BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements Dmtros PAPAGEORGIOU, Chrstos PIRIDAS, Arstds FOTIOU and ostas ATSAMBALOS, Greece ey words: GPS, software development, code measurements, relatve postonng, baselne determnaton. SUMMARY A complete software package has been developed for GPS baselne determnaton based on code data, and on double dfferences between smultaneous observatons. It s a standalone wndows applcaton (enttled BaselneByCode ) wth an educatonal user-frendly nterface wrtten on Delph-5. Although the accuracy s comparable wth the results obtaned from commercal software, ths package has the advantage of extended parameterzaton, allowng selecton of nput data types (C/A, P1, P2), ephemerdes (broadcasted, precse), onospherc and tropospherc models, optmum selecton of reference satellte, sgnal-to-nose threshold level, cut-off angle, tolerance for the synchronzaton of observatons, resdual magntude, tme nterval for all satelltes, double dfferences for selected satelltes, etc. In addton, the package dsplays and prnts on demand all ntermedate results (n textual or graphcal form), exchangng data and results wth other wndows-based applcatons. The user may study the results obtaned from adjustments wth varous parameterzaton crtera. Every soluton s obtaned wth an 1-cm convergence lmt. TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 1/12 FIG Workng Week 24
BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements Dmtros PAPAGEORGIOU, Chrstos PIRIDAS, Arstds FOTIOU and ostas ATSAMBALOS, Greece 1. INTRODUCTION A major objectve of an educatonal package s a step by step analyss and presentaton of the results durng processng. Followng ths scope, the Department of Geodesy and Surveyng has developed a wndows-based software package wrtten n Delph programmng language, whch uses solely code GPS measurements. It has a user-frendly nterface wth extended parameterzaton for processng and dsplayng. It also prnts and saves each type of results n textual or graphcal form. Varous models and useful optons for the pre- and post processng of observatons are selected by the user, so that helpful nformaton and advanced analyss can be appled by an experenced user or a researcher usng the ntermedate results. Many types of graphcal forms and report fles can be saved and modfed accordng to the user demands. The test solutons that were appled on baselnes from 5 to 2 km and the results as compared to solutons usng phase data (wth fxed ambgutes), showed dstance dfferences from.4 to 1.2 meters, as expected. Comparng wth commercal software usng only code measurements, the baselne dfferences are of the order of one dm. The package provdes onlne help for (almost) every man panel opton. 2. DATA IMPORT AND PROCESSING PARAMETERS The man objectve of the BaselneByCode software package s the baselne soluton. Upon completon of a GPS survey, the collected data are mported for each recever n RINEX format (Gurtner & Mader, 199). Most of GPS data exchanges are based on ths format, so that measurements from dfferent recever manufacturers can be used for processng. The software dsplays three man panels ( data, results, utltes ) and three auxlary ones ( nfo, prnt and help ). Wthn the frst panel ( data ), the user can select the processng parameters (see fgure 1). The upper data secton dsplays the WGS84 cartesan coordnates, from both reference and rover recevers, as exported from the RINEX observaton fles (or altered by the user), the recever type, the observng wndow, the total numbers of epochs wth the observaton rate, the post-processed coordnate correctons and the fnal baselne length wth ts assocated rms. In the mddle data secton there s a graphcal representaton of the satellte vsblty for both stes durng the observng perod. The lower secton of the data s dvded nto sx parts where the processng optons are specfed. The frst selecton s related to the type of satellte ephemers beng used. The TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. FIG Workng Week 24 2/12
