Geo-spatial Information Science 13(3): Volume 13, Issue 3 DOI /s September Article ID: (2010)

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1 Geo-spatal Informaton Scence 13(3): Volume 13, Issue 3 DOI /s September 2010 Artcle ID: (2010) Document code: A Transformaton Method of Exteror Orentaton Angular Elements Obtaned va Poston and Orentaton System Under Gauss-Kruger Projecton Coordnate System YUAN Xuxao, ZHANG Xuepng, FU Janhong School of Remote Sensng and Informaton Engneerng, Wuhan Unversty, 129 luoyu Road, Wuhan , Chna Wuhan Unversty and Sprnger-Verlag Berln Hedelberg 2010 Abstract Data obtaned va arborne poston and orentaton system (POS) s n WGS 84 global geocentrc reference frame, whle the natonal coordnate reference system for topographc mappng n Chna s generally Gauss-Kruger projecton coordnate system. Therefore, data obtaned va a POS must be transformed to natonal coordnate system. Owng to the effects of earth curvature and merdan devaton, there are some errors n the process of angle transformaton from roll, ptch, and headng ( ΦΘΨ,, ) obtaned drectly va a POS to the atttude angles of mages ( ϕ, ωκ, ) needed n photogrammetry. On the bass of effect theores of earth curvature and merdan devaton on exteror orentaton angular elements of mages, a method usng a compensaton matrx to correct the transformaton errors from atttude angles obtaned va the POS to exteror orentaton angular elements of mages s proposed n ths paper. Moreover, the rgorous formula of the compensaton matrx s deduced. Two sets of actual data obtaned va a POS AV 510, whch are dfferent n scale and terran, are selected and used to perform experments. The emprcal results not only ndcate that the compensaton matrx proposed n ths paper s correct and practcal but also show that transformaton accuracy of exteror orentaton angular elements obtaned va the POS based on compensaton matrx s relevant to the selecton of vertcal axs (a projecton of central merdan) of Gauss-Kruger projecton coordnate system; the proper vertcal axs should be the Gauss-Kruger projecton of the central merdan of projecton zone n whch the survey area locates. However, the transformaton accuracy of exteror orentaton angular elements s rrelevant to the choce of orgn of coordnate system; t s approprate that the orgn of coordnate system locates at the center pont of the survey area. Moreover, transformaton accuracy of exteror orentaton angular elements acheved based on the compensaton matrx deduced n ths paper s hgher than that obtaned va the exstng POS processng software. Keywords poston and orentaton system (POS); exteror orentaton elements of mage; earth curvature; merdan devaton; compensaton matrx CLC number P231.5 Introducton An ntegrated global postonng system and nertal navgaton system (GPS/INS) are used n aeral remote sensng to obtan the poston and atttude of a sensor, that s, the mage orentaton parameters are determned at the tme of exposure. The am s to Receved on March 22, Supported by the Natonal Natural Scence Foundaton of Chna (No , No ). YUAN Xuxao was born n 1963 n Hube, P.R. Chna. He receved the B.En., M.En. and Ph.D. degrees n photogrammetry and remote sensng from Wuhan Techncal Unversty of Surveyng and Mappng n 1985, 1994 and 1999, respectvely. He has been a professor n School of Remote Sensng and Informaton Engneerng at Wuhan Unversty snce December Hs research and teachng actvtes were n the felds of theory and method for hgh precson arborne and spaceborne photogrammetrc postonng and geometrc processng of hgh-resoluton satellte remote sensng magery. He s the author and coauthor of more than 100 publshed papers and 6 books n these felds. E-mal: yxxqxhyw@publc.wh.hb.cn

