JPNT 3(3), 3-9 (4) http://dx.doi.org/.3/jpnt.4.3.3.3 JPNT Joural of Positioig, Navigatio, ad Timig Log Baselie GPS RTK with Estimatig Tropospheric Delas Bug-Ku Choi, Koug-i Roh, Sag Jeog Lee Space Sciece Divisio, Korea Astroom ad Space Sciece Istitute, Daejeo 35-348, Korea Departmet of Electroics Egieerig, Chugam Natioal Uiversit, Daejeo 35-764, Korea ABSTRACT The real-time kiematic (RTK) is oe of precise positioig methods usig Global Positioig Sstem (GPS) data. I the log baselie GPS RTK, the ioospheric ad tropospheric delas are critical factors for the positioig accurac. I this paper we preset RTK algorithms for log baselies more tha km with estimatig tropospheric delas. The state vector is estimated b the exteded Kalma filter. We show the experimetal results of GPS RTK for various baselies (6., 393.37, 58.9, ad 83.57 km) b usig the Korea Astroom ad Space Sciece Istitute GPS data ad oe Iteratioal GNSS Service (IGS) referece statio located i Japa. As a result, we preset that log baselie GPS RTK ca provide the accurate positioig for users less tha few cetimeters. Kewords: GPS, RTK, log baselie, tropospheric delas. INTRODUCTION The Global Positioig Sstem (GPS) real-time kiematic (RTK) is oe of the methods that precisel determie the positio of a user. The GPS RTK method accuratel estimates the positio of a user usig the observables received at a GPS referece statio whose positio is accuratel kow ad GPS measuremets received b the user, i a relative maer. I geeral, a relative positioig method determies the positio of a user after elimiatig commo errors through a double differece of the observatio data of both a referece statio ad a user. The positio accurac of a user is affected b the ioosphere ad the troposphere (Rocke et al. 995, Wielgosz et al. 5). If a baselie betwee a referece statio ad a user is less tha km, the ioospheric ad tropospheric dela errors ca be elimiated usig a double differece techique assumig that GPS sigals have passed through the similar path. I cotrast, if a baselie is more tha km, the effects of the Received April 7, 4 Revised Jul, 4 Accepted Jul, 4 Correspodig Author E-mail: bkchoi@kasi.re.kr Tel: +8-4-865-337 Fax: +8-4-86-56 ioosphere ad the troposphere should be cosidered; ad the effect of the atmosphere icreases as a baselie icreases (Saastamoie 97). I particular, i the case of log baselie RTK positioig with a baselie of more tha km, the effects of differet crustal movemets ad the satellite orbit errors eed to be also cosidered i additio to a ifluece of the atmosphere (Geg et al. ). To precisel determie the positio of a user based o the GPS RTK techique (i.e. relative positioig), GPS measuremets from at least oe referece statio whose positio is accuratel kow are required. I geeral, if a baselie is less tha km, the positio of a user receivig a sigle frequec ca be determied based o the RTK techique with a cm-level accurac (Fotopoulos & Cao ). However, for log baselies, the determiatio of carrier phase iteger ambiguities is difficult due to various error factors, ad iitial covergece time is also log (Teuisse 995, Lawrece et al. 6). Whe the baselie icreases, sigle frequec users caot completel correct the error from the atmosphere, compared to dual frequec users. Thus, sigle frequec users have the disadvatage of reduced positio accurac (Davis et al. 985, Blewitt, 989, Bruer & Welsch 993). I cotrast, dual frequec users ca basicall elimiate the effect of the ioosphere, which is the largest error factor for log baselie relative positioig, Copright The Korea GNSS Societ http://www.gss.or.kr Prit ISSN: 88-887 Olie ISSN: 89-866
4 JPNT 3(3), 3-9 (4) through the liear combiatio of the frequecies of two GPS sigals. The etwork RTK techique, which is operated based o ma GPS referece statios, is used to mitigate the error factors (Rizos, Wielgosz et al. 5). The etwork RTK techique ca stabl determie accurate positio of a user i the ier etwork, but the accurac deteriorates i the outer etwork. I particular, it is sigificatl affected b abruptl chagig meteorological coditios such as local severe heav rai (Gregorius & Blewitt 998). I the case of log baselies, accurate correctio of atmospheric errors is difficult although the etwork RTK is used, ad thus, it is ot differet from the sigle baselie RTK