program can use ether broadcast or precse (n SP3 format) ephemerdes. The precse ephemers can be downloaded from a known data center (e.g. the Center for Orbt Determnaton n Europe) and the poston vectors between the gven epochs are obtaned by Lagrange nterpolaton, based on polynomal base-functons s used (Hofmann-Wellenhof et al. 1997). The second selecton refers to the choce of the code observatons. The user may select C/A or P1, P2 on both frequences. The next selecton refers to the choce for the onospherc refracton model. In addton to lobuchar s ono-model wth the eght coeffcents (lobuchar 1987), whch ncluded n the rnex navgaton fle, the program also uses the Sngle Layer Model (Georgadou & leusberg 1988, Hugentobler et.al. 21, Pkrdas & Fotou 23). The determned parameters for ths model can be mported by the user, snce the program processes code measurements only, and not phase data n order to estmate the SLM parameters. The next atmospherc selecton deals wth the tropospherc models. Most of the well-known models, lke Collns, Magnavox, Saastamonen, Hopfeld, Goad and Goodman and Marn, are ncluded. The program also computes the atmoshperc components, lke temperature, pressure and relatve humdty for each ste assumng a standard atmosphere. It should be ponted out that the user may modfy these values f a better (local profle) model s avalable. The fnal two sub-sectons are referred to restrctons on observatons. Measurements wth low sgnal-to-nose rato, usually from satelltes at low elevaton, are subjected to hgh nterference, so that the software has the opton to select observatons accordng to sgnal strength. Smlar opton s the change of the cut-off angle value for the collected data. Fnally, the user may modfy the selecton of the observng wndow and the choce of the maxmum resdual value for the double dfferences. Fgure 1, shows the data panel and all the processng optons of the BaselnebyCode package. TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 3/12 FIG Workng Week 24
Data Import Prnts Results Process Help Ephemers Import Selecton of Code Observatons Selecton of Ionospherc Models Selecton of Tropospherc Models Observaton restrctons Fg. 1: The man panel of the program Baselne by Code 3. POSITIONING MODEL SOFTWARE PHILOSOPHY The code pseudorange for a satellte and a pont (Hofmann-Wellenhof et.al. 1997, Fotou & Pkrdas 22) can be modeled as P = ρ + cδ cδ + I + T + e (3.1) where P s the measured code pseudorange between the observng ste and the satellte, ρ s the geometrc dstance, c s the speed of lght (c=299792458 m/s) I T, are the onospherc and tropospherc bases, cδ, cδ the satellte and recever clock errors TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 4/12 FIG Workng Week 24
accordngly, e the random error and gnorng multpath effect.. The pont coordnates to be estmated are mplct n the dstance ρ, wrtten as ρ = where ( ) ( ) 2 X X + Y Y + ( Z Z ) 2 2 (3.2) X, Y, Z are the components of the geocentrc poston vector of the satellte and X, Y, Z the three unknown pont coordnates of the observng pont all expressed n the ECEF (Earth Centered Earth Fxed) system. The objectve of relatve postonng s the determnaton of the coordnates of the unknown (rover) pont wth respect to a known (reference) one. Assumng two ponts A and B, and two satelltes j and k, the correspondng pseudoranges can be formulated as j j j j j j P = ρ + cδ cδ + I + T + e A A A A A A, k k k k k P B = ρ B + cδ A cδ + I B + TB + e k B (3.3) Formng the double dfference for specfc epoch, P = ρ ρ = ( ρ ρ ) ( ρ ρ ) + I + T + e (3.4) jk AB k AB j AB k B k A j B j A jk AB the cancelng effects of the recever and satellte are obvous and the other bases are reduced as well. Equaton (3.4) s used for the soluton of the GPS baselne. Accordng to the least squares adjustment (Dermans and Fotou, 1992) and usng the method of observaton equatons (method of parameters), the above equaton (3.4) has to be lnearzed wth respect to the coordnates of the unknown pont whch could be pont A or B or generally pont. Assumng a set of approxmate coordnates (X, Y, Z ) for the unknown pont (mported from the rnex observaton fle) an approxmate dstance can be calculated. The partal dervatves are gven by jk AB jk AB ρ X X = X ρ = α X ρ Y Y = Y ρ = α Y (3.5) ρ Z Z = Z ρ = α Z so that TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 5/12 FIG Workng Week 24