2 158 Geo-spatal Informaton Scence 13(3): perform drect georeferencng (DG) for aeral photogrammetry wthout aerotrangulaton wth ground control ponts (GCPs), whch wll have an expansve applcaton foreground n the future. [1-4] In order to mplement accurate drect georeferencng, the accuracy of exteror orentaton elements of mages must be hgh enough, especally these angular elements. In the process of transformaton from atttude data obtaned va a poston and orentaton system (POS) to exteror orentaton angular elements of mages, there are two man error sources: boresght msalgnment and transformaton errors between dfferent coordnate systems. [5] For the calbraton of boresght msalgnment, the most popular method s test feld calbraton approach. Frst, t s necessary to set up a calbraton feld and take a set of especal mages usng an aeral camera mounted POS over the calbraton feld. Second, the exteror orentaton angular elements are calculated by usng the tradtonal bundle block adjustment. At last, comparng the exteror orentaton angular elements obtaned va a POS wth that computed by tradtonal aeral trangulaton n the calbraton feld, the boresght msalgnment can be computed drectly. [6-8] Moreover, a novel method of self-elmnatng POS systematc errors n a POS-supported bundle block adjustment wthout the use of a specal calbraton feld s proposed to elmnate error. [9] As s well known, data obtaned va a POS are n WGS 84 global geocentrc reference frame, whle photogrammetrc products are often requred n natonal coordnate system. Therefore, data obtaned va a POS must be transformed to the natonal coordnate system. There are three optons: (1) Transformaton of the fnal products: the resttuton s performed n a sutable Cartesan reference frame frst, and the resultng model of the scene s completely transformed to the natonal coordnate system. (2) Transformaton of artfcal GCPs: Vrtual GCPs are acqured from partal scene frst, and then, an aeral trangulaton s run. Accordng to the estmated parameters, the scene can be resttuted n the natonal coordnate system. (3) Transformaton of the exteror orentaton elements: only the exteror orentaton elements are transformed, and the scene resttuton s carred out drectly n the natonal coordnate system. [10] Wthn three transformaton methods, the thrd one s the most practcal. However, the effects of the earth curvature and map projecton on transformaton have to be taken nto consderaton. [11] Atttude angles obtaned drectly by IMU n a POS are Euler angles of the IMU body coordnate system n the navgaton coordnate system, ncludng roll, ptch, and headng ( ΦΘΨ,, ). Angular elements requred n photogrammetry are rotaton angles from the object coordnate system to the mage space coordnate system, ncludng ph, omega, and kappa ( ϕ, ωκ, ). The transformaton from the object coordnate system to the mage coordnate system can be performed drectly by usng the orthogonal matrx consttuted by ( ϕ, ωκ, ). On the other hand, the transformaton also can be performed ndrectly by usng ( ΦΘΨ,, ) through a seres of transformaton matrces: the object coordnate system the earth centered earth fxed coordnate system the navgaton coordnate system the IMU body coordnate system the camera body coordnate system the mage space coordnate system. [12] Accordng to the equvalent relatonshp between the two transformatons mentoned above, atttude angles obtaned va a POS can be transformed to exteror orentaton angular elements at the tme of exposure wthout aeral trangulaton. If the object coordnate system s a Cartesan rectangular coordnate system, all the coordnate systems are rgorous three-dmensonal spatal rectangular coordnate systems. Transformaton from one coordnate system to another can be performed through an orthogonal rotaton matrx rgorously. However, the coordnate reference systems for topographc mappng n Chna are often Gauss-Kruger projecton coordnate system. The effects of the earth curvature and the merdan devaton on angle transformaton have to be taken nto account, and an addtonal compensaton s requred. [13] The objectve of ths paper s to research a transformaton method of exteror orentaton angular elements obtaned va a POS n Gauss-Kruger projecton coordnate system. The man content s about the error compensaton n the transformaton of angular elements n Gauss-Kruger projecton coordnate system. The effects of the earth curvature and merdan devaton on atttude angles are detaled n Secton 1.