techique i terms of the positio accurac. Therefore, i the preset stud, a method for icreasig the positio accurac of a user at log baselies of more tha km based o the sigle baselie RTK techique was itroduced, ad a algorithm that directl estimates tropospheric dela error as a state vector was developed for precise positioig. I additio, the positio accurac performace of a user was also compared b aalzig the positioig results depedig o various log baselies.. EASUREENT EQUATIONS For the log baselie GPS relative positioig betwee the GPS referece statio, a, ad the user, b, observatio equatios such as Eqs. () ad () are used. Based o Eqs. () ad (), GPS satellite clock ad the receiver clock errors are elimiated b a double differece techique. = = Φ = Φ Φ where P i=, is the pseudorage measuremets, Φ i=, is the carrier phase measuremets, ad f i=, represet the GPS L ad L frequecies, respectivel. For measuremets i Eqs. (3) ad, (4), ew observables are geerated usig Φ Φ, the double differece, techique; ad the desig matrix, H, for the estimatio of state parameters is show i Eq. (5). é x ê ê x H = ê ê êë x Φ = Φ Φ z z z DÑ DÑ DÑ wet wet wet L L O L ù ú ú ú ú úû (3) (4) (4) where DÑ represets the double differece, e x, e, ez are the lie-of-sight r to vectors from receiver to satellite l. ), (Hofma- a Wellehof et al. ), ad DÑwet = wet, a( k) - wet, a( i ) - ( ( tropospheric wet dela mappig fu wet, b( k) - wet, b( i )) is the double differeced tropospheric uctio. wet dela represets mappig afuctio. k represets a referece satellite. State parameters that eed mato be estimated b the relative x = x = (,,,,,, x =, ( ) positioig techique usig Eqs. (3-5) were,, ) defied,, as show,, i, Eq. )(6).,, x = (,,,,,,,, ),,,,, ) (6),,,, ) (5) P = r + I + T + e ij ij ij ij ab ab ab ab F = r - I + T + l N + e F ij ij ij ij ij ab ab ab ab ab P () () where P ij ab is the double differeced pseudorage measuremet; Φ ij ab is the double differeced carrier phase measuremet; ρ ij ab is the double differeced geometric distace betwee the satellite ad the receiver; Ι ij ab is the double differeced ioospheric error; T ij ab is the double differeced tropospheric error; λ is the wavelegth of the frequec; N ij ab is the double differeced float ambiguities; ε P ad ε Φ are the code ad carrier oises respectivel; ad i ad j represet the GPS satellites, where i deotes the referece satellite. I this stud, to cacel = out the effect of the ioosphere, which is a large error Φ = for loe Φbaselies, Ioospheric-free Φ (IF) liear combiatio was applied usig dual frequec observatio data, as show i Eqs. (3) ad (4) (Hofma- Wellehof et al., Kouba 3). Fig.. The data processig flow for log baselie GPS RTK. http://dx.doi.org/.3/jpnt.4.3.3.3
Bug-Ku Choi et al. Log Baselie GPS RTK 5 I other words, estimated state parameters cosist of the positio of a user (b x, b ad b z ) the double differeced tropospheric wet dela (ZWD ab ), ad the float ambiguities (N i ab, N i ab,, N i3 ab ). Fig. shows the flowchart of the data processig for the estimatio of state parameters. First, the iitial positio of a user is determied usig GPS code observatio data. The, commo satellites ad a referece satellite are determied usig measuremets of both the GPS referece statio ad the user. I this regard, the referece satellite represets a satellite where the elevatio agle is the largest at the referece statio. Earth tides ad phase wid-up correctios were also applied; ad for the efficiet epoch-b-epoch estimatio of state parameters, the exteded Kalma filter as used. I the preset stud, iteger ambiguities were ot directl used, but validatio (ratio test) procedure for iteger ambiguities was just performed usig the Leastsquares ABiguit Decorrelatio Adjustmet method. The aim of this stud is to cotribute to the improvemet of the positio accurac of a user b directl estimatig tropospheric wet delas as a state vector i log baselie GPS RTK. Table. Data processig strateg of GPS RTK for log baselies. Items Descriptio Processig filter Exteded Kalma filter easuremets Code-carrier phase double differece Ioosphere Elimiatio b IF liear combiatio Troposphere Estimatio with GPT/GF Tidal effect IERS covetios & FES4 Phase ceter offsets ad IGS8.atx Phase ceter variatios Phase wid up Wu et al. (993) GPT: global pressure ad