Direct sensor orientation based on GPS network solutions

Transcription

1 Direct sesor orietatio based o GPS etwork solutios KEY WORDS: GPS, IMU, Direct image orietatio ABSTRACT: Helge Wegma a, Christia Heipke b, Karste Jacobse b a Igeieurbüro Wegma, Leo-Roseblatt-Weg 6, Haover, Germay ifo@ib-wegma.de b Istitute for Photogrammetry ad GeoIformatio, Uiversity of Haover, Nieburger Str. 1, Haover, Germay heipke, jacobse@ipi.ui-haover.de Commissio I, WG V Direct sesor orietatio, i.e. the determiatio of exterior orietatio based o GPS ad iertial measuremets without the eed for photogrammetric tie poits, has gaied cosiderable popularity over the last years. Oe pre-coditio for direct sesor orietatio is a correct sesor ad system calibratio. The calibratio ca oly be carried out by a combiatio of a photogrammetric solutio ad a GPS/iertial solutio, which is equivalet to the cocept of itegrated sesor orietatio. I the work carried out so far, GPS has bee idetified as the most critical part i terms of achievable accuracy. Strategies for improvig differetial GPS results are available for terrestrial applicatios, but have ot yet bee used i direct ad itegrated sesor orietatio. Oe of these solutios cosists i usig a etwork of referece statios rather tha a sigle statio oly. I this paper we preset our work o direct sesor orietatio usig a GPS etwork. After describig the related mathematical models we report the results of a experimetal test. The test data were draw from the OEEPE test Itegrated sesor orietatio. The results show, that while for may applicatios a etwork may ot be ecessary i case of short baselies ad good GPS data, it still improves the accuracy of direct sesor orietatio to some degree. More importat is the fact, that our approach is able to detect gross errors i the referece statio data ad therefore has the potetial to improve also the reliability of the results. 1 Itroductio The developmet of sesors ad related processig methods for the ecoomic, accurate ad reliable collectio of 3D geospatial iformatio has bee a topic of itese photogrammetric research i recet years. Besides the ew digital aerial cameras, sesors for directly determiig the exterior orietatio based o GPS ad iertial measuremet uits (IMU) have foud large iterest. The itegratio of GPS ad the iertial measuremet system has bee strogly promoted at the Uiversity of Calgary for a log time already (Schwarz et al. 1984; 1993) ad i the meatime a series of tests ad pilot projects has bee coducted demostratig the potetial of these methods (e.g. Skaloud 1999, Cramer 1999, Heipke et al. 2002b). The curret situatio is that GPS has bee idetified as the most critical part i terms of achievable accuracy. Whe usig GPS ad IMU observatios to determie the exterior orietatio of photogrammetric images, oe ca differetiate betwee the so called itegrated sesor orietatio, i which all available iformatio icludig tie poits is processed simultaeously to achieve highest accuracy, ad direct sesor orietatio, i which the exterior orietatio is computed based o GPS/IMU observatios oly, ad object space coordiates are derived i a separate step (Heipke et al, 2002a). Direct sesor orietatio cosists of three steps - a sesor calibratio step to be carried i advace, as well as GPS/IMU pre-processig ad the determiatio of the exterior orietatio for the actual missio. Durig sesor calibratio the parameters describig each sesor idividually ad those describig the relatioship betwee the differet sesors eed to be determied. These parameters iclude the iterior orietatio of the camera, the agular differeces betwee the IMU ad the image coordiate system (boresight misaligmet), ad additioal parameters modellig e.g. GPS errors. The system calibratio parameters, ad i particular the boresight misaligmet, ca oly be determied by comparig a photogrammetric solutio based o image coordiates of groud cotrol ad tie poits with the pre-processed GPS/IMU results. GPS/IMU pre-processig icludes the trasformatio of the raw GPS sigal ad IMU measuremets ito trajectories i object space for the camera projectio cetres ad roll, pitch ad yaw values at a high frequecy (usually Hz). The commo method of itegratig GPS ad IMU observatios is via Kalma filterig. It provides the optimum estimatio of the system based o all past ad preset iformatio (for details see Grewal et al. 2001). The determiatio of the exterior orietatio parameters the cosists i applyig the sesor calibratio to the preprocessed GPS/IMU values. Oe of the applicatios of direct sesor orietatio is 3D poit determiatio via spatial forward itersectio based o the refied exterior orietatio parameters. I this paper, we deal with direct sesor orietatio ad preset as a ovel aspect of our work a GPS etwork solutio for photogrammetric poit determiatio. I the ext sectio we describe our model for sesor calibratio based o preprocessed GPS/IMU data. We do ot deal with GPS/IMU pre-processig itself. We the itroduce our test data which are draw from the OEEPE test Itegrated Sesor Orietatio. We derive sesor calibratio parameters, ad compute 3D coordiates of idepedet check poits which we compare to the kow values, both with sigle referece statios, ad usig the GPS etwork. Fially, we commet our results ad draw some coclusios for future work.