3 YUAN Xuxao, et al./ Transformaton Method of Exteror Orentaton 159 At the base of these analyses, a rgorous compensaton matrx s deduced. Afterward, the transformaton equatons of atttude angles obtaned va a POS under Gauss-Kruger projecton coordnate system are consummated n Secton 2. At last, two sets of actual mages wth POS data are selected and used to demonstrate the valdty and practcablty of compensaton model deduced n ths paper. The emprcal results are analyzed and dscussed n Secton 3. 1 Effect factors on angle transformaton under Gauss-Kruger projecton coordnate system 1.1 Effects of the curvature of the Earth on angle transformaton Generally, the planar coordnate system s under Gauss-Kruger projecton, and the elevaton system s based on the Yellow Sea elevaton system n coordnate reference system for topographc mappng n Chna. Horzontal and vertcal coordnate systems cannot compose a rgorous three-dmensonal Cartesan rectangular coordnate system. When survey area s larger or accuracy demand s hgher, the effects of the earth curvature must be properly consdered. [14] The ellpsod can be replaced by a polyhedron of tangental planes, wth each plane set up at the nadr pont of the projecton center. Ths together wth the heght related to the respectve tangental plane for each mage create a small ndvdual Cartesan rectangular coordnate system. The correcton needed for ths replacement can remove the effect of ellpsodal curvature. [15] In the process of angle transformaton from atttude angles ( ΦΘΨ,, ) obtaned va a POS to exteror orentaton angular elements ( ϕ, ωκ, ) needed n photogrammetry, the orgn of the object coordnate system s often selected at one pont (B 0, L 0 ) n the survey area. Therefore, usng the rgorous transformaton between Cartesan rectangular coordnate systems, the tangental plane coordnate system at each projecton center can be transformed to parallel wth the tangental plane coordnate system at orgn of coordnate system. In ths way, the effects of earth curvature on angles can be removed. The transformaton between two ponts on ellpsodal surface can be performed through the contnuous rotatons n the merdan and prme vertcal (see Fg.1). Accordng to the locaton relatonshp of ponts on ellpsodal surface, from P 2 (B, L) to P 1 (0, 0), the tangental plane coordnate system s n the followng rotaton order: the frst rotaton: B around X m axs; the second rotaton: L around Y m axs (after the frst rotaton). The combnaton of the rotatons results n the followng transformaton matrx: R R R (0,0) (0, L) (0,0) ( B, L) ( B, L) (0, L) cosl 0 snl 0 cosb snb sn B cos B sn L 0 cos L cos L 0 sn L sn Bsn L cos B sn Bcos L cos Bsn L sn B cos Bcos L Fg.1 Relatonshp of ponts on ellpsodal surface (1) Accordng to the above transformaton matrx, the transformaton from orgn of the object coordnate system (B 0, L 0 ) to projecton center (B, L) can be performed ndrectly by usng the mddle poston (0, 0). The transformaton matrx s as follows: ( BL, ) (0,0) ( BL, ) (0,0) (0,0) T R( B0, L0) R( B0, L0) R(0,0) R( B0, L0) R ( B, L) cos L0 0 sn L0 sn B0sn L0 cos B0 sn B0cos L 0 cos B0sn L0 sn B0 cos B0cos L 0 cos L sn Bsn L cos Bsn L 0 cosb snb (2) sn L sn Bcos L cos Bcos L In order to express Eq.(2) convenently, the followng substtutons are made Δ B B0 B, Δ L L0 L. Take the projecton zone of 3 for example, the maxmum of ΔL s 1.5 n the same projecton zone. In the process of computaton, ΔL should be unted nto radan, and then, ΔL can be regarded as a small angle. If the lattudnal range of survey area s not too

