Establishment of Geodetic Control in Jebba Dam using CSRS PPP Processing Software

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1 Journal o Emergng Trends n Engneerng and Aled Scences (JETEAS) (5): Scholarlnk Research Insttute Journals, (ISSN: 4-76) jeteas.scholarlnkresearch.org Journal o Emergng Trends n Engneerng and Aled Scences (JETEAS) (5): (ISSN: 4-76) Establshment o Geodetc Control n Jebba Dam usng CSRS rocessng Sotware R. Ehgator-Irughe; M. O. Ehgator and 3 S. A. Uzoekwe Sberan State Academy o Geodesy, Novosbrsk, Russa Faculty o Basc Scence, Deartment o hyscs. Benson Idahosa Unversty, Benn Cty, Ngera, 3 Faculty o Basc Scence, Deartment o Chemstry, Benson- Idahosa Unversty, Benn Cty, Ngera Corresondng Aurthor: R. Ehgator-Irughe Abstract Most GS users who requre hgher recson now oerate derentally wth resect to a known reerence staton to elmnate the eects o SA and sgncantly reduce common staton errors. As the dstance between a rovng recever and ts reerence ncreases, the commonalty o errors s reduced and alyng range correctons rom a sngle reerence staton may not rovde otmal results or ont ostonng. Daly, the Geodetc Survey Dvson (GSD), Natural Resources Canada (NRCan) generates recse GNSS satellte orbts and clocks n a standard ormat whch are contrbuted to the Internatonal GNSS Servce or Geodynamcs (IGS). Hgher requency satellte clocks are subsequently comuted rom the Canadan Actve Control System (CACS). New develoments n GNSS ostonng show that a user wth a sngle GNSS recever can obtan ostonng accuracy comarable to that o derental ostonng (.e., centmeter to decmeter accuracy). In ths study, the GS data or a control ont BM_AMOS was submtted to CSRS or ost rocessng. Sources o errors and the model used n the soluton are dscussed. The earth and sace based models or attanng the derved accuraces s hghlghted Keywords: GNSS, Model, ITRF, IGS, Ionosherc delay, BM_AMOS INTRODUCTION Canadan Satal Reerence System recse ont ostonng (CSRS-) uses the so-called ont ostonng aroach (user doesn t need to be near an Actve control onts (AC), IGS or contnuous reerence staton (CORS). Unlke derental GS methods, does not requre data rom any other GS recevers. Instead uses recse aror values o the GS orbts and o ther clocks. These values are obtaned rom the Internatonal GS Servce (IGS) and are usually avalable, n batches o 4 hours, 7 hours ater the end o the GS day. The recse orbts and clocks remove a large art o the GS errors. In addton, rocessng must also roerly account or several other eects on the oston o the GS recever (Kouba and Heroux, ). recse ont ostontng s a technque o GNSS measurement n whch absolute oston o onts are determned by elmnatng systematc errors through recse modellng o many o the error sources such as onosherc delay, trooherc as well as recever antenna n ths method, the coordnates o a ste are determned wth resect to the orbts o the satelltes (Kouba and Heroux, ). The aroach resented here s an mlementaton o recse ont ostonng that was eectvely submtted data va nternet to CSR center or observatons on BM _ AMOS usng Trmble GS Recever or observaton that lasted or more than sx hours (Ahmed El-Rabbany, ). Reerence Frames or Solutons Coordnates estmates rom are usually n the same global rerence rame as the satellte orbts. In usng IGS orbts, the recever coordanates are rerenced to IGS realzaton o nternatonal Terrestral reerence rame (ITRF). However n mang alcaton the user would lke to transorm the ITRF coordnates nto local rames. ITRF s normally used or dual requancy code and hase statc data n whch case should rovde at least cm level I or n horzontal and 4 to 5 cm n vertcal anywhere on the world (On-lne recse ont ostonng, 4). recse ont ostonng It has been shown that code-based ont ostonng soluton could be mroved to match the DGS soluton through the use o onoshere-ree, underenced seudorange wth recse ehemers and clock data. To acheve the hghest ossble ont ostonng accuracy, both carrer-hase and 763