temperature, GF: global mappig fuctio, FES: fiite elemet solutios, IERS: iteratioal earth rotatio service 3. RESULTS AND ANALYSIS I the preset stud, a log baselie GPS RTK algorithm was directl developed; ad to verif the performace of log baselie positioig usig GPS dual frequec observatio data, a total of four baselies were selected as show i Fig.. All of the baselies were more tha km. I particular, to verif the positioig performace of a ver log baselie of more tha, km, the Tsukuba (TSKB) GPS referece statio i Japa was selected. Fig.. The experimetal sites for log baselie GPS RTK. Fig. 3. The positioig errors of KOHG site estimated b GPS RTK. Table summarizes the models used for the log baselie positioig. For the GPS observatio data, code ad carrier phase were used together; ad the ioospheric error was elimiated b IF liear combiatio. Also, the tropospheric error was estimated epoch-b-epoch, ad the earth tide loadig effect (crust/ocea/pole) was cosidered because the GPS referece statio ad the user that were located o differet crustal plates could have differet motios whe the baselie icreased. The phase ceters of the GPS satellite atea ad the receiver atea ad their variatios were calculated, respectivel, ad were used for data processig. Lastl, the carrier phase wid-up effect due to the relative motio of the GPS satellites ad the receiver was cosidered. To verif the performace of the log baselie GPS RTK positioig, the observatio data received at each GPS referece statio o Jauar, 4 were used. The data processig was performed o a dail basis, ad the state parameters were also calculated ever 3 secods. To reduce the effect of the orbital errors of the GPS satellites, the ultra-rapid product from the IGS was used. Fig. 3 shows the positio errors (i.e., each directioal http://www.gss.or.kr
6 JPNT 3(3), 3-9 (4) Fig. 4. Variatios of the umber of commo GPS satellites betwee JEJU ad KOHG. The red dot-circle represets less tha four commo satellites. Variatios of the umber of commo GPS satellites betwee JEJU ad BHAO. The red Fig. 6. Variatios of the umber of commo GPS satellites betwee JEJU ad BHAO. The red dot-circle represets less tha four commo satellites. Fig. 5. The positioig errors of BHAO site estimated b GPS RTK. Fig. 7. The positioig errors of SKCH site estimated b GPS RTK. compoet) of the KOHG referece statio calculated b the relative positioig betwee the Jeju (JEJU) ad Goheug (KOHG) GPS referece statios. I this regard, the positio iformatio of the JEJU ad KOHG referece statios (i.e., true values) were obtaied usig the Global Navigatio Satellite Sstem Precise Poit Positioig (GNSS PPP) Software developed b the Korea Astroom ad Space Sciece Istitute. I Fig. 3, the X-axis represets the Uiversal Time (UT), ad the Y-axis represets the positio error of the user. The calculated results were the mea ad root mea square (RS) values of the positio errors durig a da i the east-west, orth-south, ad up-dow directios, respectivel. The mea positio errors of KOHG were less tha cm for ever directioal compoet, ad the RS values i the east-west, orthsouth, ad up-dow directios were.3 cm,.89 cm, ad.55 cm, respectivel. It is oteworth that the positioig results were ustable at aroud 3: UT. This was because the umber of commo satellites betwee JEJU ad KOHG was less tha four as show i Fig. 4. Durig a da, the umber of commo satellites chaged betwee 3 ad, as show i Fig. 4. Fig. 5 shows the dail positio errors of the BHAO GPS referece statio calculated b the relative positioig betwee the JEJU ad Boheosa (BHAO) GPS referece statios. The baselie betwee JEJU ad BHAO was about 393.37 km, ad the mea positio errors of BHAO i the east-west, orth-south, ad up-dow directios were.5 cm, -.33 cm, ad -. cm, respectivel. Also, the RS values for each compoet were.95 cm,.4 cm, ad 3.65 cm, respectivel. The RS values of the BHAO were larger tha those of the KOHG referece statio, i ever directioal compoet. I particular, the RS value i the up-dow directio was the largest similar to the case of KOHG. I Fig. 6, the positioig results were istataeousl ustable at 3: UT. It is thought that the abrupt decrease i the umber of commo satellites at 3: UT show i Fig. 6 affected the positioig results. http://dx.doi.org/.3/jpnt.4.3.3.3