4 160 Geo-spatal Informaton Scence 13(3): broad, ΔB can also be regarded as a small angle. Therefore, takng the small angle approxmaton cos Δ B 1, cosδ L 1,sn Δ B ΔB,snΔ LΔ L, and neglectng the quadratc terms of ΔB, ΔL n the expanson, the followng lnear form of Eq.(2) can be obtaned: 1 ΔLsnB ΔLcosB ( BL, ) R ( B0, L0) ΔL sn B 1 B Δ ΔL cos B ΔB 1 1 ( L0 L) sn B ( L0 L) cosb ( L0 L) snb 1 ( B B0) ( L0 L) cos B ( B B0) 1 (3) 1.2 Effects of the merdan devaton on angle transformaton In Gauss-Kruger projecton coordnate system, the central merdan of projecton zone and the Equator are projected nto perpendcular beelnes, and they are regarded as y axs and x axs of the coordnate system, respectvely. At the same tme, all the other merdans n ths projecton zone become curves after projecton, whch dstrbute at x axs symmetrcally and are concave to y axs. There wll be angles between the central merdan and merdans of the projectve ponts after projecton, and they are merdan convergence of the projectve ponts. In Fg.2, p s the projecton of pont p on ellpsodal surface; pn s projecton of merdan at pont p; pn s the tangent of pn at pont p ; and pt s the parallel of y axs. The angle between pn and pt s the merdan convergence of pont p, whch s expressed by γ. [16] where t tan B, η e cos B; e s the second eccentrcty; B s the lattude of projectve pont; and l s the longtude dfference between projectve pont and central merdan. In Gauss-Kruger projecton coordnate system, the scale factors of the horzontal and vertcal drectons at projectve pont are dfferent because of the mappng length dstorton. Moreover, the merdan devaton s affectng the orentaton n respect to geographc orentaton. [13] Gauss-Kruger projecton s an orthomorphc projecton, so there s no angle dstorton n plane before and after projecton. Nevertheless, there s a dstorton of γ n vertcal drecton due to the merdan devaton. [10] Therefore, n order to correct the effects of merdan devaton on angles, the coordnate system has to be rotated γ around Z m axs. The transformaton matrx s as follows: cosγ snγ 0 R γ snγ cosγ 0 (5) In common topographc survey, merdan convergence can be computed approxmately as follows: γ l sn B (6) Merdan convergence γ s a small angle. Takng the small angle approxmaton cosγ 1,sn γ γ, Eq.5 can be replaced by 1 γ 0 1 lsnb 0 R γ γ 1 0 lsnb ( L0 gk L)snB 0 ( L0 gk L)snB 1 0 (7) where L 0gk s the central merdan longtude of projecton zone; L s longtude of projecton pont. 1.3 Compensaton matrx of angle transformaton Fg.2 Merdan convergence The common computatonal formula of merdan convergence s as follows: [16] γ sn Bl + sn Bcos B(1 + 3η + 2 η ) l 3 1 sn cos 4 (2 2 ) 5 ( 5 + B B t l + O l ) (4) 15 Accordng to the analyses n Sectons 1.1 and 1.2, the earth curvature and the merdan devaton can affect the angle transformaton n Gauss-Kruger projecton coordnate system. The earth curvature affects azmuth angle, whle the merdan devaton affects zenth angle. Therefore, syntheszng these two effect factors, the correcton of angle transformaton obtaned va a POS can be performed through Eqs.(2)

5 YUAN Xuxao, et al./ Transformaton Method of Exteror Orentaton 161 and (7). The compensaton matrx of angle transformaton n Gauss-Kruger projecton coordnate system can be expressed as follows: m ( B, L) R R R m ( B, L ) γ cos L0 0 sn L0 sn B0sn L0 cos B0 sn B0cos L 0 cos B0sn L0 sn B0 cos B0cos L 0 cos L sn Bsn L cos Bsn L 0 cosb snb sn L sn Bcos L cos Bcos L 1 ( L 0gk L) snb 0 ( L 0gk L) sn B 1 0 (8) If the range of survey area s not too large, Eq.(8) can be smplfed accordng to the dsposal prncple of Eq.(2). The result of Eq.(8) s m R m 0 1 ( L0 L0gk )sn B ( L0 L)cosB ( L0 L0gk )snb 1 ( B B0) ( L0 L)cos B ( B B0) 1 (9) 2 Transformaton of angles obtaned va a POS under Gauss-Kruger projecton coordnate system The transformaton from atttude angles ( ΦΘΨ,, ) obtaned drectly va a POS to exteror orentaton angular elements ( ϕ, ωκ, ) requred n photogrammetry can be performed ndrectly through a seres of transformaton: the object coordnate system (m) the earth centered earth fxed coordnate system (E) the navgaton coordnate system (n) the IMU body coordnate system (b) the camera body coordnate system (c) the mage space coordnate system (). [12] The transformaton s as follows: R m ( ϕωκ,, ) R m R E R n ( ΨΘΦ,, ) R b R c (10) E n b c j where R s the orthogonal transformaton matrx from coordnate system to coordnate system j. If the object coordnate system s a Cartesan rectangular coordnate system, Eq.