2 Journal o Emergng Trends n Engneerng and Aled Scences (JETEAS) (5): (ISSN: 4-76) seudorange measurements should be used. In addton, the remanng unmodelled errors, namely troosherc delay, satellte atttude error, and ste dslacement eect, must be dealt wth. Ths aroach s commonly known as the recse ont ostonng, or. The onosherc-ree combnatons o dual-requency GS seudorange () and carrer-hase observatons (Φ) are related to user oston, clock, trooshere and ambguty arameters accordng to the ollowng smled observaton equatons (Kouba and Heroux, ). = ρ + C(dt-dT) + T r + ε () ф = ρ + C(dt-dT) + T r + N λ + ε ф where: s the onoshere-ree combnaton o L and L seudoranges ( ), ф s the onoshere-ree combnaton o L and L seudoranges (.54ф -.54 ф ), dt dt C T r s the staton clock oset rom GS tme, s the satellte clock oset rom GS tme, s the vacuum seed o lght, s the sgnal ath delay due to the neutralatmoshere (rmarly the trooshere), Λ s the carrer, or carrer-combnaton, wavelength, N s the ambguty o the carrer-hase onoshere-ree combnaton, and ε, ε Φ are the relevant measurement nose comonents, ncludng multath. Symbol ρ s the geometrcal range comuted as a uncton o satellte (s, Ys, Zs) and staton (x, y, z) coordnates accordng to (Schoeld, 6) ρ=( + Y + Z ) / () Fgure seudo Range Fgure s the seudo Range result rom the submtted GS observaton at BM_AMOS. Exressng the troosherc ath delay (T r ) as a uncton o the zenth ath delay (zd) and mang uncton (M) and removng the known satellte clocks (dt) gves the ollowng mathematcal model n the smlest orm (Ahmed El-Rabbany, ) 764 l = ρ + C dt + M zd + ε - = (3) l = ρ + C dt + M zd + N λ + ε - = (4) Φ Φ Φ Adjustment Model Lnearze observaton equatons (3) and (4) around the a-ror arameters and ater some rearrangement and transormaton we have A δ + W V =, (5) where A s the desgn matrx, δ s the vector o correctons to the unknown arameters, W = (, ) s the msclosure vector and V s the vector o resduals. The artal dervatves o the observaton equatons wth resect to, consstng o our tyes o arameters: Staton oston (x,y,z), clock (dt), trooshere zenth ath delay (zd) and (non-nteger) carrer-hase ambgutes (N), orm the desgn matrx A (Schaer et al, 998). The least squares soluton wth a-ror weghted constrants ( x ) to the arameters s gven by: T T A A A W (6) (7) wth covarance matrx C T A A (8) Adjustment rocedure The adjustment rocedure develoed s eectvely a sequental lter that adats to varyng user dynamcs. The mlementaton consders the varatons n the states o the arameters between observaton eochs and uses arorate stochastc rocesses to udate ther varances. The current model nvolves our tyes o arameters: staton oston (x, y, z), recever clock (dt), trooshere zenth ath delay (zd) and carrer-hase ambgutes (N). Fnally, the nonnteger carrer-hase ambgutes (N) wll reman constant as long as the carrer hases are ree o cycle-sls, a condton that requres close montorng. Usng subscrt to denote a secc tme eoch, we see that wthout observatons between eochs, ntal arameter estmates at eoch are equal to the ones obtaned at eoch - (Heroux et al ). (9) To roagate the covarance normaton rom eoch - to, durng an nterval Δt, has to be udated to nclude rocess nose reresented by the covarance matrx Cε t where C C t ()

3 Journal o Emergng Trends n Engneerng and Aled Scences (JETEAS) (5): (ISSN: 4-76) C t C ( x) t C ( y) t C ( z) t C ( dt) t C ( zd) t C ( N j ( j, nsat ) t every eoch, as a ure random walk rocess (Langley, 999).The dynamc model s n the orm: N N w where w s Gaussan nose. () recse ont ostonng Correcton Models Develoers o GS sotware are generally well aware o correctons they must aly to seudorange or carrer-hase observatons to elmnate eects such as secal and general relatvty, Sgnal delay, satellte clock osets, atmosherc delays, etc. All these eects are qute large, exceedng several meters, and must be consdered even or seudorange ostonng at the meter recson level. When attemtng to combne satellte ostons and clocks recse to a ew centmeters