A Rigorous Model for Spaceborne Linear Array Sensors

Transcription

1 A Rgorous Model for Spaceborne Lnear Array Sensors Danela Pol Abstract A rgorous sensor model for the georeferencng of magery from CCD lnear array sensors wth along-track stereo vewng s presented. The model s based on the classcal collnearty equatons, whch are extended for the specfc characterstcs of the acquston of CCD lnear scanners. It ncludes the sensor poston and atttude modelng wth second-order pecewse polynomals dependng on the acquston tme and a self-calbraton for the correcton of radal and decenterng lens dstortons, prncpal pont(s) dsplacement, focal length(s) varaton and CCD lne(s) rotaton n the focal plane. Usng well-dstrbuted GCPs and, addtonally, Te Ponts (TPs), the external orentaton and self-calbraton parameters, together wth the TPs ground coordnates, are estmated n a least-square adjustment. In order to demonstrate the flexblty of the model, stereo mages from pushbroom sensors wth dfferent characterstcs have been orented wth sub-pxel accuracy n the checkponts. The results are presented and dscussed. Introducton Lnear array sensors for Earth observatons are wdely used for the acquston of magery n pushbroom mode from spaceborne and on arborne platforms. They offer panchromatc and multspectral mages wth spatal resoluton rangng from few centmeters (arborne sensors) up to thousands of meters (spaceborne sensors). Images provded by these sensors have very hgh potental for photogrammetrc mappng at dfferent scales and for remote sensng applcatons. For example, they can be used for the generaton of Dgtal Elevaton Models (DEM), that represent an mportant bass for the creaton of Geographc Informaton Systems, and the producton of 3D texture models for vsualzaton and anmaton purposes (Grün et al., 2004). In the classcal photogrammetrc chan that starts wth the radometrc preprocessng of the raw mages and goes to the generaton of products lke the DEMs, the orentaton of the mages s a fundamental step, and ts accuracy s a crucal ssue durng the evaluaton of the entre system. For pushbroom sensors, the trangulaton and photogrammetrc pont determnaton are rather dfferent compared to standard approaches, whch are usually appled for full frame magery, and requre specal nvestgaton of the sensor geometry and the acquston mode. Moreover, pushbroom scanners n use show dfferent geometrc characterstcs (optcal systems, number of CCD lnes, scannng mode, and stereoscopy), and for each data set, specfc nformaton s avalable (ephemers, GPS/INS observatons, calbraton, and other nternal parameters). For the georeferencng of magery acqured by pushbroom sensors, geometrc models wth dfferent complexty, CyberCty AG, Inder Luberzen 3, CH 8902, Urdorf, Swtzerland (dpol@cybercty.tv). rgor, and accuracy have been developed as descrbed for example n Frtsch and Stallmann (2000), Hattor et al. (2000), Dowman and Mchals (2003), and Toutn, (2004b). In most cases, rgorous models such as Ratonal Polynomal Models (RPM), Drect Lnear Transformatons (DLT), and affne projectons are used. In ths paper we wll focus on rgorous models. These models try to descrbe the physcal propertes of the mage acquston. Whle n frame photogrammetry each mage s geometrcally descrbed by a central perspectve, mages acqured by pushbroom sensors are the result of a perspectve projecton n each lne and parallel projecton between lnes. Usng rgorous models, the collnearty equatons have to be extended n order to nclude the external (and eventually nternal) orentaton modelng. The dfferences between the proposed rgorous models exst n the nternal and external orentaton modelng and ther flexblty; some rgorous models are desgned for specfc sensors, whle others are more general and can be used for dfferent sensors. Few models are desgned for both spaceborne and arborne lnear scanners. As an example, n the software SPOTCHECK (Kratky, 1989), the satellte poston s derved from known nomnal orbt relatons, whle the atttude varatons are modeled by a smple polynomal functon (lnear or quadratc). For selfcalbraton, two addtonal parameters are added: the focal and the prncple pont correcton. Ths model has been used for the orentaton of SPOT (Baltsavas and Stallmann, 1992), MOMS-02/D2 (Baltsavas and Stallamann, 1996), and MOMS-2P (Pol et al., 2000). An advantage of ths software s that t can easly ntegrate new pushbroom nstruments, f the correspondng orbt and sensor parameters are known. The model was also nvestgated and extended n (Frtsch and Stallmann, 2000). At the Char of Photogrammetry and Remote Sensng at the Techncal Unversty of Munch, the exstng block adjustment program CLIC has been extended for the photogrammetrc pont determnaton of arborne and spaceborne three-lne scanners (Ebner et al., 1992). For the external orentaton, a polynomal approach wth orbtal constrants n case of spaceborne magery s utlzed. In the arborne case the exteror orentaton parameters are estmated only for so-called orentaton ponts at certan tme ntervals and n between, the parameters of each thrd mage-lne are expressed as polynomal functons (e.g., Lagrange polynomals) of the parameters at the neghborng orentaton ponts. If dfferental GPS and INS measurements are mported, systematc errors of the poston and atttude observatons are modeled through addtonal strp- or blocknvarant parameters for each exteror orentaton functon. Photogrammetrc Engneerng & Remote Sensng Vol. 73, No. 2, February 2007, pp /07/ /$3.00/ Amercan Socety for Photogrammetry and Remote Sensng PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING February