ρ + = ρ + a XδX + ayδy azδz (3.6) Fnally, wth the help of (3.6) the system of lnear observatons equatons s formed and the estmaton of the unknown pont coordnates s obtaned by the well know least squares adjustment. 4. UTILITIES AND RESULTS PRESENTATION As has been stated n the ntroducton, BaselneByCode publshes all ntermedate results. Ths opton s easly actvated from the results panel. There are two types of presentaton, text fles and graphcal forms. In the textual form, the software outputs (upon user request) the clock offsets fle for each epoch, the sngle and double dfference resduals, the desgn matrx and ts transpose, the weght matrx, the excluded observatons, and for each observaton pont (reference and rover), the satellte postons as a seres of tme-tagged Earth Center Earth Fxed (ECEF) coordnates (see Fgure 2), as well as all the necessary nformaton for the selected atmospherc models. As long as the graphcal form s concerned, the program llustrates the satellte elevaton, dluton of precson factors, onospherc and tropospherc refracton for each satellte accordng to ts elevaton durng the observng wndow and the estmated satellte resduals. Fgure 3, shows a representatve resduals dagram for a selected satellte, where, the blue dots are the resduals values and the red lne s the satellte elevaton. It must be emphaszed that for the graphs of the atmospherc refracton there are actve optons lke the geographcal locaton, (lattude and longtude) of the recever, the satellte elevaton and azmuth, the reference atmospherc values and all atmosphere-related crtcal parameters. The user has the opton to alter these values n order to montor the correspondng dsturbance. Fgure-2 s an orbt nformaton text fle, whch ncludes all the necessary nformaton for each common epoch (e.g. satellte poston, elevaton, azmuth, satellte clock offsets, etc). Ths nformaton s made avalable to the user for further research. TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 6/12 FIG Workng Week 24
Fg. 2: The orbt nformaton text fle of the program Baselne by Code Fg. 3: The satellte resdual panel of the program Baselne by Code TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 7/12 FIG Workng Week 24
In fgure 4 the tropospherc refracton usng all the avalable models (usng dfferent color lnes) accordng to satellte elevaton s plotted. Ths dagram can be easly vewed from the utltes panel. Same optons are also avalable for the onospherc models and appear n fgure 5. Fg. 4: The computed tropospherc refracton Vs satellte elevaton. Fg. 5: The computed onospherc refracton Vs satellte elevaton TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 8/12 FIG Workng Week 24
4. COMPARISONS WITH COMMERCIAL SOFTWARE PACAGES In order to evaluate BaselneByCode and to assess the relablty of ts results, we reprocessed the same data usng the recever manufacturer s software, choosng the same parameters. Fgure 6 shows the baselnes dfferences for the above process usng C/A or P code measurements for varous baselne lengths. An nterestng remark s that usng the P code data for baselnes below 5 m the baselne dfferences are greater than when usng the C/A code. Ths pont needs to be further nvestgated. Dstance Dfferences between Baselne by Code and Commercal Software Dfferences (m) 3, 2,5 2, 1,5 1,,5, -,5 5 1 15 2 25 Baselne Length (m) C/A CODE P CODE Fg. 6: The baselne dstance dfferences between BaselneByCode and commercal software usng C/A and P code measurements 5. CONCLUDING SUMMARY As an educatonal - purpose software, BaselneByCode has been developed for the determnaton of a baselne usng solely code GPS measurements. All tests that have been contacted, lead to the followng useful remarks. The fnal results depend upon a number of ntally selected processng parameters. Sometmes, these parameters may play a crtcal role for the fnal accuracy and many of them are not well known to the nexperenced user or to a student. It s essental for these users to study the effect of certan parameters on the fnal results. For ths reason, the user may change or adjust crtcal factors (lke, cut-off angle, sgnal qualty, maxmum zero, sngle and double dfference resdual, etc.) to ther proper values n order to acheve the hghest possble accuracy. The montorng of each atmospherc model accordng to the satellte elevaton or to ts characterstcs s supported from wthn the utlty panel. TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 9/12 FIG Workng Week 24