Bug-Ku Choi et al. Log Baselie GPS RTK 7 Variatios of the umber of commo GPS satellites betwee JEJU ad SKCH. The red Fig. 8. Variatios of the umber of commo GPS satellites betwee JEJU ad SKCH. The red dot-circle represets less tha four commo satellites.. Variatios of the umber of commo GPS satellites betwee JEJU ad TSKB. The re Fig.. Variatios of the umber of commo GPS satellites betwee JEJU ad TSKB. The red dot-circle represets less tha four commo satellites. Fig. 9. The positioig errors of TSKB site estimated b GPS RTK. Fig.. Compariso of the three-dimesioal RS positio errors betwee oe (ot applied as a state parameter) ad ZWD estimatio with GPS RTK. Fig. 7 shows the results of the relative positioig betwee the JEJU ad Sokcho (SKCH) GPS referece statios. The baselie betwee the two referece statios was about 58.9 km, ad the dail mea positio errors were less tha cm for ever directioal compoet. The RS values for ever directioal compoet were less tha 4 cm. Similar to the data processig explaied earlier, the positioig results were ver ustable at 3: UT. It is also thought that the positioig results were affected b the fact that the umber of commo satellites decreased to less tha 4. At aroud 3: UT show i Fig. 8, the umber of commo satellites was less tha 4 for about miutes, ad thus, the positio errors sigificatl icreased durig these periods. Fig. 9 shows the results of the relative positioig betwee JEJU ad TSKB GPS referece statios. The baselie betwee the two referece statios was about 83.58 km, which was more tha twice the baselie betwee JEJU ad SKCH. The dail mea positio errors for each compoet were all less tha 3 cm, ad the mea positio error i the orth-south directio was relativel larger tha those i the east-west ad up-dow directios. Also, the RS values for ever directioal compoet were less tha 6 cm. As show i Fig. 9, the positio errors icreased at 3: UT, ad this cause is thought to be similar to that explaied earlier. Fig. shows the chages i the umber of commo satellites betwee two GPS referece statios. As show i the figure, the umber of commo satellites abruptl decreased at 3: UT. Fig. shows the compariso of the three-dimesioal RS positio errors betwee the case where the tropospheric wet dela was estimated as a state vector ad the case where such estimatio was ot applied. As show i Fig., the positio precisios of KOHG, SKCH, ad TSKB were higher whe the tropospheric wet dela was directl estimated. However, the positio precisio of BHAO was slightl lower whe the tropospheric wet dela was directl estimated. Further research is eeded to determie whether this is simpl due to a effect of a certai baselie, or due http://www.gss.or.kr
8 JPNT 3(3), 3-9 (4) to the effect of the altitude correctio i the tropospheric model because BHAO is located,34 m above sea level, or due to other factors. The overall positioig results depedig o the baselie idicated that the positioig stabilit decreased as the baselies betwee the referece statio ad the user icreased. I other words, the correlatios betwee the dail mea positio errors ad the baselies were weak, while the RS values for the positio errors icreased i proportio to the baselies. Also, the iitial covergece time for the stabilizatio of a user positio became loger as the baselies icreased. 4. CONCLUSIONS I this stud, a techique for log baselie GPS RTK betwee a GPS referece statio ad a user was developed usig GPS dual frequec observatio data, ad the positioig results depedig o the baselie were preseted. To verif the performace of the relative positioig, a total of four baselies of more tha km (KOHG, BHAO, SKCH, ad TSKB) were selected, ad data processig was carried out. The ioospheric dela error, which has a large effect depedig o the baselie, was elimiated through IF liear combiatio; ad the tropospheric dela error was estimated as a state parameter, ad was used for data processig. I the case of KOHG with the shortest baselie, the dail mea positio errors were less tha cm for ever directioal compoet (east-west, orth-south, ad up-dow directios). I the case of TSKB with the logest baselie, the dail mea positio errors were less tha 3 cm for ever directioal compoet. As the baselie icreased, the RS values of the positio errors for all the baselies icreased. Also, as the baselie icreased, the iitial covergece time