2 The model was tested on MOMS-02/D2 and 2P (Ebner et al., 1992), MEOSS (Ohlhof, 1995), HRSC and WAOSS (Ohlhof and Kornus, 1994) sensors. The same model has been adopted at DLR for the geometrc n-flght calbraton and orentaton of MOMS-2P magery (Kornus et al., 1999). The Unversty College London (UCL) suggested a dynamc orbtal parameter model (Gugan and Dowman, 1988). The satellte movement along the path s descrbed by two-orbtal whch are modeled wth lnear angular changes wth tme. The atttude varatons are descrbed by drft rates. Ths model was successfully appled for SPOT level 1A and 1B, MOMS-02 and IRS-1C (Valadan et al., 1999) magery. In (Dowman and Mchals, 2003), ths approach was nvestgated and extended for the development of a general sensor model for along-track pushbroom sensors. The results obtaned wth SPOT-5/HRS are reported n (Mchals and Dowman, 2004). The IPI Insttute n Hannover has developed the program BLASPO for the adjustment of satellte lne scanner mages (Konecny et al., 1987). Only the general nformaton about the satellte orbt together wth the vew drectons n-track and across-track are requred. Sx exteror orentaton parameters represent the unform moton, and eght addtonal parameters descrbe the dfference between the approxmate unform movement and the realty. Systematc effects caused by low frequency motons are handled by self calbraton wth addtonal parameters Ths program seems very flexble, because t has been used for the orentaton of dfferent pushbroom sensors carred on satellte, lke MOMS-02 (Büyüksalh and Jacobsen, 2000), SPOT and IRS-1C (Jacobsen et al., 1999), Ikonos and QuckBrd (Jacobsen and Passn, 2003), SPOT5-5/HRS (Jacobsen, 2004) and on arborne sensors, such as DPA (Jacobsen and Passn, 2003). Another flexble and rgorous model for pushbroom sensors has been developed by Toutn (Toutn, 2004a) and embedded n PCI Geomatca. The model takes nto account the dstortons relatve to the platforms, to the sensor, to the Earth, and the cartographc projecton. In other models, such as n Westn (1990), the orbtal model used s smpler than n the prevous models. A crcular orbt nstead of ellptcal orbt s used. Usng SPOT data, seven unknown parameters need to be computed for each mage. At the Insttute of Geodesy and Photogrammetry, ETH Zurch, a rgorous model has been developed for the georeferencng of pushbroom sensors carred on spaceborne and arborne platforms. The man requrement was to be as flexble as possble and adaptable to a wde class of lnear array sensors, but stll beng based on rgorous photogrammetrc formulatons. The man characterstcs of the model and the approach used are presented. For testng, the model has been appled on sensors wth dfferent characterstcs (mult-lne and sngle-lne sensors at dfferent ground resoluton wth synchronous and asynchronous acquston modes) carred on satelltes and arborne platforms. The results acheved wth the three lne sensor StarImager by Starlabo, Tokyo have been already reported n (Pol, 2002). In ths paper, we wll concentrate on satellte applcatons and present the results acheved wth MOMS-2P, SPOT-5/HRS, and the ASTER-VNIR sensors. Sensor Model Each mage acqured by CCD lnear array sensors conssts of lnes ndependently acqured at dfferent tmes and wth a dfferent sensor external orentaton (poston and atttude). Today, geopostonng systems provde the drect measurement of the sensor poston and atttude at specfc nstants of tme, then, accurate nterpolaton technques allow the calculaton of the correspondng data at any tme and for each mage lne. Furthermore, the satellte trajectores can be predcted or smulated by usng the physcal propertes of the satellte orbts. Ths nformaton, together wth sutable nterpolatng technques, may be used to calculate the sensor poston and atttude for the partcular nstants of acquston and apply a drect georeferencng. Otherwse, an ndrect georeferencng approach based on a bundle adjustment s requred. Our sensor model ncludes both approaches. Accordng to the avalablty of nformaton on the sensor nternal and external orentaton, the drect or the ndrect georeferencng methods are used. The methods are descrbed n the followng paragraphs. Drect Georeferencng The prncple of drect georeferencng s to estmate the ground coordnates of the homologous ponts measured n the mages through a forward ntersecton usng as nternal orentaton, the results of laboratory calbratons; and as external orentaton, the data provded by the geopostonng systems carred on the platform, or the trajectory, calculated by mathematcal formulas (only for satellte-based sensors). Ths approach does not requre any ground control ponts, except for fnal checkng, and does not estmate any addtonal parameters modelng the nteror and exteror orentaton. For ths reason, the effectveness and relablty of ths method depend on the accuracy of the nternal and external orentaton data. In the case of arborne pushbroom sensors the use of GPS and INS systems s essental for the georeferencng of the magery. In fact, wth these sensors, a bundle adjustment s unrealstc, because the number of unknown external orentaton parameters (sx for each mage lne) would be too large. Moreover, the arcraft trajectory cannot be predcted and modeled, as n the satellte case. Therefore, the drect measurement of the sensor poston and atttude s ndspensable. For the magery acqured by pushbroom sensors carred on a satellte, the sensor external orentaton can be computed from the physcal propertes of the orbts, through the Kepleran elements, or from the state vectors contaned n the ephemers. The poston and orentaton of a satellte along ts orbt n the ECI system can be calculated usng the Kepleran parameters. The assumpton s that the satellte s subjected to the gravtatonal force only and no perturbatons occur. Dependng on the mage metadata format, the state vectors can be avalable. In general, a state vector s a set of poston, velocty and atttude values for a partcular tme. The number of state vectors, the tme nterval between the observatons and the reference systems used are varyng from a space agency to the other. The poston, velocty and atttude are usually measured wth nstruments carred on board. Star trackers, for example, take an mage of a regon of the sky usng a CCD-lke optcal camera, and compare successve mages to determne how much the orentaton of the satellte has drfted. Ths nformaton s used by the spacecraft pontng system to determne the actual pontng drecton of the satellte at any nstant. In other satelltes, ths nformaton s sent to an atttude control system whch then corrects for the drft by usng on-board thrusters or other moton-generatng devces to mantan the correct satellte pontng (Image, 2005). The poston and velocty vectors n the satellte ephemers are used to calculate the external orentaton of the camera wth respect to the Earth Centered Inertal (ECI) the Earth Centered Fxed (ECR) coordnate systems. The dfference between the two frames s that ECI s an nertal system, therefore, t does not rotate wth respect to the Earth and s fxed wth respect to the celestal frame. 188 February 2007 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

