Coordinates Transformation by Zoning Method for Parameters Computing between WGS84 and North Sahara

Transcription

1 Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Nouedde KHELOUFI, Algea Kewods: Catogaph GPS, Lad eadjustmet, postog SUMMAR The global tasfoms model (busa wolf, molodeskbadekas) ae the famous method used to cmpute paamete tasfomato betwee geodetc sstems. I ou case, fo a huge teto lke algea, these model ae ot most appopate to gve a good accuaces ove these paametes, because fomatuo about local geod ove ellpsod clake 88 s ot avalable. but the two dmeso models such as geodetc les, multple efesso,..., have gve best esults appled ove the algea aea. That s wh we ae hold to use a ew method to compute the tasfom paametes wth good accuaces, ths method s called oage ad t cocst to delmtate ou teto to lttle oe ode to appl thee dmeso models (busa wolf, molodeskbadekas), ths case we ca avod geat geod udulato wch geeate eos o computato of patametes ad gve thus a bad accuac. These paametes whle computed, could be used to tasfom a ew pot ove all the oe, the esults ae valdatg b a computato pogamm called TRANSFOR PS 5.3 Refeece Fame /5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6

2 Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Nouedde KHELOUFI, Algea. INTRODUCTION The global tasfoms models (Busa Wolf, MolodeskBadekas) ae the famous method used to compute tasfomato paametes betwee geodetc sstems. I ou case, fo a huge teto lke Algea, these models ae ot most appopate to gve a good accuaces ove these paametes, because fomato about local geod ove ellpsod Clake 88 s ot avalable but the two dmeso models such as geodetc les, multple egesso,..., have gve best esults appled ove the Algea aea. That s wh we ae hold to use a ew method to compute the tasfom paametes wth good accuaces, ths method s called og ad t cosst to delmtate ou teto to lttle oe ode to appl thee dmeso models (busa wolf, molodeskbadekas), ths case we ca avod geat geod udulato whch geeate eos o computato of paametes ad thus gve a bad accuac. These paametes whle computed, we ca use them to tasfom a ew pot ove the ete oe, ad the esults ae valdated b a computato pogam called TRANSFOR.. GENERAL EPRESSION OF TRANSFORMATION Où : posto vecto. T : taslato R : otato aoud 3 aes Δk : scale facto vaato. 3. GLOBAL MODELS 3. BURSA WOLF model NS T+ (+Δk).R (E, E, E). WGS84 It s a (7) seve paametes model wth geeal equato: T + ( + Δk).(I + ΔR). Whee: : coodates vecto the fst sstem (). : coodates vecto the secod sstem (). I : Idett mat. PS 5.3 Refeece Fame /5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6

3 PS 5.3 Refeece Fame 3/5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6 Matcal epesso fo oe pot s : ( ) + Δ +. E E E E E E. k T T T B puttg the ukow the same vecto, we obta the BURSA WOLF model ude hs matcal fom. Fo oe () pot : The BURSA WOLF model ca be wte.. T T T k E E E + Δ fo pots (>3) : we obta : Δ E E E k T T T Ths sstem ca be esolved b the least squaes method.

4 PS 5.3 Refeece Fame 4/5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6 3. MOLODENSKBADEKAS Model The MOLODENSKBADEKAS model Catesa fomalsm s obtaed b seto of vecto defg a tal pot aoud wch the thee otatos (E, E, E ) ae caed out. Ths pot s cosdeed as a gavt cete usuall called «sobacete», the both coodates sstems. Ths model s geeall used fo local tasfomatos lke cadastal oes. We take as a tal pot, the gavt cete epessed the two () sstems: Sstm Sstem, Wth dffeece of BURSAWOLF, MOLODENSKBADEKAS toduce hs model, a tal pot such as: ) R).( k).(i ( + T + Δ + Δ + It s a seve (7) paametes model, wth geeal equato: whee : : coodates vecto the fst sstem (). : coodates vecto the secod sstem (). : coodates vecto of gavt cete. I : Idett mat. The matcal wtg fo oe pot s : ( ) + Δ +. E E E E E E. k T T T