(10) wll be accurate rgorously. However, coordnate system for topographc mappng n Chna s under Gauss-Kruger projecton coordnate system. For the above transformaton, the effects of the earth curvature and the merdan devaton on angle transformaton must be consdered. Accordng to the analyses n Secton 1, Eq.(10) should be extended to the followng one: 0 0 R m ( ϕωκ,, ) R m R m R E R n ( ΨΘΦ,, ) R b R c (11) m E n b c m0 m where Rm s the transpose of matrx R. m The other 0 parameters are the same as that n Eq.(10), the detaled models are shown n Reference [12]. a1 a2 a3 m0 Settng R ( ωϕκ,, ) b1 b2 b 3 and adoptng c1 c2 c 3 angular elements system of ϕ ω κ, the exteror orentaton angular elements of each mage requred n photogrammetry can be gven as follows, accordng to matrx R (,, ) m0 ω ϕ κ n Eq.(11): a3 ϕ arctg( ) c 3 ω arcsn( b3 ) (12) b 1 κ arctg( ) b2 3 Experments and results analyss 3.1 Emprcal test desgn In ths work, two sets of actual mages taken from expermental projects that are dfferent n terran and photographc scale are selected and used for experment. They were taken n November of 2004 and October of 2005, respectvely. The man techncal parameters of the emprcal mages are lsted n Table 1. Table 1 Techncal data of the expermental mages Test 1 Test 2 Aeral camera Leca RC-30 Leca RC-30 POS system POS AV 510 POS AV 510 Flm Kodak 2442 Kodak 2402 Focal length mm mm Frame 23 cm 23 cm 23 cm 23 cm Photographc scale 1:2500 1:60000 Longtudnal overlap 61% 64% Lateral overlap 32% 30% Number of strps 9 4 Number of photos Number of ground control ponts Maxmum terran undulaton m m

6 162 Geo-spatal Informaton Scence 13(3): Transformaton of exteror orentaton angular elements obtaned va a POS n WGS 84 Gauss-Kruger projecton coordnate system Atttude angles obtaned drectly va a POS are Euler angles from the IMU body coordnate system to the navgaton coordnate system, whch nclude roll, ptch, and headng ( ΦΘΨ,, ). Accordng to Eq.(10), exteror orentaton angular elements wthout earth curvature and merdan devaton compensaton can be obtaned after a seres of coordnate system transformaton. These exteror orentaton angular elements are n the coordnate system composed by WGS 84 ellpsod after Gauss-Kruger projecton (referred to as WGS 84 Gauss-Kruger projecton coordnate system smply n ths paper). Usng WuCAPS system, [9] exteror orentaton angular elements n WGS 84 Gauss-Kruger projecton coordnate system can be computed by GPS-supported bundle block adjustment usng four full GCPs n the four corners of the adjusted block. Comparng exteror orentaton angular elements wthout compensaton wth the ones computed by WuCAPS system, the accuraces of exteror orentaton angular elements wthout compensaton are obtaned (referred to as Uncompensated n Table 2). After that, errors of exteror orentaton angular elements caused by the earth curvature and the merdan devaton can be corrected by Eq.(8). Accordng to Eqs.(11) and (12), exteror orentaton angular elements n WGS 84 Gauss-Kruger projecton coordnate system after compensaton can be computed. Comparng exteror orentaton angular elements computed by ourselves wth the ones computed by WuCAPS system, the accuraces of exteror orentaton angular elements after compensaton are obtaned (referred to as Compensated n Table 2). On the other hand, comparng the exteror orentaton elements computed by the POS wth the ones computed by WuCAPS system, the accuraces of exteror orentaton angular elements obtaned va the POS are obtaned (referred to as POS n Table 2). All the results are lsted n