3 On the other hand, the ECR s fxed wth respect to the Earth frame and s synchronzed wth the Earth s rotaton. In both systems the X- and Y- axes lay on the Equatoral plane and Z s drected along the Earth rotaton axs, but n case of ECI system X s drected toward the vernal equnox (fxed n the celestal frame), whle n case of ECR system X s drected toward the Greenwch merdan (sold for the Earth s rotaton). The transformaton between ECI and ECR frames s a rotaton around the Z-axs dependng on tme; the angle s computed through physcal well-known formulas (Sedelmann et al., 1992). The tme of acquston of each lne s calculated wth a lnear nterpolaton usng the tme of acquston of a lne of reference and the ntegraton tme, that s, the tme requred by the optcal system to scan one lne on the ground. For the nterpolaton of the poston and atttude, cubc splnes are used. If avalable, the nternal orentaton s the result of a pre-flght or an n-flght calbraton. The parameter defnton vares wth the space agency. For example, n case of SPOT-5/HRG and SPOT-5/HRS the vewng drectons of each pxels s gven; for ASTER also the same nformaton s gven but only for a lmted number of so-called lattce ponts. In case of arborne sensors, such as the ADS40 or StarImager, the poston of each pxel n the focal plane s gven. Usng the sensor external orentaton estmated for each lne and any nternal orentaton parameters avalable from laboratory calbraton, the mage coordnates of homologous ponts are transformed n the object system through a forward ntersecton (drect georeferencng). Lke n frame photogrammetry, the ponts are measured n the mage and transformed from mage to camera system, through an affne transformaton and from camera to object system, based on the collnearty equatons. Then, the object coordnates are estmated wth forward ntersecton n two steps. In the frst one, the approxmaton of the ground coordnates are calculated by ntersectng the two most external mages, because the base over heght rato s larger, and the stereoscopy s more favorable. Once the approxmate ground coordnates are known, they are refned wth a least squares soluton n the second step, usng all the avalable lnes. The relatonshp between camera and ground (or object) coordnates s descrbed by the collnearty equatons: X Y Z XC Y C x0 C, Z C mr(v C,k ) x C y y 0 f where [X, Y, Z] are the pont coordnates n the ground system, [X C, Y C, Z C ] s the PC poston n the ground system, [x, y]: pont coordnates n the camera system; [x 0, y 0 ] are the prncpal pont coordnates n the camera system; f s the focal length, m s the scale factor and R( C, C, C ) represents the rotaton matrx from camera to ground system. The object system used for the georeferencng s the local tangental system for arborne sensors and the ECR systems for spaceborne sensors. For the evaluaton of the accuracy of the method a suffcent number of Check Ponts (CPs) s requred. The CPs are measured n the mages and n the object space. After applyng the drect georeferencng, the estmated ground coordnates of the CPs are compared to the correct ones and the RMSE are calculated.for the orentaton of pushbroom magery, the approach based on drect georeferencng s very powerful because t allows the determnaton of the ground coordnates of the ponts measured n the mages wthout the use of Ground Control Ponts (GCPs), wth a consderable reducton of the processng tme, costs, and efforts. It s a (1) very useful tool for the evaluaton of the accuracy that can be acheved n the object space usng only the nformaton provded by laboratory calbraton and postonng systems carred on arcraft or spacecraft. For example, the algorthm has been used for the determnaton of the ground coordnates of ponts measured n Meteosat scenes (Sez et al., 2004). Indrect Georeferencng The ndrect georeferencng model s a bundle adjustment for the estmaton of the correct sensor external and nternal orentaton. It s used f the nteror or the exteror orentaton measurements are not sutable for hgh precson mappng wth drect georeferencng. Accordng to ths approach, the collnearty equatons are extended n order to ncluded: mult-lens sensors, the external orentaton modelng, the ntegraton of any avalable GPS/INS, and the systematc errors due to the lens and CCD lnes. For sensors whose optcal systems consst of more lenses, addtonal geometrc parameters descrbng the relatve poston and atttude of each lens wth respect to the nadr one are mported n the collnearty equatons. For each lens j, d xj, d yj, d zj represent the relatve poston and j, j, j, the relatve atttude wth respect to the reference one. The sensor external orentaton s modeled by Pecewse Polynomal Functons (PPM) dependng on tme. Due to the possblty of changng the number of segments and the polynomal degree, ths functon produces qute flexble results and s applcable to both satellte and arplanes trajectores (Hofmann et al., 1982; Kratky, 1989; Valadan- Zoej and Fooman, 1999; Grün and Zhang, 2002). If one segment only s used, a parabolc functon s obtaned. Accordng to the PPM approach, the platform trajectory s dvded nto segments and n each segment, wth tme extremes and, the varable t s defned as: t n t fn t t t n t n t fn [0,1] where t s the tme of acquston of a generc mage lne. Then, n each segment the sensor external orentaton [X C, Y C, Z C, C, C, C ] s modeled wth second-order polynomals dependng on t : X C ( t ) X 0 X 1 t X 2 Y C ( t ) Y 0 Y 1 t Y 2 Z C ( t ) Z 0 Z 1 t Z 2 C ( t ) 0 1 t 2 C ( t ) 0 1 t 2 C ( t ) 0 1 t 2 (2). (3) At the ponts of conjuncton between adjacent segments, constrants on the zero, frst, and second order contnuty are mposed on the trajectory functons; we force the values of the functons and ther frst and second dervatves computed n two neghborng segments to be equal at the segment s boundares. The proposed approach can also nclude any drect measurement of the sensor poston and atttude wth GPS and INS nstruments or ephemers data. These observatons may not be optmal for hgh-precson drect georeferencng. Frst of all, n case of GPS/INS measurements, the observatons refer to the GPS antenna and the INS nstrument, not to the sensor perspectve center (as requred n the collnearty PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING Feburary