5 PS 5.3 Refeece Fame 5/5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6 Wth puttg ( ) ad wth odoate the mat, MOLODENSKBADEKAS model become fo pots: E E E Δk T T T «ONING» METHOD PRESENTATION. The method of teatmet wth "og" Fo the thee dmesos models, ol the applcatos o lage scales gave good esults, oe ca epla that b the fact thus that the popagato of eos o the lage geodetc oes affect the accuac detemato of the coodates of the pots afte Tasfomato, oe could obta elatvel lage esdues fo the applcato o a small scale (case of Algea). O the othe had, fo the cadastal applcatos (geat scales), all the models wee cosdeed to be good bus the gave geodetc accuaces detals (cetmetc). Thus fo the cadastal applcatos, all the models gve satsfacto esults. The toducto of the ew tasfomato (appoach of the geodetc les) made t possble o the othe had to obta guaatos esults wth the geodetc equemets (5 à cm aveage) some s the etet (case of Algea) wth the povso of takg accout of the coecto of amuth ad scale. It s otced that fo the applcatos o lage scales, the smlat plaes was suffcet fo ths kd of applcato (the etwoks GPS ad the Nothe Sahaa ae almost cofomt). A tme t s to be aouced that ths wok appoaches the twodmesoal aspect b hghlghtg the majot of the methods of tasfomatos such as the multple egesso, the tasfomato closel coected ad the geodetc les. The thd dmeso whch s a fudametal ukow facto, s appoached the two theedmesoal models (Busa Wolf

6 _ og, MolodeskBadekas_og) but beg detfed wth the ellpsodc heght, because of the lack of fomato o the heght of the geoïd elatg to the ellpsod Clake 88, ad followg the coheece whch ests betwee the coodates of the pots, the accuaces detals o the esults esultg fom these two models ae faded. It s thus ecessa to ca out a og of the teto questo to avod especall the poblem of the geat udulatos geod fo the thee dmesos models. The tadtoal methods, cuetl eplaced ew methods faste ad because of the completo peod ad of the cost of wok. The tegato of the GPS geodes, egstes, topogaph wll make t possble to obta a savg of tme ad pecso ad wll educe cosdeabl wok of goud (ecogto, duato of obsevatos ). 3. DESCRIPTION OF THE PROGRAM "TRANSFOR" WITH ONING D eas the pcpal wdow of pogam TRANSFOR, a thd butto was added, called "3D_oage tasfom", t gves the possblt of selectg total models wth og whle etug us to the butto "models 3dog" whch makes t possble ts tu to make the choce betwee the two total models "Busa Wolf", "Molodesk Badekas", whose souce codes wee mplemeted b outes of og, fall, the model beg selected, oe has the choce betwee seveal as "gog fom 5 to km ad a fee choce of aothe value of the a b usg o the butto "othe values", whch oce clcked, a wdow of dalogue appeas Oû oe ca ete a value to the choce of R, all these ado opeato buttos ae placed o a pael amed "aos_og", ths pat added wth the pogam makes t possble to delmt a teto eteded such as Algea small oes followg of the selected as ad to make the tasfomatos b applg the theedmesoal models (Busa Wolf, Molodesk, etc.). Results wee obtaed o each oe estmatg the esdues ad the pecse detals fo each model ad o delmted oes. 3. Ma Wdow of the Pogam Ths wdow called a of og makes t possble dug the eecuto to make the choce ad to etu a value to the choce of the a fo whch oe caes out calculato. These values va betwee 5 km ad km ou case wth a opto to ete a uspecfed value fo whch the pogam makes the choce of the pots of suppot whch ae a a of a value equal o lowe tha the selected a. The pot thus chose, the pogam takes to accout ts coodates geogaphcal (o Catesa, that depeds o the choce) calculato, thus oe makes the teatmet o a educed oe (cadastal), ad oe thus avods the geat udulatos geod whch especall affect the sstematsm of teatmet fo the total models. A page of teatmet s publshed O û oe posts the fles of selected pots of suppot, the paametes of tasfomato calculated fo og as well as a statstcal aalss gvg the values of the "Rms" o the "Eastg" ad "Nothg" fo the pots of suppot ad the pots of cotol, as well as the ew pots tasfomed b og. PS 5.3 Refeece Fame 6/5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6

7 3D oage Tasfomato Fee choce of Aothe adus Busa Wolf model wth og Pael of dfféets og adus 3. Edto of teatmet Results Fg. Ma wdow of the pogam. Postg of model wth adus value. Edto of esult fle both sstem Fg. Edto of teatmet esults fles. PS 5.3 Refeece Fame 7/5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6