Table 2. Table 2 Accuracy of exteror orentaton angular elements n WGS 84 Gauss-Kruger projecton coordnate system (arcsecond) Uncompensated Compensated POS Project φ ω κ φ ω κ φ ω κ Test Test Note: RMS n Table 2 s calculated from the error Δ ( ϕ, ωκ, ) between exteror orentaton angular elements of n mages computed by dfferent methods, that s, μ Δ 2 / (same to the followng Tables). n Fg.3 Accuracy of exteror orentaton angular elements n WGS 84 Gauss-Kruger projecton coordnate system (compared to WuCAPS) The followng conclusons can be drawn from that n Table 2 and Fg. 3: 1) Transformaton accuracy of exteror orentaton angular elements uncompensated n WGS 84 Gauss-Kruger projecton coordnate system s lower, contanng obvous errors; but after the compensaton matrx s used, transformaton accuracy of exteror orentaton angular elements mproves evdently. These results ndcate that the effects of earth curvature and merdan devaton on angle transformaton have to be taken nto account under Gauss-Kruger projecton coordnate system, and t s necessary to adopt compensaton matrx n the process of exteror orentaton angular elements transformaton obtaned va a POS. 2) In WGS 84 Gauss-Kruger projecton coordnate system, the accuracy of exteror orentaton angular elements compensated s equal to that computed by

7 YUAN Xuxao, et al./ Transformaton Method of Exteror Orentaton 163 the POS, whch means that the compensaton matrx proposed n ths paper s vald and feasble. 3) In WGS 84 Gauss-Kruger projecton coordnate system, the accuracy of exteror orentaton angular elements compensated cannot catch up wth that computed by aeral trangulaton. The dfferences between them change along wth the dfferent strps, but there s no obvous systematc error. The reason s that the whole survey area adopts one same compensaton matrx, whch cannot well reflect the change rule of errors n each strp. 3.3 Transformaton of exteror orentaton angular elements wth dfferent vertcal axs n WGS 84 Gauss-Kruger projecton coordnate system In order to analyze the relatonshp between the transformaton of exteror orentaton angular elements and vertcal axs of the coordnate system, two neghborng projecton zones are selected on ether sde near the projecton zones of the survey area (takng projecton zone of 3 for an example). Central merdans of these fve projecton zones are used as the vertcal axs of the Gauss-Kruger projecton coordnate system, and basng on that, exteror orentaton angular elements are transformed n WGS 84 coordnate system wth dfferent vertcal axs, respectvely. Comparng the transformaton results wth the exteror orentaton angular elements computed by WuCAPS, the accuraces of exteror orentaton angular elements wth dfferent central merdans can be computed. The results are lsted n Table 3. It can be seen n Table 3 that transformaton accuracy of exteror orentaton angular elements s relevant to the choce of central merdan; the larger the dstance between test area and central merdan s, the lower the transformaton accuracy of exteror orentaton angular elements wll be. The reason s that the merdan convergence s defned n each projecton zone; and t s the angle between the merdan of projecton pont and the central merdan of projecton zone the projecton pont locates after projecton. Therefore, when the survey area spans more than one projecton zone, the transformaton of exteror orentaton angular elements should choose the central merdan of the area as the vertcal axs of the coordnate system n each projecton zone. 3.4 Transformaton of exteror orentaton angular elements wth dfferent orgn of coordnate system n WGS 84 Gauss-Kruger projecton coordnate system In order to analyze the effect of the orgn of coordnate system on the transformaton of exteror orentaton angular elements, two ponts are selected on ether sde near the central pont of survey area; the space s 1 