4 condtons); the offsets and boresght angles between the GPS, INS, and camera systems, f not known or not accurate enough, should be mported n the collnearty equatons, estmated, and removed from the observatons. Another mportant aspect to take nto account s that the observatons may contan resdual systematc errors that were not elmnated n the flterng procedures. For these reasons, the external orentaton modelng must be extended n order to ntegrate and correct the GPS and INS observatons. The PPM approach s approprate for ths extenson, as already proved n (Grün and Zhang, 2002). The trajectory s agan dvded nto segments; the sensor atttude and poston of each mage lne l belongng to segment, ndcated wth [X C, Y C, Z C, C, C, C ] l, are modeled as the sum of the measured poston and atttude data for that lne [X nstr, Y nstr, Z nstr, nstr, nstr, nstr ] l plus the second order polynomal functons dependng on t : C ( t ) nstr X 0 1 t 2 Y C ( t ) Y nstr Y 0 Y 1 t Y 2 C ( t ) nstr 0 1 t 2 C ( t ) nstr 0 1 t 2 C ( t ) nstr 0 1 t 2 C ( t ) nstr 0 1 t 2. (4) The constant terms [X 0, Y 0, Z 0, 0, 0, 0 ] compensate for the shfts and angular drfts between the mage system and the GPS and INS systems, whle the lnear and quadratc terms [X 1, Y 1, Z 1, 1, 1, 1 ] and [X 2, Y 2, Z 2, 2, 2, 2 ] model the addtonal systematc errors contaned n the GPS and INS measurements. Agan, at the ponts of conjuncton between adjacent segments, constrants for the zero, frst, and second order contnuty are mposed on the trajectory functons. The number of segments s decded for each case study accordng to the trajectory length and smoothness. In general, for satellte orbts, two segments are suffcent, but for sensors carred on arplane or helcopter, a larger number of segments s recommended, as the trajectory s less smooth. The degree of the polynomal functons modelng the external orentaton can be reduced. In fact, all the PPM parameters are ntroduced n the model as pseudo-observatons wth sutable weght (accordng to ther accuracy) and can be fxed to sutable values. An nterestng applcaton s that by fxng the second-order parameters to zero, the polynomal degree s reduced to 1 and lnear functons, nstead of quadratc functons, are obtaned. Ths opton allows the modelng of the sensor poston and/or atttude n each segment wth second- or frst-order polynomals, accordng to the characterstcs of the trajectory. The ndrect model also ncludes the mprovement of the nternal orentaton. The self-calbraton s used to correct the observatons from systematc errors due to the magng nstrument. Among the errors that may occur n the geometry of the CCD arrays and n the optcal system, the followng ones are taken nto account: the dsplacement of each lne n the focal plane, the focal length varaton, the symmetrc radal and decenterng lens dstortons, the scale factor n CCD lne drecton, and the CCD lne rotaton n the focal plane. They are modeled wth sutable functons dependng on the so-called addtonal parameters (APs). The system s solved wth a least-square bundle adjustment, usng a sutable number of well-dstrbuted GCPs. The weghts for the observatons (collnearty, pseudo-observatons for the unknowns) are calculated accordng to the accuracy of the correspondng measurements. When the bundle adjustment s completed, the nternal and external accuracy of the ground coordnates of the observed ponts are analyzed. For the nternal accuracy the sgma naught a-posteror and the planmetrc and heght precson of the ground coordnates of GCPs and TPs are calculated. For the evaluaton of the external accuracy of the adjustment the RMSE of the TPs are computed and compared to ther theoretcal (expected) values. Furthermore the sgnfcance of the self-calbraton parameters s evaluated through ther statstcal values (mean value and standard devaton). The determnablty of the external and nternal orentaton parameters s decded accordng to correlatons n order to remove any overparameterzaton. A blunder detecton s also performed wth Baarda s data snoopng technque. Once the parameters modelng the nternal and external orentaton are estmated, t s possble to estmate the ground coordnates of any homologous pont measured n the mages through forward ntersecton. Applcatons The sensor model has been used to orent mages acqured by arborne and spaceborne pushbroom sensors wth dfferent geometrc characterstcs. As already mentoned n the Introducton, n ths paper we report the results acheved wth spaceborne sensors. In order to demonstrate the flexblty of the model, mages acqured wth sngle and mult-lens optcal systems, synchronous and asynchronous acquston modes, and dfferent resolutons have been used as reported n Table 1. Among the pushbroom sensors used for photogrammetrc applcatons, the choce of the sensors to use for our tests depended exclusvely on ther avalablty. The MOMS-02 dataset was avalable at our Insttute, the MISR and ASTER ones was downloaded at no cost (MISR) and at very low prce (ASTER, $55 USD per scene) from NASA, whle the EROS- A1 and SPOT-5/HRS mages came from external scentfc collaboratons. In ths secton, the results obtaned wth MOMS-2P, SPOT-5/HRS, and ASTER-VNIR are descrbed. For each sensor the analyss and processng of the data has been carred out followng these steps: 1. Analyss of metadata fles for the extracton of the acquston tme of each mage lne, the sensor external and nternal orentaton (f avalable), and any addtonal nformaton on the mages. 2. Radometrc preprocessng of the mages n order to mprove the radometrc qualty and facltate the pont measurement. 3. Measurement of object ponts. The mage coordnates are usually estmated wth template least-squares matchng, whle the ground coordnates are gven by external provders (.e., SPOT-5/HRS and EROS-A1 cases), are measured n topographc maps (.e., MOMS-2P, ASTER, and MISR cases) or n rectfed scenes from other sensors (.e., Landsat). 4. Drect georeferencng of the mages. The ground coordnates of the te ponts measured n the mages are estmated through a forward ntersecton usng the avalable external and nternal orentaton. The process accuracy s analyzed TABLE 1. SENSORS TESTED WITH OUR RIGOROUS SENSOR MODEL SPOT-5/ ASTER/ EROS-A1 HRS VNIR MOMS-2P MISR Preprocessng x x x x x Orentaton x x x x x DTM generaton x x GIS applcatons x 190 February 2007 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