wth onosherc-ree carrer hase observatons (wth mllmeter resoluton), t s mortant to account or some eects that may not have been consdered n seudorange or recse derental hase rocessng modes (Gao and Chen, 5). Fgure seudo Range sky dstrbuton Resolvng the nteger ambgutes The rocess o resolvng the nteger ambgutes s called ntalzaton and may be done by settng-u both recevers at each end o a baselne whose coordnates are accurately known. In subsequent data rocessng, the coordnates are held xed and the ntegers determned usng only a sngle eoch o data. Unlke the double derenced carrer hase, the underenced analyss estmates only real numbers o ambgutes, or loated solutons. In act, ambgutes are rearameterzed ambgutes whch are collectons o ambgutes o L and L, wth carrer hase onoshere-ree scalng actors. Fgure 3 s the Ambgutes result rom the submtted GS observaton at BM_AMOS. The rearameterzed ambgutes ( N) are estmated. Fgure 3 Ambgutes Code Measurement The GS code measurement s a lnear measurement known as seudo range n meters. seudo Range s a measure o the dstance between the satellte and recever at the tme eoch o transmsson and receton o the sgnals. The transmt tme o the sgnals s measured by comarng (correlatng) dentcal seudo Random Nose (RN) codes generated by the satellte and the recever (FIG commsson 5 ublcaton ) = R + C (dt dt) + d on + d t ro + d math. () where R = True range between the SV (at transmt tme) and recever (at r recever tme) C = Seed o lght (m/s) dt = Recever clock error (sec) dt = Satellte clock error (sec) d on = Ionosherc delay arameter dt ro = Measurement delay due to trooshere (m) = Measurement delay due to multath d math Carrer Measurement The constant moton o the GS satellte constellaton n orbt demands that the recever be caable o takng care o the changng Doler requency sht on L. In the case o Dual requency recevers both L and L are tracked. L wavelength s 9cm and L wavelength s 4cm. The sht n requency arses due to the relatve moton between the satellte and the recevers. Integraton o the Doler requency oset results n an extremely accurate measurement o the advance n sgnal carrer hase between tme eochs (Gao and Chen 5). Once the recever locks on to a artcular satellte, t not only make C/A and or (Y) code seudo range measurements on L and L ( L s resent) but t also kees a runnng count based 765

4 Journal o Emergng Trends n Engneerng and Aled Scences (JETEAS) (5): (ISSN: 4-76) uon the Doler requency sht resent on L and L carrer requences. Mathematcally the relatonsh s as ollows (Klobuchar, 996).. n. n. n. n In I n. Where In I n o. r r dr. dr.. Where. (3) Where s the accumulated hase at the eoch shown n and n- are the current and mmedate ast eochs D - s the Doler requency as a uncton o tme s the ractonal hase measured at the eoch shown - s requency o ncomng sgnal n Hz N e - s the electron densty n electron / m 3 e- s the electron change = Coulomb n - s the ermeatvty o ree sace = Farad / m m- s the rest mass o electron = Kg Ө- s the angle o the ray wth resect to the earth s magnetc eld. V- s the electron neutron collson requency and H - s the electron gyro requency tycally.5mhz Troosherc Delay Troosherc delay occurs as a result o the GS sgnals assage through the Earth s lower atmoshere. Ths regon extends to an alttude aroxmately km above the earth s surace. The stratoshere s also consdered art o the lower atmoshere. It extends uward rom the trooause to an alttude o aroxmately 5 klometers. In these two sectons o the atmoshere, electromagnetc reracton slows the GS rado sgnals causng a delay n ts arrval at the recever (Kouba, and Heroux, ) Fgure s the Estmated Trooshere result rom the submtted GS observaton at BM_AMOS Fgure 4 Carrer - hase Fgure 4 above resent the carrer hase results rom the submtted GS observaton at BM_AMOS Ionosherc Delay. The onoshere s the art o the uer atmoshere where ree electrons occur n sucent densty to have an arecable nluence on the roagaton o rado requency electromagnetc