are presented n Fgures 4 and. These two products have a demand from meteorologcal and tme transfer sectors. Fgures 7 and 8 show knematc results usng GPS C real-tme correctons for a two-hour data
set. A summary of the results s shown n Table 4. cm accuracy n the horzontal drecton and cm accuracy n vertcal drecton s achevable wth a convergence tme of mn. The results of IGS data and GPS C data suggest that convergence depends on the accuracy of the precse data. The results obtaned wth GPS C correctons mght be mproved snce the system s stll n a test phase. Wth GPS C real-tme clock correctons at a two-second nterval, no accuracy degradaton assocated wth nterpolaton wll occur. Moreover, GPS C correctons can be wdely used n real-tme applcatons snce they can be provded to users n Canada as well as to global users n real-tme. North(m) East(m) Up(m) 5-5 5-5 5-5 4 4 78 Fg. 7 Poston Error Usng GPS C Real-Tme Correctons Clock(m) ZTD(m) -5 - -.4. 4 4 78 Fg. 8 Conclusons The method of Pont Real-Tme Knematc Postonng (P-RTK) has been descrbed n ths paper. Compared to the conventonal RTK method, P-RTK can offer much greater operatonal flexblty to help n the full mplementaton of RTK technology n many applcatons n the future. Test results have ndcated that P-RTK postonng at centmeter to decmeter level accuracy s achevable. Usng IGS fnal products, an accuracy of several centmeters has been acheved. Usng real-tme GPS C data, an accuracy below cm s achevable n the horzontal components, and below cm n the vertcal drecton. Although the results are promsng, several challenges stll exst wth respect to error mtgaton, carrer phase ambguty convergence, and ambguty resoluton. Acknowledgement Mr. Perre Heroux from Natural Resources Canada s acknowledged for many valuable dscussons. Ths research s partally supported by GEOIDE. References Gao, Y. and X. Shen (). A New Method Of Carrer Phase Based Precse Pont Postonng, Navgaton: Journal of the Insttute of Navgaton, Vol. 4, No.. IGS, (). The IGS- Annual Report. Kouba, J and P. Heroux (). GPS Precse Pont Postonng Usng IGS Orbt Products, GPS Solutons, Vol.5, No., Fall. Mchael J. Gabor () Characterstcs Of Satellte-Satellte Sngle Dfference Wdelane Fractonal Carrer Phase Bases. Proceedngs of ION GPS, Salt Lake Cty, UT, - September. Teunssen, P.J.G. and A. Kleusberg (Eds.) (8). GPS for Geodesy. Second Edton, Sprnger- Verlag, New York. Satelltes Usng GPS C Real-Tme Correctons Zumberge James. F., M. M. Watkns and F. H. Table 4. Knematc Postonng Accuracy Statstcs Usng GPS C Real-Tme Correctons Mean (m).4. -.5 RMS (m)...8 STD (m).48..75 Webb (7). Characterstcs And Applcatons Of Precse GPS Clock Solutons Every Seconds. Navgaton, Journal of the Insttute of Navgaton. 44(4), 44-45 wnters 7-8. GPS*C ICD,, Natural Resources Canada. URL: www.cdgps.com/e-test/cdgps_documents/ %5B4%5D%-%ICD%-%GPSC%- %--.pdf