5 through the resduals (RMSE) between the estmated and the correct ground coordnates of the ponts. In all the case studes reported n ths paper, sub-pxel accuracy n the RMSE could not be acheved and the ndrect georeferencng approach was used. 5. Indrect georeferencng of the mages. A bundle adjustment s performed n order to estmate the ground coordnates of the te ponts, the pecewse polynomal model (PPM) parameters for the external orentaton and the self-calbraton parameters. Dfferent tests are performed varyng the number and dstrbuton of GCPs, the PPM parameters (number of segments, degree) and the number of selfcalbraton parameters. In some cases the tests are lmted by the small number of GCPs. The adjustment s evaluated through both the nternal accuracy (standard devaton of unt weght a posteror, standard devaton of estmated parameters) and the external accuracy (RMSE of CPs). In order to avod over-parameterzaton, the correlaton between the unknown parameters, and the sgnfcance of the parameters are also analyzed. In addton, the Baarda test s performed to remove blunder observatons. MOMS-2P The ndrect georeferencng model was used to orent a stereo par acqured by the German MOMS-02, mounted on the Russan MIR staton durng Prroda msson. The data were provded by DLR. As two lenses acqured the stereo par, the extensons for mult-lens was used. The values of the addtonal parameters descrbng the relatve orentaton between the lenses were avalable from the MOMS-2P calbraton report (Kornus, 1996), provded by DLR. From the avalable 29 object ponts, some of them were used as GCPs and the others as CPs. The parameters used to control the nternal accuracy of the adjustment are: the sgma naught a posteror and the sgma of the CPs. The reference system used n the adjustment was the ECR. The tests were set as follows: (a) external orentaton modelng wth quadratc functons, varyng the number of segments and GCPs, no self-calbraton; (b) external orentaton modelng wth lnear and quadratc functons, varyng the number of segments and GCPs, no self-calbraton; and (c) self-calbraton wth best external orentaton modelng confguraton. The sgma naught, sgma and RMSE of CPs obtaned by the tests are summarzed n Table 2. As Test 1 addresses, the spacecraft trajectory was dvded nto 2 and 4 segments (NS 2 and NS 4) of the same length; 6 and 10 ponts were used as GCPs. The correspondng results are reported n the frst four rows n Table 2. In all cases RMSE and sgma of CPs are smaller than 1 pxel. The best RMSE n the CPs, acheved wth 10 GCPs and 4 segments, correspond to 0.4, 0.4, and 0.5 pxels n X, Y, and Z, respectvely. As expected, by ncreasng the number of segments, the external orentaton functons can better ft the real trajectory, mprovng the adjustment performance. Ths s demonstrated by the decrease of the sgma naught a posteror and the sgma of CPs. The dfference n the CPs RMSE between 2 segments and 4 segments confguratons s less than 0.5 m, correspondng to 3 percent of the ground pxel sze. By ncreasng the number of GCPs, sgma naught a posteror remans approxmately constant and the sgma of the CPs decreases, beng the system s more stable. Test 2 was performed n order to establsh f the polynomal degree of the poston or atttude functons could be reduced. Usng 6 and 10 GCPs and 2 and 4 segments for the PPM, quadratc functons for the poston and lnear functons for the atttude (pos Q, att L, second group of rows n Table 2) and lnear functons for both poston and atttude (pos L, att L, thrd group of rows n Table 2) were tested. The comparson between the results acheved wth quadratc and lnear functons show that, at least wth ths partcular dataset, quadratc functons for both poston and atttude are recommended, because they better ft the true trajectory and produce the best results. Fnally, a self-calbraton was appled usng the confguraton wth 10 GCPs and 17 CPs, 2 and 4 trajectory segments and quadratc external orentaton functons (pos Q, att Q). The flexblty of the software allows the user to fx any unknown parameters to the desred values wth pseudo-observatons. Due to the very hgh correlaton between the nternal and external orentaton for each test wth self-calbraton, the external orentaton parameters were fxed to the values estmated n the same confguraton wthout self-calbraton, and only the selfcalbraton parameters were estmated. In order to determne only the addtonal parameters (APs) of nterest, the tests were repeated wth dfferent self-calbraton confguratons. In the frst run, all the self-calbraton parameters were freed, and ther mean values, sgma, and correlatons were analyzed. The unpredctable or correlated parameters were fxed to constant values. The estmated APs were the rotaton angle of the CCD lne n the focal plane, the radal and decenterng dstortons for both lenses. Among them, the rotaton angle and the second-order radal dstorton param- TABLE 2. RESULTS OBTAINED FROM A MOMS-2P STEREO PAIR USING DIFFERENT GCPS AND CPS CONFIGURATION AND EXTERNAL ORIENTATION MODELING OPTIONS. NS NUMBER OF SEGMENTS IN PPM, SC SELF CALIBRATION (Y YES, N NO), DEG DEGREE OF POSITION ( POS) AND ATTITUDE ( ATT) POLYNOMIALS (Q QUADRATIC, L LINEAR) DEG RMSE CPs CPs ŝ 0 NS pos att SC GCP CP ( m) X Y Z X Y Z 2 Q Q N Q Q N Q Q N Q Q N Q L N Q L N Q L N Q L N L L N L L N L L N L L N Q Q Y Q Q Y PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING Feburary