8 Pogam Stuctue. TRANSFOR maages the modules mplemeted the followg achtectual fom: PRESENTATION TRANSFOR HELP (HLP) Fles Fomat Fles opeg () Sotg of the pots of suppot ad cotol Teatmets Results Vsualsato of pots etwok (gaphc) Peselecto D 3D 3D _oage Ellpsod selecto (A &t B) Coodates Natue (geogaphc, catesa, aute) Dmeso (gades, adas, ) Tasfomato tpe D (geat geodtc,.) ou 3D ( Busa Wolf,.) Geat geodetc les Geodetc les (Gde échelle) Multple Regessos Affe Tasfomatos Busa Wolf Molodesk Badekas Busa Wolf _og Molodesk Badekas_og og adus selecto (5, 5, autes) Fgue 3. Stuctue of Pogam wth mplemetato of oage PS 5.3 Refeece Fame 8/5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6

9 4 RESULTS AND ANALSIS. 4. Global Models 4.. Busa Wolf The table heeafte summaes the statstcal esults of the teatmet b the model of Busa Wolf wth og, oe defes hee the RMS elatg to the vaous adus of og used the pogam (5 to km). MODELS RADIUS (KM) COMPONENTS MINIMUM (M) MAIMUM (M) AVERAGE (M) RMS (M) Busa Wolf Aute (5) PS 5.3 Refeece Fame 9/5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6 Table : BURSAWOLF Model Results Aalss : suppot pot Resdues.

10 4.. Molodesk Badekas Ce tableau lluste pou le modèle de Molodesk les ésultats statstques ssues du tatemet pa le pogamme. MODELS RADIUS (KM) COMPONENTS MINIMUM (M) MAIMUM (M) AVERAGE (M) RMS (M) MOLODENSK Aute (5) PS 5.3 Refeece Fame /5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6 Chat.: Busa Wolf model wth out og. 4. Compaatve Aalss betwee the Vaous Ras of og. To set the deas o the evoluto of the values of the RMS accodg to the as of og, oe takes wth the choce a mmal value ad a mamum value wth aothe temedate value ad oe taces fo each adus, a statstcal table cludg/udestadg the mmum, the mamum, aveage ad RMS.

11 4.. Busa Wolf wth out og appled ove Algea teto Model Compoets Mmum Mamum Aveage RMS Busa Wolf Table. : Busa Wolf Model wth out og. The model of Busa Wolf wthout og s teated memo of maste (4), the table of top shows how the RMS ae of ode metc fo thee compoets, ad, because appled to a teto eteded such as Algea wth deteoatos of the etwok as well as a lack of fomato o the geod, these pecse detals ae ot geodetc. 4.. Busa Wolf wth og (case of Algea) Radus equal 5 Km. Model Compoets Mmum Mamum Aveage RMS Busa Wolf Table.3: Busa Wolf Model wth og (5 km). Table, shows well that the use of og (Ra equales 5 km) gves a bette esult; the pecse detals ae cetmetc, theefoe geodetc. Ths etus to the fact that the applcato of a thee model fact BusaWolf o a educed oe, compesates fo the lack of fomato o the geod ad thus gves RMS acceptable. Radus equal 5 Km. Model Compoets Mmum Mamum Aveage RMS Busa Wolf Table.4: Busa Wolf model wth og (5 Km). It s otced that fo a adus og of 5 km, the pecse detals ema alwas cetmetc but of a hghe ode tha that of twet fve klometes. PS 5.3 Refeece Fame /5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6

12 3 Radus equal 5 Km. Model Compoets Mmum Mamum Aveage RMS Busa Wolf Table.5: Busa Wolf wth og (5 Km). Oe ceases the adus of og up to 5 K m, we obtas pecse detals geodetc, hghe has those of the lowe adus (5 ad 5km), whch let us coclude that wth the fu R ad as the a of og ceases, L ae pecse detals ceases NT utl eachg a metc ode, ths case oe s eteme cases of a model wthout og. The table whch follows llustates these emaks. BURSA WOLF MODEL V V V Rms(m) Wthout og og Radus(Km) Fg.4: esdues of the adus of og 4.3 Molodesk Badekas wth out og (case of Algea) Model Compoets Mmum Mamum Aveage RMS Busa Wolf PS 5.3 Refeece Fame /5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6 Table. : Molodesk model wth out og. The model of Busa Wolf wthout og s teated memo of maste (4), the table of top shows how the RMS ae of ode metc fo thee compoets, ad, because