waves. It s a weak onzed lasma extendng rom aroxmately 5Km to Km above the surace o the earth and can aect rado wave roagaton n varous ways (htt:// Ionoshere s a dsersve medum. The reractve ndex s a uncton o the oeratng requency. The reractve ndex n o the onoshere can be exressed as (Kouba and Heroux, ). n Y Z Where Nee m and n v Z w Y 4 Z 4 Z Cos ; YL H ; w sn ; Y H Y L (4) 766 Fgure 5 Estmated Trooshere Recever Nose Recever nose can be consdered as whte nose as t s uncorrelated over tme. In the case o GS, t s the error n hase and code measurement due to merect trackng o the GS sgnals by the hase and delay lock loos. The trackng error s random and s assumed to have a Gaussan dstrbuton. The magntude o the nose s a uncton o the measurement tye and the sgnal strength. The C/A code measurement can be tracked wth a tycal accuracy o.5 meters but t may vary between. and 3 meter deendng uon the strength o the recever sgnal. Tycal recever nose or (Y) code measurement s 3cm. Code and carrer hase measurement nose can be smoothed by an estmate o a zero baselne test. The GS sgnal s slt nto

5 Journal o Emergng Trends n Engneerng and Aled Scences (JETEAS) (5): (ISSN: 4-76) two and ed to two searate but same tyes o recevers. In statc alcaton, the redomnant error comonent n carrer hase nose s jtter o the hase lock loo caused by thermal nose. Ths can be exressed accordng to; (Langley, 999) as: B n TC n LL meters C no no where B n - carrer loo nose band wdth n Hz C n o (5) - s the carrer to nose ower exressed as C/No/ wth C/No n db - Hz T- s the redetectons ntegraton tme n seconds - s carrer wavelength Recever Clock Estmaton Recever clock can be estmated usng a Gauss- Markov rocess. The recever clock can be modeled as whte nose. However, t s better to model t as random walk. Snce we have seudorange observatons whch nclude the clock term, an aroxmate rato o the change n the clock rom the current eoch. The dynamc model can be drectly exress s; (Gao and Chen 5). R ( cdt ) (6) R ( cdt ) R clk R (7) Because many satelltes are observed at the same tme, t s addtonally better to average out the random error by averagng the rato o all avalable satelltes. The soluton obtaned rom the random walk rocess wth a ror normaton o the rato o recever clock shows a slght soluton mrovement than that usng the whte nose rocess (Ovstedal Ola et al, 6). Satellte orbt errors result rom the uncertanty n orbtal normaton s used to comute the satellte oston. The satellte ostons are comuted rom a set o Keleran orbt and erturbaton arameters wth clock arameters whch are redcted states or the satellte orbt and are udated every 5 mnutes. Fgure 6 s the Staton Clock result rom the submtted GS observaton at BM_AMOS Mult ath Mult ath reers to the exstence o sgnals relected rom objects n the vcnty o a recever s antenna that corrut the drect lne-o-sght sgnals rom the GS satelltes, thus degradng the accuracy o both code-based and carrer hase-based measurements. The object may be tall buldngs, televson and Telehone masks, etc. The error n the hase s gven by (Zunberge el ta 997) (8) Soluton Convergence and Results convergence as a uncton o tme deends on ntal arameter varances and the synergy o GS seudorange and carrer hase observatons, at the ntal eoch. Because o unknown carrer-hase ambgutes, the soluton reles entrely on the seudorange observatons and the qualty o the oston relects GS recever code resoluton and the multath envronment at the trackng staton. As tme asses and hase observatons are added to the soluton, the onosherc ree ambgutes and staton oston comonents (n statc mode) converge to constant values whle the troosherc zd and recever clock arameters vary as a uncton o ther assgned rocess nose. Fgure 7 shows the Ellsodal; Heght lattude and Longtude resectvely o BM_AMOS comuted usng recse orbt and clock nterval g 8, resent the ellsodal heght role above the staton. Fg 9 reresents the seudo Range and Aror correcton or staton BM_AMOS. Fgure 6 Staton Clock Fgure 7 - Ellsodal; Heght lattude and Longtude 767