6 eter results were nsgnfcant. The maxmum effect of the other parameters for both lenses s computed for the pxels on the border (u 1488). The maxmum values are for p 1 : x mm (1 pxel), for p 2 : y mm (1 pxel) and for k 1 : y mm (2 pxels). Comparng the values n Table 2 correspondng to NS 2 and NS 4, pos Q, att Q, GCP 10, CP 17, wthout (SC N) and wth selfcalbraton (SC Y), t can be observed that usng selfcalbraton the system converges easer to the soluton: the sgma a posteror of the full adjustment reduces consderably together wth the sgma of the CPs. The RMSE dffers few centmeters, wth smaller values n X and Y and larger values n Z (maxmum 40 cm). Consderng the ground pxel sze of 18.0 m, these RMSE dfferences are not sgnfcant. The fnal RMSE dstrbuton wth self-calbraton s shown n Fgure 1. Apart of the tests where both the poston and atttude are modeled wth quadratc functons, the dfferences between the RMSE and the standard devaton of the CPs vary between 0.5 m and 4 m. Even f these values represent a small fracton of the pxel sze (0.45 pxels), they show that the theoretcal (expected) accuracy s slghtly better than the acheved one. Ths fact can be explaned wth a wrong weght assgnment to the mage and ground coordnates of the object ponts. In (a) (b) Fgure 1. Resduals dstrbutons for MOMS-2P n X, Y (a) and Z (b) usng quadratc functon for poston and atttude (pos Q, att Q), NS 2, 10 GCPs (marked wth trangles) and 17 CPs (marked wth crcles) wth self-calbraton. fact, n our software the same weght s used for all the ponts. If a pont s measured wth a dfferent accuracy, t may negatvely affect the adjustment process. In order to evaluate the performance of our model, the same stereo par has been orented usng the Spotcheck software by Kratky Consultng (Kratky, 1989) mentoned n the Introducton. Usng 10 GCPs (the same ponts used n our tests) and modelng the atttude wth quadratc functons, the sgma naught a posteror was 2.2 m and the resduals acheved n 19 CPs were 5.2 m n East, 4.4 m n North and 11.1 m n heght n the Gauss-Krüger coordnate system. The correspondng values acheved wth our model n Gauss- Krüger system are 5.5 m, 4.3 m and 11.3 m for East, North, and heght, respectvely. The results obtaned by the two models are very smlar; takng nto account the ground resoluton (18 m), the dfferences are not sgnfcant. In both cases the modelng of the atttude wth quadratc functons gave better results, and the correcton of the nternal orentaton parameters (n partcular, the focal length and prncpal pont poston) usng the laboratory calbraton or the selfcalbraton, s recommended. SPOT-5/HRS In 2003, the Insttute of Geodesy and Photogrammetry (IGP), ETH Zurch, joned the HRS Scentfc Assessment Program (HRS-SAP), organzed by CNES and ISPRS. Ths ntatve, announced n Denver n 2002 at the ISPRS Commsson I Symposum and concluded n Istanbul at the XX th ISPRS Congress, was organzed to nvestgate the potental of the SPOT-5/HRS sensor for DEM generaton, n order to help CNES to mprove ts future Earth Observaton systems and all users to better know and trust the accuracy and qualty of the HRS nstrument and the derved DEM. IGP joned the Intatve as co-nvestgator and processed the dataset Number 9, over the Chemsee Lake, n Germany. For more nformaton about the Intatve, see Baudon et al. (2004). Ths dataset contaned: two stereo mages from SPOT5- HRS sensor wth correspondng metadata fles, the descrpton of the exact poston of 81 object ponts n Germany measured wth surveyng methods, and seven reference DEMs produced by a dfferent method. The two stereo mages were acqured on 01 October 2002 n the mornng over an area of approxmately 120 km 60 km n Bavara and Austra. Each mage s 12,000 pxels 12,000 pxels, wth a ground resoluton of 10 m across and 5 m along the flght (parallax) drecton. The scenes were acqured n panchromatc mode n stereo vewng along the flght drecton wth a base over heght rato of 0.8. The two telescopes contaned n the HRS nstrument scan the ground wth off-nadr angles of 20 (forward mage) and 20 (backward mage). Each telescope has a 580 mm focal length and a focal plane wth a CCD lne of 12,000 detectors, 6.5 m sze. The scenes are could free and cover an area wth flat, hlly, and mountanous (Alps) terran, rural zones, towns, rvers, and lakes. The heght ranges between 400 m and 2,000 m. The drect georeferencng approach was used n order to test f the camera calbraton and the ephemers avalable n the metadata fles were accurate enough for hgh precson mappng. The nformaton on the nternal orentaton was gven through the vewng angles of each detector expressed wthn the sensor coordnate frame. From these data, the locaton of each detector n the focal plane was computed. The poston and velocty vectors determned by the onboard Doppler Orbtography and Radopostonng Integrated by Satellte (DORIS) postonng nstrument were used for the estmaton of the sensor atttude n the ECR system. Then, the poston and atttude were nterpolated wth cubc splnes for the acquston tmes of the mage lnes. A forward ntersecton was appled to calculate the ground 192 February 2007 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

7 TABLE 3. RESULTS OBTAINED FROM A SPOT-5/HRS STEREO PAIR USING DIFFERENT GCPS AND CPS CONFIGURATION AND EXTERNAL ORIENTATION MODELING OPTIONS. X, Y AND Z REFER TO ECR SYSTEM. NS NUMBER OF SEGMENTS IN PPM, SC SELF CALIBRATION (Y YES, N NO) RMSE CPs (m) CPs (m) ŝ 0 NS SC GCP CP ( m) X Y Z X Y Z 2 N N N N Y Y Y Y coordnates of the object ponts. The resultng coordnates were compared to the correct values and the RMSE were evaluated. The results showed a large systematc error both n planmetry (2 to 3 pxels) and n heght (approxmately 3 pxels). Therefore, the ndrect georeferencng model was requred for the nternal and external orentaton refnement. From the avalable 41 ponts, a group of them was used as GCPs and the remanng as CPs. The a pror standard devaton of the GCPs was 3 m. The tests have been carred out wth dfferent nput confguratons as n the case of MOMS-02 dataset. As already encountered wth MOMS-02, the PPM gave better results wth quadratc functons, than wth lnear ones. Usng lnear functons, the RMS and standard devaton values were close to one pxel. The RMSE and the sgma of the CPs and the sgma naught of the adjustment obtaned wth quadratc functons wthout and wth self-calbraton are reported n Table 3. Takng nto account the results acheved wthout self-calbraton (frst four rows of Table 3), t can be seen that ncreasng the number of PPM segments the adjustment converges better (smaller sgma naught a posteror and sgma of the CPs) and the RMS values reman qute constant. As expected, the use of more GCPs gves better solutons, n terms of nternal and external accuracy. The RMSE szes and dstrbutons n the object space are evdence that f only the external orentaton