n lattudnal drecton. These fve ponts are used as the orgn of the Gauss-Kruger projecton coordnate system. Then, exteror orentaton angular elements are transformed wth dfferent orgn, respectvely. Comparng the transformaton results wth the exteror orentaton angular elements computed by WuCAPS, the accuraces of exteror orentaton angular elements wth dfferent orgns of coordnate system can be computed. The results are lsted n Table 4. Table 3 Accuracy of exteror orentaton angular elements wth dfferent central merdan (arcsecond) y-axs Central merdan Central merdan 3 Central merdan +3 Central merdan 6 Central merdan +6 φ ω κ φ ω κ φ ω κ φ ω κ φ ω κ Test Test Table 4 Orgn of coordnate system Accuracy of exteror orentaton angular elements wth dfferent orgn of coordnate system (arcsecond) Center pont of survey area Center pont of survey area 1 Center pont of survey area +1 Center pont of survey area 2 Center pont of survey area +2 φ ω κ φ ω κ φ ω κ φ ω κ φ ω κ Test Test

8 164 Geo-spatal Informaton Scence 13(3): It can be seen n Table 4 that the choce of orgn of coordnate system has no effect on the transformaton of exteror orentaton angular elements. The reason s that orgn of coordnate system s chosen to transform all the tangental plane coordnate system at each projecton center to a unform tangental plane coordnate system; t s rrelevant to the locaton of the orgn of coordnate system. Generally speakng, t s approprate that the orgn of coordnate system locates at the center pont of the survey area. 3.5 Transformaton of exteror orentaton angular elements n natonal coordnate system Usng three parameters on angles n seven transformaton parameters, the atttude angles of IMU body system n navgaton coordnate system based on WGS 84 reference ellpse can be transformed to the reference ellpse that the natonal coordnate system wll adopt. Accordng to the Eqs.(11) and (12), after a seres of coordnate transformaton and angle compensaton, the exteror orentaton angular elements n the natonal coordnate system can be computed fnally. Comparng the transformaton results of exteror orentaton angular elements wth the exteror orentaton angular elements n the natonal coordnate system computed by WuCAPS, the transformaton accuracy of exteror orentaton angular elements n the natonal coordnate system can be obtaned (referred to as Proposed by ths paper n Table 5). On the other hand, comparng the exteror orentaton elements obtaned by the POS wth that computed by WuCAPS system, the accuraces of exteror orentaton angular elements obtaned by POS are obtaned (referred to as Proposed by POS n Table 5). All the accuracy data are shown n Table 5. Table 5 Accuracy of exteror orentaton angular elements n natonal coordnate system ( ) Transformaton Proposed by ths paper Proposed by POS method φ ω κ φ ω κ Test Test It can be seen n Table 5 that compared wth the exteror orentaton angular elements computed by GPS-supported bundle block adjustment n WuCAPS, the total accuracy of exteror orentaton angular elements computed based on the compensaton matrx deduced n ths paper s hgher than that obtaned va the POS. 4 Concluson Coordnate reference systems for topographc mappng n Chna are often Gauss-Kruger projecton coordnate system. The effects of the earth curvature and merdan devaton on angle transformaton have to be taken nto account n the process of computng exteror orentaton angular elements by a POS. On the bass of effect theores of earth curvature and merdan devaton on exteror orentaton angular elements, the method usng a compensaton matrx to correct the transformaton errors from atttude angles obtaned va a POS to exteror orentaton angular elements of mages s proposed n ths paper. Moreover, the rgorous equaton of the compensaton matrx s deduced. Two sets of actual data obtaned va a POS AV 510 that are dfferent n scale and terran are