6 Journal o Emergng Trends n Engneerng and Aled Scences (JETEAS) (5): (ISSN: 4-76) Fgure 8 Ellsodal Heght role. Fgure 9 - seudo Range and Aror correcton Table s the CSRS- rocessng summary or the control ont BM_AMOS. The estmated oston s resented under the headng o as ITRF5 () below. Table : CSRS rocessng Summary o BM _ AMOS DISCUSSION AND CONCLUSION The aer demonstrate that ont ostonng technque s able to oer mm level accuracy n statc mode usng the lastest IGS satellte orbts and clock eoducton. The man actors that may lmt the accuarcy are the recson o satellte orbts, clocks and eects o unmodelled errors. The s an ecent and ast way o determng staton coordnates. The observaton equatons, estmaton technque and staton/satellte models used or the mlementaton o GS recse ont ostonng usng IGS orbt/clock roducts were descrbed. A ost-rocessng aroach that uses dual-requency seudorange and carrer-hase observatons rom a sngle GS recever and estmates staton coordnates, troosherc zenth ath delays and clock arameters was develoed. Results show that global centmeter ostonng recson can be realzed, drectly n ITRF, when usng recse orbts/clock roducts rom derent IGS Analyss Centre (ACs) and the IGS combnatons. The sngle ont ostonng mode resented here orms an deal nterace to the IGS orbt/clock roducts and ITRF. The aroach s equally alcable to global knematc ostonng/navgaton at the cm-dm recson level. REFERENCES Abdel-Salam, M. (5) recse ont ostng usng un-derenced code and carrer hase observaton. h.d dssertaton, Deartment o Geomatcs Engneerng, Schulch School o Engneerng, Unversty o Calgary, Alberta, Canada. Ahmed El-Rabbany (), recse GS ont ostonng: the Future Alternatve to Derental GS. Surveyng roceedngs o the ION GS-, Oregon Conventon Centre, ortland, Oregon, USA, Setember 4-7 CSRS- (NRCANGSD): Servce rovded by Natural Resource, Canada. htt:// gc.ca/roductsroduts/_e.h. FIG commsson 5 ublcaton () cost eectve GNSS ostonng technques, FIG ublcaton No. 49. Gao Y and Chen K (5 () Imrovng Ambuguty Convergence n Carrer hase Based recse ont ostonng, roceedngs N, GS, Salt Lake Cty, Utah. Gao Y and Chen K () A New Method or Carrer hase Based recse ont ostonng Navgaton, Journal o the Insttute o Navgaton Vol 49, No.. 768

7 Journal o Emergng Trends n Engneerng and Aled Scences (JETEAS) (5): (ISSN: 4-76) Gao Y and Chen K (5) erormance analyss o recse ont ostonng usng real tme orbt and clock roducts Journal o Global ostonng system Vol 3 No Heroux, Kouba J, Collns and Lahaye F () GS carrer hase ont ostonng wth recse orbt roducts. ubl Klobuchar J.A. (996) Ionosherc Eects n GS n arkngson & Slker or (Eds) Global ostonng Systems: Theory and Alcaton rogress n Astronautcs and Aeronautcs, Vol 63 ubl o the Amercan Insttute o Aeronautcs and Astronautcs Inc. Kouba, S. and Heroux, () recse ont ostonng Usng The IGS Orbt And clock roducts, GS Solutons Vol 5() 8. Langley R (999) GS Recevers and the observables. In GS or Geodesy Tennssen and Kleberg A (eds) Srnger verlag On-lne recse ont ostonng (4). How To Use Document, Natural Resources Canada. Canada Centre or Remote Sensng Geodetc Survey Dvson. Ovstedal, O. () Absolute ostonng wth Sngle Frequency GS Recevers GS Soluton Vol 5(4) Ovstedal Ola, Kjorsvc N. S. and Gjevestad JGo (6) Surveyng Usng recse ont ostonng. roceedngs o III FIG Congress TS43 GNSS rocessng and Alcaton, Munch, Germany, October 8 3, 6. Schaer, S, Gurtner W, and Fettens J (998) IONE, the IONOSHERE: Ma Exchange Format Verson. February 5, 998, n roceedngs o the 998 IGS Analyss Centres Worksho, ESOC, Darmstadt, Germany, February 9, 998. Schoeld. W (993) Engneerng Surveyng Butterworth-Henemann Ltd, Oxord. W. Schoeld. (6): Engneerng Surveyng; Theory and Examnaton roblems or Students, Fth Edton Kngston Unversty, London. Zunberge J.F, Heln M.B, Jeerson D C, Watkns M N and Webb F.H (997) recse ont ostonng or the ecent and robust analyss o GS data rom large networks Journal o Geohyscal Research vol