s modeled, the systematc errors are not completely removed. Usng self-calbraton (last four rows of Table 3 wth SC Y), an mprovement both n the nternal and external accuracy s seen. The sgnfcant self-calbraton parameters were the symmetrc radal dstorton (through k 1 ) and the scale n y drecton, wth the focal length fxed. These parameters were dfferent for each lens and ther effect could not be compensated durng the estmaton of the external orentaton parameters only, whch s unque for the entre system. The maxmum effects of the estmated parameters for each lens are calculated for the pxels on the mage borders (u 6,000) for k 1 and s y. They are reported n Table 4. TABLE 4. MAXIMUM ERRORS IN LENSES 1 (FORWARD) AND 2 (BACKWARD) CAUSED BY LENS DISTORTION. THE ERRORS ARE EXPRESSED IN MM AND IN PIXELS: K 1 : Radal Dstorton, s y : Scale n CCD Lne Drecton y 1 y 2 y 1 y 2 Lens 1 Lens 2 (mm) (mm) (pxel) (pxel) k s y The orentaton of SPOT-5/HRS stereo scenes has also been nvestgated n many other research nsttutes that were nvolved n the HRS-SAP. The results acheved for the dataset Number 9 are reported and compared to the performances of our model. At the Insttute of Geodesy and Photogrammetry another approach based on Ratonal Polynomal Coeffcents (RPC) was used to orent the mages. Ths algorthm s mplemented n the SAT-PP software, developed at IGP (Grün et al., 2005). In case of SPOT-5/HRS the mages were orentated wth four GCPs, wth resduals of 5.6 m, 4.0 m, and 2.4 m n East, North, and heght, respectvely (Gauss-Krüger system). The RMSE obtaned wth our rgorous model n the Gauss-Krüger system are: 5.9 m, 4.2 m, and 3.5 m shown n Fgure 2. The dfferences between the two methods are not very sgnfcant. It must be taken nto account that, n general, the rgorous models are senstve to the GCPs dstrbuton n the mages, and n our case, the GCPs were located n the left part of the mage only. On the other hand, the RPC were derved from the strct model desgned for the full scene and the use of a block adjustment could compensate addtonal systematc errors. The dfferences n the orentaton performance are of course present n the DSMs also, wth values n the order of 5 percent of the pxel. More than 30 publcatons on the orentaton of HRS scenes wthn the HRS-SAP are avalable n the Proceedngs of the XX th Congress of the Internatonal Socety for Photogrammetry and Remote Sensng n Istanbul, Turkey n July Among them, we can menton (Jacobsen, 2004; Toutn et al., 2004; Renartz et al., 2004; Mchals and Dowman, 2004). In partcular, the DEMs obtaned by the HRS-SAP prncpal nvestgators and the co-nvestgators over the test area Number 9 were compared wth the same strategy and reported n (Rudowsk, 2004). In ths analyss the DEMs generated at IGP usng our sensor model and the RPC model (Pol et al., 2004) and two others have been evaluated through the 2.5D heght dfference wth the reference terran models, produced wth laser scanner (heght accuracy 0.5 m), contour lnes (heght accuracy 5.0 m), or photogrammetrc methods (heght accuracy 2.0 m). The best mean and RMSE values for 98 percent of the compared ponts were acheved n about all the reference areas by P1 and P2. The dfferences between P1 and P2 have already been documented. The mean values obtaned wth our model were n the range (2.9 m to 4.1 m) n flat and hlly terran, up to 6.7 m n mountanous areas. The RMSE was n the range (2.8 m to 4.3 m) n flat and hlly terran, and up to 7.9 m n mountanous areas. Ths comparson confrms that for ths dataset our sensor model can acheve an accuracy both n the CPs and n the nterpolated ponts n the same order or even better than the one obtaned usng other software and approaches. PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING Feburary

8 (a) (b) Fgure 2. Resduals n planmetry (a) and heght (b) for SPOT-5/HRS n Gauss-Krüger system for all object ponts n the confguraton wth two segments n the PPM and eght GCPs (marked wth trangles) wth self-calbraton. ASTER The Advanced Spaceborne Thermal Emsson and Reflecton Radometer (ASTER) s one of the nstruments flyng on the NASA s Earth Observng System (EOS). The ASTER nstrument conssts of three downlookng sub-systems: the Vsble and Near-nfrared (VNIR), the ShortWave Infrared (SWIR), and the Thermal InfraRed (TIR). The nstrument used for the DEM generaton s the VNIR, the only one wth stereo capablty. It conssts of two ndependent telescopes lookng nadr (channels 1, 2, and 3N) and backward (channel 3B), wth an angle of Channels 3N and 3B acqure n the same spectral range (nfrared). The CCD lnes for each band consst of 5,000 detectors, but not all of them are actve at one tme. The detector pxel sze s dfferent n the two telescopes. In the nadr one, the sze s 7.0 m 7.0 m, whle n the backward one t s 6.1 m 6.1 m. The ASTER scenes are avalable at dfferent processng levels, as descrbed n (Abrams and Hook, 2002). For our purposes, level 1A s used, because t s not georeferenced and reflects the orgnal acquston geometry. The scenes were acqured on 25 June 2003 n the mornng over Swtzerland (orbt 18714, path 195, row 27). They cover an area of approxmately 60 km 60 km. The stereo par formed by the 3N and 3B mages has been orented usng the ndrect georeferencng model. The software has been adapted n order to treat stereo mages, such as these, wth dfferent sze and CCD detector dmensons. For the orentaton, the same procedure used for MOMS-2P and SPOT-5/HRS has been followed. For each test the nternal and external accuracy of the system have been analyzed through the sgma naught a posteror, the standard devaton and the RMSE of the CPs. Usng the blunder detecton ncluded n the model wth a threshold of 3.0 (crtcal value of the t-student dstrbuton wth nfnte redundancy and a confdence nterval of 99.9 percent), eght ponts have been dentfed as outlers and elmnated. After the blunder removal, the ndrect georeferencng model was re-appled. The RMSE of the CPs showed errors n the order of 1 to 2 pxels for almost all confguratons, wth theoretc values (sgma) of about one pxel and sgma naught a posteror of 3.5 m to 3.7 m. The bundle adjustment was repeated wth self-calbraton, fxng the external orentaton to the values prevously estmated wthout self-calbraton and keepng the APs free. Dfferent tests