13 appled to a teto eteded such as Algea wth deteoatos of the etwok as well as a lack of fomato o the geod, these pecse detals ae ot geodetc Molodesk Badekas avec oage applqué su l Algée Rao de 5 Km. Model Compoets Mmum Mamum AVERAGE RMS Busa Wolf Tableau.3 : Molodesk model wth og ( 5 Km). Table, shows well that the use of og (Ra equales 5 km) gves a bette esult, the pecse detals ae cetmetc, theefoe geodetc. Ths etus to the fact that the applcato of a thee dmesos model fact BusaWolf o a educed oe compesates fo the lack of fomato o the geod ad thus gves RMS (Quadatc Aveage Eos) acceptable. Rao de 5 Km. Model Compoets Mmum Mamum Aveage RMS Busa Wolf Tableau.4 : Modèle de Molodesk avec oage Rao de 5 Km. It s otced that fo a a of og of 5 km, the pecse detals ema alwas cetmetc but of a hghe ode tha that of twet fve klometes. 3 Radus equal 5 Km. Model Compoets Mmum Mamum Aveage RMS Busa Wolf Tableau.5: Modèle de Molodesk avec oage Rao de 5 Km. PS 5.3 Refeece Fame 3/5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6

14 MOLODENSKBADEKAS MODEL V V V RMS(m) ONING RADIUS(Km) 5 WITHOUT ONING Fg 4 : Resdues of og adus. We cease the a of og up to 5 K m, oe obtas pecse detals geodetc, hghe has those of the lowe as (5 ad 5km), whch let us coclude that as the a of og ceases the ode of the pecse detals ceases utl eachg a metc ode, ths case oe s eteme cases of a model wthout og. The table whch follows llustates these emaks. REFERENCES Bullet Géodésque [985].Volume 59 3 Edteu Iva I.Muelle Octobe 985. AIG Pas Face. Bullet Géodésque [987]. Volume 6 Edteu c.c Tsheg Avl 987. AIG Pas Face. S KAHLOUCHE [986]. Pefomaces de la techque dopple su satelltes pou le postoemet absolu et dfféetel. Thèse de doctoat IGN PARIS986. MD PAQUET [986]. Les sstèmes TRANSIT et GPS : avgato et localsato. Mathématques spatales. CNES Toulouse. CEPADUES Edtos Face. P VANICEK J. KRAKIWSK []. GEODES: THE CONCEPTS. Secod edto NORTHHOLLAND AMSTERDAM NEW ORK OFORD TOKO. A LEICK []. GPS satellte suveg. (Depatmet of suveg egeeg. Uvest of Mae ORONO). A Wle tescece Publcato Joh Wle & so. BUREAU TECHNIQUE DE LA GEODESIE [96]. Le sstème géodésque Nod Sahaa. IGN St Madé Face. H DUPRA [994]. La méthode GPS.Ecole Poltechque Fédéale de LAUSANNE cous de géodése.nouvelle édto octobe 994. J.J.LEVALLOIS [969]. La géodése bdmesoelle (tome ).Edto EROLLES PARIS FRANCE. PS 5.3 Refeece Fame 4/5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6

15 BIOGRAPHICAL NOTES A.EGGAI [996]. Itégato des doées GPS e vellemet. Thèse de magste.cnts AREW. Jullet 996. A.EGGAI [3]. Tasfomatos ete sstèmes de éféeces géodésques. Cous Magste. CNTSAREW. mas 3 S KAHLOUCHE, A. EGGAI, A. AOUA [998] POSITIONNEMENT TEMPS REEL PAR GPS DIFFERENTIEL EN MEDITERRANEE OCCIDENTALE Tametfoust Alges 998 CONTACTS Attached of Reseach Nouedde Khelouf Natoal Space Techcs Cete BP 3, Rue de Paleste Aew ALGERIA Tel Fa OR Emal: ou.kh@caamal.com Web ste: PS 5.3 Refeece Fame 5/5 Nouedde Khelouf Coodates Tasfomato b og Method fo Paametes Computg betwee WGS84 ad Noth Sahaa Shapg the Chage III FIG Cogess Much, Gema, Octobe 83, 6