7-5-5 NATIONA TECHNICA UNIVERSITY OF ATHENS SCHOO OF RURA AND SURVEYING ENGINEERING DEPARTMENT OF TOPOGRAPHY AORATORY OF GENERA GEODESY Α complt procssng mthodology for D montorng usng GNSS rcvrs Gorg Pantazs Assocat Profssor of NTUA gpanta@cntralntuagr Sofa, ulgara 7- May 5 5 6 9 8 Two Masurmnt campagns (I, II) aslns Masurmnt 5 4 7 rlatv statc postonng mthod 4 Only non-trval baslns ar usd for th adustmnt n ordr to nsur dffrnt condtons and to avod bas at th calculatons FIG Workng Wk 5
7-5-5 Mthodology soluton of ach basln For ach campagn Dtrmnaton of th componnts ΔΧ, ΔΥ, ΔΖ nth Cartsan gocntrc rfrnc systm btwn th occupaton ponts and rlabl stmaton of th wghts of ΔX, ΔY andδz lnar quatons ar formd and th unknown gocntrc coordnats X, Y, Z ar calculatd by a last squars adustmnt th full VCV matrx s provdd for ach campagn us of th Excl or Matlab softwar Mthodology Th dffrncs of th coordnats Χ, Υ, Ζ, btwn succssv campagns ar calculatd transformaton of Χ, n a local procton plan Υ, E V δe,n,up Ζ, th full VCV matrx s calculatd accordng to th low ofpropagaton rrors by usng th full VCV matrx of th dsplacmnts V δx,y,z th rror llpss or llpsods of th control ponts ar calculatd for th dtcton of th pont s dsplacmnt N Up FIG Workng Wk 5
7-5-5 st mthod Wghts stmaton Αn obctv stmaton of th rrors Χ Y a prlmnary last squar qual wght adustmnt could b appld accordng to thr th mthod of ndrct obsrvatons or th mthod of condton quatons ndrct obsrvatons,qual wght adustmnt Χ = Χ Χ Υ = Υ Υ Ζ = Ζ Ζ Th numbr of quatons of ach systm s qual to th masurd baslns Z nd mthod Th condton quatons ar formd by ntwork s loops closur by usng th masurd ΔΧ, ΔΥ, ΔΖ as follows Χ + Χ + Χ Y + Y + Y Z + Z + Z k k = k k = k k = Th numbr of quatons n vry systm s qual to th numbr of th unary loops Th obctv rrors of th unknown componnts for ach pont of th ntwork s prsntd by th root of thvaranc for ach on n VCV matrcs Χ Y Z nd mthodmprcal Wghts stmaton Thmsclosurofthunaryloopsofthntwork(mc)sth rror, whch th loop contans for thr partcpatng baslns So a dcnt stmaton of ths rror for ach componnt ΔΧ,ΔΥ,ΔΖ s gvn by th followng quaton Χ mc loopx Y mc Thn th man rrors of th baslns componnts dtrmnaton ar calculatd as follows sthnumbrofthloops Y Z Χ t = Χ m Consdrng that for ach basln, th followng quatons ar vald = + Χ Χm Assumng that = Χ Χ Χ thn Χ Y Y loopy Z t= Y m = + Y Ym = Z = Z Y Χ Χ Y Z mc loop Z Zm Z m t = Z = + Y Y Z Z Z FIG Workng Wk 5
7-5-5 Absolut dsplacmnts calculaton Accordng to th ndrct obsrvatons mthod th followng systm of rgular quatons s formd Χ = Χ Χ Υ = Υ Υ Ζ = Ζ Ζ ) T - Ô Ô x = (A Ρ A) Á Ρ l = N Á Ρ l Th absolut poston changs of ntwork s ponts n btwn two squntal masurmnt campagns (I and II) ar calculatd δ IΙ-Ι Χ Y Z Χ+ Y + = Z+ Χ n Yn Z n I II Th varancs and covarancs of ths changs V δx, Y,Z = VX,Y,Z + VX,Y,Z Th changs ΙΙ Χ Ι,,, of ach pont must b convrtd n Υ, Ζ, an orntd local plan procton, δeast, δnorth and δup n ordr to b mor prcptbl and to dfn thr drctons and thr trnds n rlaton to th arth s surfac Absolut dsplacmnts calculaton th total rotaton matrx S A for th (n-) unknown ponts of th ntwork S A sn ë sn ö cos ë cos ö cos ë = cos ë sn ö sn ë cos ö sn ë cosö sn ö sn ö sn ë + + + cos ë cos ö cos ë + + sn ö + + cos ë + sn ë cosö sn ë + + cos ö sn ö + + sn ë n- n- n- sn ö cosë cosö cos ë n- n- cos ë sn ö n- n- n- sn ë cos ö sn ë n- n- cos ö n- sn ö n- th poston changs of ach pont (,, ) n a local procton plan E N Up Th CV matrx for th componnts E, N, Up ar calculatd accordng to th law of propagaton rrors by usng th approprat J matrx as T δe, N,Up δx,y,z J matrx s formd by th partal drvaton of th prvous quaton J=S A V = J V J FIG Workng Wk 5 4