have been run to check the correlaton between the APs and the ground coordnates of CPs, and decde whch parameters had to be estmated. From ths analyss, the most sgnfcant parameters were the radal and decenterng dstorton and the scale n the CCD lne drecton. The maxmum combned effect of these parameters (evaluated at the extremes of the mage lnes) was about 14 m (2.0 pxels) for 3N and 13 m (2.1 pxels) for 3B. As expected, the correcton of the nternal orentaton parameters mproved the nternal and external accuracy of the adjustment. The results obtaned wth four segments n the PPM, wth eght and 12 GCPs and wth/wthout selfcalbraton are reported n Table 5. The dstrbuton of the resduals s shown n Fgure 3. These results confrm that for ths dataset, the self-calbraton was requred n order to model more accurately the acquston geometry of the ASTER scenes. After the orentaton, a 3D pont cloud has been produced usng the estmated parameters for the sensor nternal and external orentaton and about 1,800,000 ponts matched wth least-squares matchng. The accuracy of the resultng pont cloud has been evaluated comparng the 3D dstance between each pont of the measured pont cloud and the surface generated from the DHM25 product by Swsstopo (1 to 3 m accuracy). For the analyzed test stes (sx blocks wth sze 17.5 km 12.0 km), the mean values are smaller than one pxel, whle the RMSE and standard devatons are slghtly larger than one pxel. The effect of the trees, whch was proved wth further analyss, was not removed. The results acheved n the mage orentaton and n the DEM accuracy are wthn the specfcatons of the absolute DEM product (5 to 15 m for the RMSE of GCPs, 7 to 30 m for the DEM (Hrano et al., 2003), and n accordance wth the results obtaned by other authors. In Toutn and Cheng (2001) an ASTER stereo par over Drum Mountans, U.S. was orentated usng PCI Geomatca OrthoEngne software and eght GCPs. The resduals n sx CPs were 15.8 m, 10.5 m, and 7.9 m. The correspondng DEM was generated and compared wth an USGS 7.5-Mnute DEM (30 m grd spacng), wth a 7.5 m RMS error. The elevaton dfference had a mnmum value of 109 m, a maxmum value of 155 m, a mean value of 1.9 m, and a standard devaton of 11.5 m wth an 85 percent level of concdence. In Hrano et al. (2003) four ASTER stereo-scenes located n dfferent mountanous areas have been used for DEM generaton wth R-WEL DMS software, usng from 5 to 12 GCPs. The RMSE n heght n the CPs was between 7.3 m and 26.3 m. 194 February 2007 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

9 TABLE 5. RESULTS OBTAINED FROM AN ASTER/VNIR STEREO PAIR USING DIFFERENT GCPS AND CPS CONFIGURATION AND EXTERNAL ORIENTATION MODELING OPTIONS. X, Y AND Z REFER TO ECR SYSTEM. NS NUMBER OF SEGMENTS IN PPM, SC SELF CALIBRATION (Y YES, N NO) RMSE CPs (m) CPs (m) ŝ 0 NS SC GCP CP ( m) X Y Z X Y Z 4 N N Y Y (a) (b) Fgure 3. RMSE n planmetry (a) and heght (b) for ASTER-VNIR for all object ponts n the confguraton wth four segments n the PPM, eght GCPs (marked wth trangles) and selfcalbraton. Conclusons In ths paper, a rgorous model for ther orentaton of pushbroom sensors has been presented. The magery acqured by these sensors have very hgh potental for photogrammetrc mappng at dfferent scales from arborne and satellte platforms, and ts orentaton s a fundamental step n the processng chan for the generaton of orthomages and Dgtal Elevaton Models (DEMs). The proposed model ncludes two dfferent orentaton approaches. In the drect georeferencng model, the ground coordnates of the homologous ponts measured n the mages are estmated through a forward ntersecton, usng as external orentaton the data provded by geopostonng systems carred on board (GPS, INS, star trackers) or the trajectory calculated by mathematcal formulas descrbng the sensor trajectory (only for satellte-based sensors). The alternatve orentaton method s a self-calbratng bundle adjustment, modfed accordng to the pushbroom sensors characterstcs. If GPS and INS are avalable, they are ntegrated n the PPM. The parameters modelng the nternal and external orentaton, together wth the ground coordnates of the te ponts, are estmated through a least-squares bundle adjustment usng well-dstrbuted ground control ponts. The use of pseudoobservatons allows the user to run the adjustment fxng any unknown parameters to certan values. A blunder detecton procedure s ntegrated for the automatc detecton of wrong mage coordnate measurements. The false measurements removal s manual. Thanks to ths approach, the resultng model has the advantage of beng s very flexble, and therefore can be used for a large number of pushbroom sensors, carred on arborne and spaceborne platforms. In order to demonstrate ths, the model was tested wth pushbroom sensors dfferent characterstcs (sngle-lens and mult-lens optcal systems, varous number of lnear arrays, synchronous and asynchronous acquston modes), carred on satellte and helcopter platforms. The results acheved wth arborne sensors are descrbed n Pol (2002). In ths paper, the results obtaned wth MOMS-2P, SPOT-5/HRS, and ASTER have been reported. Addtonal tests wth asynchronous sensors (EROS-A1) are n Gulo-Tonolo and Pol (2003). For each test both the drect and ndrect models have been used, and n all cases the drect georeferencng was not accurate enough for hgh accurate mappng. The ndrect model has been appled wth dfferent ground control pont dstrbutons, varyng the PPM confguratons (number of segments, polynomals degree) and wth and wthout selfcalbraton. All the magery has been orented wth subpxels accuracy n the checkponts usng a mnmum number of sx ground control ponts. Further nvestgaton could be carred out on the selecton of the addtonal parameters n an automatc way wth sutable tests after each teraton. References Abrams, M., and S. Hook, ASTER User HandBook, URL: (last date accessed: 15 November 2006). Baltsavas E.P., and D. Stallmann, Metrc nformaton extracton from SPOT mages and the role of polynomal mappng functons, Internatonal Archves of Photogrammetry and Remote Sensng, Vol. 29, Part B4, Washngton D.C., pp Baltsavas, E.P., and D. Stallmann, Geometrc potental of MOMS-02/D2 data for pont pos-tonng, DTM and orthomage, PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING Feburary