of user positio icreased. I other words, the positioig stabilit of a user icreased as the relative baselie decreased, but the positioig stabilit decreased as the baselie icreased. The positio accurac of a user based o relative positioig is affected b various factors such as the surroudig eviromets of a referece statio ad a user, differet characteristics of the upper atmosphere (troposphere/ioosphere) depedig o the baselie, ad the earth tide loadigs. This stud showed that precise positio could be obtaied based o log baselie GPS RTK. The results of this stud are thought to be useful for improvig the accurac of log baselie surveig ad for moitorig earthquakes ad tsuamis. ACKNOWLEDGENTS This research was supported b the 4 Leadig Core Research Project of the Korea Astroom ad Space Sciece Istitute (project: Developmet of GNSS Data Aalsis Egie). REFERENCES Blewitt, G. 989, Carrier phase ambiguit resolutio for the global positioig sstem applied to geodetic baselies up to km, JGR, 94, 87-3, http://dx.doi. org/.9/jb94ib8p87 Bruer, F. K. & Welsch, W.. 993, Effect of the troposphere o GPS measuremets, GPS World, 4, 4-5 Davis, J. L., Herrig, T. A., Shapiro, I. I., Rogers, A. E. E., & Elgered, G. 985, Geodes b radio iterferometr: Effects of atmospheric modellig errors o estimates of baselie legth, Radio Sciece,, 593-67, http:// dx.doi.org/.9/rsi6p593 Fotopoulos, G. & Cao,. E., A overview of multiple-referece statio methods for cm-level positioig, GPS Solutios, 4, -, http://dx.doi. org/.7/pl849 Geg, J., Teferle, F. N., eg, X., & Dodso, A. H., Towards PPP-RTK: Ambiguit resolutio i real-time precise poit positioig, ASR, 47, 664-673 http:// dx.doi.org/.6/j.asr..3.3 Gregorius, T. & Blewitt, G. 998, The effect of weather frots o GPS measuremet, GPS world, 9, 5-6 Hofma-Wellehof, B., Lichteegger, H., & Collis, J., GPS Theor ad Practice (New York: Spriger), p.93 Kouba, J. 3, A Guide to usig Iteratioal GNSS Service (IGS) product, ftp://igscb.jpl.asa.gov/igscb/resource/ pubs/guidetousigigsproducts.pdf Lawrece, D., Lagle, R. B., Kim, D., Cha, F. C., & Perva, B. 6, Decorrelatio of troposphere across short baselies, Proceedigs of IEEE/ION PLANS 6, Sa Diego, Califoria, 94- Rizos, C., Network RTK research ad implemetatio A geodetic perspective, Joural of Global Positioig Sstems,, 44-5 Rocke, C., Va Hove, T., Johso, J., Solheim, F., Ware, R., et al. 995, GPS/STOR GPS sesig of atmospheric water vapour for meteorolog, Joural of Atmospheric ad Oceaic Techolog,, 468-478, http://dx.doi. org/.75/5-46(995)<468:gsoawv>.. CO; Saastamoie, J. 97, Atmospheric correctio for the http://dx.doi.org/.3/jpnt.4.3.3.3
Bug-Ku Choi et al. Log Baselie GPS RTK 9 troposphere ad stratosphere i radio ragig of satellites, Geophsical oograph, 5, 47 5, http:// dx.doi.org/.9/g5p47 Teuisse, P. J. G. 995, The least-squares ambiguit decorrelatio adjustmet: A method for fast GPS iteger ambiguit estimatio, Joural of Geodes, 7, 65-8, http://dx.doi.org/.7/bf86349 Wielgosz, P., Kashai, I., & Grejer-Brzeziska, D. 5, Aalsis of log-rage etwork RTK durig a severe ioospheric storm, Joural of Geodes, 79, 54-53, http://dx.doi.org/.7/s9-5-3- Wu, J., Wu, S., Hajj, G., Bertiger, W., & Lichte, S. 993, Effects of atea orietatio o GPS carrier phase, auscripta Geodaetica, 8, 9-98 Bug-Ku Choi received the Doctor s degree i Electroics from Chugam Natioal Uiversit i 9. He has bee workig at the Korea Astroom ad Space Sciece Istitute sice 4. His research iterests iclude GNSS PPP, Network RTK ad Ioospheric TEC modelig. Koug-i Roh received his BS, S, ad PhD i astroom ad space scieces from Yosei Uiversit, Rep. of Korea, i 997, 999, ad 6, respectivel. From 7 to 8, he worked as a postdoctoral researcher at GeoForschugsZetrum, Germa, where he was ivolved i GRACE baselie determiatio ad satellite orbit desig of Swarm missio. Sice 8, he has bee with Korea Astroom ad Space Sciece Istitute as a seior research staff member. He is curretl ivolved i developmet of high precisio GNSS data processig software. His research iterests iclude satellite GNSS data processig, high precisio orbit determiatio, ad their applicatios to space geodes. Sag Jeog Lee received the Doctor s degree i Cotrol ad easuremet i Seoul Natioal Uiversit i 987. His research iterests iclude GNSS ad Robust Cotrol. http://www.gss.or.kr