selected and used to perform experments. The emprcal results not only ndcate that the compensaton matrx proposed n ths paper s correct and practcal but also show that transformaton accuracy of exteror orentaton angular elements obtaned va a POS based on compensaton matrx s closely related wth the choce of vertcal axs of coordnate system; proper vertcal axs should be the Gauss-Kruger projecton of the central merdan of projecton zone n whch survey area locates. However, the accuracy of exteror orentaton angular elements s rrelevant to the choce of orgn of coordnate system. It s approprate that the orgn of coordnate system locates at the center pont of the survey area. Moreover, the transformaton accuracy of exteror orentaton angular elements computed based on the compensaton matrx deduced n ths paper s hgher than that obtaned va the POS. Because of the lmtatons n experments, transformaton method of exteror orentaton angular elements obtaned va a POS stll requres further researches and experments. Acknowledgement The emprcal data acquston was supported by

9 YUAN Xuxao, et al./ Transformaton Method of Exteror Orentaton 165 the Insttute of Remote Sensng Applcatons n Chnese Academy of Scences, Zhongfe General Avaton Company, Laonng Jngwe Surveyng & Mappng Technology INC, Swe Avaton Remote Sensng Co. Ltd., and others. Ths support s gratefully acknowledged. References [1] L Xueyou (2005) Prncple, method and practce of IMU/DGPS-based photogrammetry [D]. Zhengzhou: Informaton Engneerng Unversty ( n Chnese) [2] Mostafa M, Hutton J (2001) Arborne remote sensng wthout ground control [C]. Proceedngs of IGARSS 01, Sydney [3] Müller R, Lehner M, Müller R, et al. (2002) A program for drect georeferencng of arborne and spaceborne lne scanner mages [J]. Internatonal Archves of Photogrammetry and Remote Sensng, 34(A1): [4] Cramer M, Stallmann D, Haala N (2000) Drect georeferencng usng GPS/Inertal exteror orentatons for photogrammetrc applcatons [J]. Internatonal Archves of Photogrammetry and Remote Sensng, 33(B3): [5] Yastkl N, Jacobsen K (2005) Influence of system calbraton on drect sensor orentaton [J]. Photogrammetrc Engneerng and Remote Sensng, 71(5): [6] Jacobsen K, Wegmann H (2002) Dependences and problems of drect sensor orentaton [C]. Proceedngs of OEEPE Workshop on Integrated Sensor Orentaton, Hanover [7] Cramer M, Stallman D (2002) System calbraton for drect georeferencng [J]. Internatonal Archves of Photogrammetry and Remote Sensng, 34(A3):79-84 [8] Jacobsen K (2002) Calbraton aspects n drect georeferencng of frame magery [J]. Internatonal Archves of Photogrammetry and Remote Sensng, 34(A1): [9] Yuan Xuxao (2008) A novel method of systematc error compensaton for a poston and orentaton system [J]. Progress n Natural Scence, 18(8): [10] Legat K (2006) Approxmate drect georeferencng n natonal coordnates [J]. ISPRS Journal of Photogrammetry and Remote Sensng, 60(4): [11] Skaloud J, Legat K (2008) Theory and realty of drect georeferencng n natonal coordnates [J]. ISPRS Journal of Photogrammetry and Remote Sensng, 63(2): [12] Lu Jun, Zhang Yongsheng, Wang Dondhong, et al. (2004) Computng method of exteror Orentaton elements of POSAV510-DG system [J]. Geomatcs Technology and Equpment, 6(4): 43-47(n Chnese) [13] Bäumker M, Hemes F J (2002) New calbraton and computng method for drect georeferencng of mage and scanner data usng the poston and angular data of an hybrd nertal navgaton system. [C]. Proceedngs of OEEPE Workshop on Integrated Sensor Orentaton, Hanover [14] Gray I D (1997) Effects of the earth's curvature on radar trackng system [J]. Radar System, 449: [15] Ressl C (2002) The mpact of conformal map projectons on drect georeferencng [J]. Internatonal Archves of Photogrammetry and Remote Sensng, 34(3A): [16] Kong Xangyuan, Me Shy (1996) Controllng surveyng [M]. Wuhan: Wuhan Unversty Press (n Chnese)