All of the ntermedate results are extracted to graphcal or textual forms. Advanced analyss and useful educatonal examples can be produced from these results. The program uses the RINEX observatons and navgaton fles n order to determne the baselne. The soluton results are compared wth GPS recever manufacturer software on dfferent baselne lengths n order to evaluate ts relablty. The dfferences are varyng from.2 to 2.5 meters, so that the program can easly work for low accuracy GPS applcatons (e.g. GIS projects) usng low cost handheld recevers. 6. SOFTWARE AVAILABILITY -ROYALTIES BaselneByCode has been developed as an educatonal package. Colleagues from academc nsttutons may download the self-extracted software from the followng URLs, provded that they wll gve proper credt to the authors. http://www.softwaypro.gr/fles/other/gps/nstblbc.exe http://users.auth.gr/kvek/baselnebycode/ REFERENCES Dermans A. and Fotou A.(1992). Methods and Applcatons of observaton adjustment. Arstotle Unvesrty of Thessalonk, Edtons Zt, Greece. Dermans A.(1999). Space Geodesy and Geodynamcs. Arstotle Unvesrty of Thessalonk, Edtons Zt, Greece. Farrel J. and Barth M. (1998). The Global Postonng System and Inertal Navgaton. Edtons Mcgraw Hll. Fotou A. and Lveratos E.(2) Geometrcal Geodesy and networks. Arstotle Unvesrty of Thessalonk, Edtons Zt, Greece. Fotou A. and Pkrdas C. (22). The Global Postonng System GPS. Lecture Notes, Arstotle Unvesrty of Thessalonk, Greece. Georgadou Y. and leusberg A. (1988). On the effect of Ionospherc Delay on Relatve GPSPostonng, Manuscrpta Geodaetca, Vol.13, pp. 1-8. Gurtner W. and Mader G. (199). Recever Independent Exchange Format verson 2. GPS Bulletn, 3(3): 1-8. Hugentobler U.,Schaer S., Frdez P.(21). Bernese GPS software verson 4.2. Astronomcal Insttute, Unversty of Bern. Hofmann-Wellenhof B., H.Lchtenegger and J.Collns. (1997). Global Postonng System. Theory and Practce, fourth revsed edton, Spnger-Verlag, New York. lobuchar J. A. (1987). Ionospherc Tme-Delay Algorthm for Sngle-Frequency GPS Users, IEEE Transactons on Aerospace and Electronc Systems, Vol. 23, No.3, pp.323-331. Papaparaskevas P. (22). Software Development for GPS Sngle Pont Postonng. Msc. Thess, Department of Geodesy & Surveyng, Arstotle Unvesrty of Thessalonk, Greece. Papageorgou D. (23). Software Develpoment for Baselne Determnaton Usng GPS Code Data. Msc. Thess, Department of Geodesy & Surveyng, Arstotle Unvesrty of Thessalonk, Greece. TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 1/12 FIG Workng Week 24
Pkrdas C. (1999). The use of GPS Technology and the Qualty Control n Geodetc Applcatons. Ph.D. Thess, Arstotle Unversty of Thessalonk, Department of Geodesy & Surveyng, Thessalonk, Greece. Pkrdas C. and Fotou A. (23). Evaluaton of the Effect of Ionospherc Refracton on Relatve GPS Postonng. Applcaton n the Broader Area of Thessalonk usng GPS Permanent Staton Data. Tech. Chron. Scentfc Journal. Techncal Chamber of Greece, vol.1. Rzos C. (1999). Prncples and Practce of GPS Surveyng. SNAP group, UNSW, Australa. Rosskopoulos D. (1999). Surveyng Networks and Computatons. Arstotle Unversty of Thessalonk, Edtons Zt, Greece. BIOGRAPHICAL NOTES Dmtros Papageorgou. M.Sc. n GeoInformaton from the Arstotle Unversty of Thessalonk. Surveyor Engneer at the Prefecture of Vota, Central Greece. Chrstos Pkrdas. Lecturer at the Department of Geodesy and Surveyng of the Arstotle Unversty of Thessalonk. Hs man nterests are on GPS error analyss, data processng, engneerng applcatons and deformaton studes. Arstds Fotou. Professor at the Department of Geodesy and Surveyng of the Arstotle Unversty of Thessalonk and he expertse n adjustment theory, geometrcal geodesy, geodetc networks and n hgh precson GPS applcatons ostas atsambalos. Professor at the Department of Geodesy and Surveyng of the Arstotle Unversty of Thessalonk. Man nterests: geodetc surveyng, gravty feld determnaton, GPS applcatons and software development. CONTACTS Dmtros Papageorgou Prefecture of Vota Fdppdou, 2 St. 321 Levada GREECE Emal: dpap@softwaypro.gr Web ste: http://www.softwaypro.gr TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 11/12 FIG Workng Week 24
Chrstos Pkrdas Arstotle Unversty of Thessalonk Unv. Box 432, 54124 Thessalonk GREECE Tel. + 3 231 996 11 Fax + 3 231 996 48 Emal: cpk@topo.auth.gr Web ste: http://users.auth.gr/~kvek/cvpi.html Arstds Fotou Arstotle Unversty of Thessalonk Unv. Box 473, 54124 Thessalonk GREECE Tel. + 3 231 996135 Fax + 3 231 99648 Emal: afotou@topo.auth.gr Professor ostas atsambalos Arstotle Unversty of Thessalonk Unv. Box 469, 54124 Thessalonk GREECE Tel. + 3 231 996 123 Fax + 3 231 996 48 Emal: kvek@ topo.auth.gr Web ste: http://users.auth.gr/~kvek/ TS29 Postonng and Measurement Technologes and Practces III Applcatons and Processng Dmtros Papageorgou, Chrstos Pkrdas, Arstds Fotou and ostas atsambalos TS29.4 BaselneByCode: An Educatonal -Purpose Software Package for GPS Baselne Determnaton Usng Code Measurements. 12/12 FIG Workng Week 24