7-5-5 Absolut dsplacmnts calculaton Contnuously th chang vctor r and ts barng b, n rgard to north, r = (δe ) + (δn ) δε b = arctan I, II δν Th horzontal dsplacmntscould b chckd by applyng at a glanc gnral on dmnson chck f r < ó II z and r I, < ó z thn thr s no horzontal dsplacmnt I, II δe δn f r > ó II λ δe I, and r > ó λ I, II thn thr s horzontal dsplacmnt δn th full chck procdur th absolut rror llps s drawn for ach pont for a spcfc confdnc lvl and th dsplacmnt vctor of ach pont s ovr dsgnd th vrtcal dsplacmnts dtcton f δup < σ I, II z thn s no vrtcal dsplacmnt of th pont, othrws δup pont has a vrtcal dsplacmnt for th slctd confdnc lvl w a total approach of th absolut dsplacmnt s chck could b don by th calculaton of th rror llpsod s axs for ach pont ów ów óu u óu óv óv v postonng vctors Rlatv dsplacmnts calculaton In ordr to calculat th rlatv dsplacmnts btwn two pontsandofthntworkthchang svctors, ÄÍ ÄUp, btwn two squntal masurmnt campagns I and II ar calculatd by usng th quatons Ε,, Ε ÄÍ II I = ( Ε Ε, ) ( Ε Ε) = Ε II É = ( Ν Ν, ) ( Ν Ν ) = Ν Ε Ν δup Ι, ΙΙ II I Ι, ΙΙ Ι, ΙΙ = (Up Up, ) (Up Up ) = δup δup Samchcks FIG Workng Wk 5 5
7-5-5 Dscusson Th nflunc of th full CV matrx us s vry mportant for th dsplacmnts dtrmnaton as t maks dffrnc not only to th magntud of th rror llpss axs but also to th orntaton of ts man axs a δr =llps wth Full CV matrx =llps only wth varancs mm mm N N δr E b Th mscalculaton of th llps lads to wrong conclusons about th dsplacmnts of th control pont, as th dsplacmnt vctor may l accdntally outsd or nsd th llps δr δr E Conclusons ThlackofthfullCVmatrxasoutput th ovrstmatd standard rrors of th baslns soluton as wll as th black box followd procdur, ar th man dsadvantags of th maorty commrcal GNSS softwars whn usd n th D montorng In th advantags of th proposd procssng mthodology ar rgstrd th lnar quatons, whch ar formd, rlas th procdur from approxmatons Th ntr procdur can b carrd out n an asy Excl or Matlab nvronmnt as smpl quatons systms ar solvd thus no spcal softwar dvlopmnt s rqurd FIG Workng Wk 5 6
7-5-5 Conclusons Th wght dfnton proposd tchnqu avods th unralstcally optmstc standard rrors calculaton du tothgnssabltytocollctplthoraofdata Thrby, t nsurs th rlablty of th adustmnt as t llustrats th obctv achvd standard rrors n th orgnal capturd data Th us of spcfc rotaton matrx for ach pont n ordr to calculat thr th absolut and rlatv dsplacmnts accordng to th law of propagaton s rror nsur th corrctnss of th rsults Th full CV matrx formaton allows th accurat rror llps or rror llpsod calculaton, th rght valuaton of th dsplacmnts Conclusons Thcomparsonofthszandthrotatonofthrror llpsswhcharformdbyusngthfullcvmatrxor th dfcnt on prov that thr s a strong possblty to xtract dffrnt conclusons for a pont s dsplacmnt as manly th llps s orntaton s compltly dffrnt Th proposd procssng mthodology allows th total survllanc of th adustmnt s stps, th obctv wghts dfnton and th full CV matrx formaton t s valuatd as ffcnt and rlabl for such a trustabl and srous actvty as th D montorng by usng GNSS rcvrs FIG Workng Wk 5 7
7-5-5 NATIONA TECHNICA UNIVERSITY OF ATHENS SCHOO OF RURA AND SURVEYING ENGINEERING DEPARTMENT OF TOPOGRAPHY AORATORY OF GENERA GEODESY Α complt procssng mthodology for D montorng usng GNSS rcvrs Gorg Pantazs Assocat Profssor of NTUA gpanta@cntralntuagr Sofa, ulgara 7- May 5 FIG Workng Wk 5 8