2 2 Mathematical model for itegrated sesor orietatio For sesor calibratio a commo model of all three groups of observatios (image coordiates of tie ad groud cotrol poits (GCP), pre-processed data for the projectio cetre coordiates, pre-processed data for the agles of exterior orietatio) eeds to be set up. This model is the same as used i itegrated sesor orietatio, where all available iformatio is processed simultaeously i order to obtai the highest accuracy. I this sectio, the model is outlied i some degree of detail. We fially tur to the descriptio of the GPS etwork solutio. 2.1 Model for image coordiates The image coordiates are coected to the object space coordiate system via the well-kow colliearity equatios. The colliearity equatios are based o a orthoormal coordiate system. Obviously, the atioal coordiate systems (e.g. UTM) do ot correspod to this requiremet. I traditioal photogrammetry the effects of o-orthogoality are sometimes compesated by a earth curvature correctio applied to the image coordiates. For a combied adjustmet with image coordiates ad direct observatios of positio ad attitude this approach is ot sufficiet, because also the attitude observatios eed to be corrected, ad differet scale factors must be itroduced for plaimetry ad height (see e.g. Jacobse 2002; Ressl 2002). A more straightforward way is to trasform all object space iformatio ito a orthoormal system a priori, e.g. a local tagetial system. I the followig we use such a local tagetial system. Where ecessary, this system is deoted by the symbol m. The system of o-liear observatio equatios reads r11( X Xo) + r21( Y Yo) + r31 ( Z Zo) x' + vx' = x' o f * + dx' (1) r13( X Xo) + r23( Y Yo) + r33( Z Zo) r12 ( X Xo) + r22( Y Yo) + r32( Z Zo) y' + vy' = y' o f * + dy' r ( X Xo) + r ( Y Yo) + r ( Z Zo) x, y, v x, v y X,Y,Z Xo,Yo,Zo r ik image coordiates ad related residuals object space coordiates for tie poits ad GCP object space coordiates of projectio cetre elemets of rotatio matrix R m i (ω,φ,κ) betwee the image coordiate system ad the object space coordiate system x o, y o image coordiates of the pricipal poit dx,dy correctios of the image coordiates f calibrated focal legth I order to itroduce stochastic properties for the coordiates of the GCP, they are itroduced as ukows ito the adjustmet, ad direct observatios for the cotrol poit coordiates are set up withi the model. 2.2 Positio equatios The secod part of the itegrated sesor orietatio model deals with the pre-processed observatios for the positio of the projectio cetre. These observatios are ofte give i some Earth-fixed referece system, e.g. WGS 84, ad eed to be trasformed ito the local tagetial system prior to usig them i itegrated sesor orietatio. The model is exteded by bias ad drift parameters to describe liear systematic effects of positio, as is sometimes also doe i GPSsupported aerial triagulatio (Jacobse 1991; Ackerma 1994). A additioal parameter dt takes care of a possible time sychroisatio offset betwee the istat of image exposure ad the GPS/IMU time. X X v X O Y () t + v = Y ( t + dt) + YGPS / IMU O Z v Z Z O dx _ camera b Xo d _ Xo / ( t + dt) ( ωρκ,, ) + _ + ( t+ dt to) d _ Yo camera dz b _ Zo camera d _ Zo GPS IMU m Ri dy b Yo X,Y,Z (GPS/IMU) object space coordiates of IMU cetre of v X,v Y,v Z(GPS/IMU) mass ad related residuals t dt t o (2) observatio time of GPS/IMU sychroisatio offset betwee GPS/IMU time ad istat of camera exposure referece epoch for drift computatio Xo,Yo,Zo object space coordiates of projectio cetre, time depedet R m i(ω, φ,κ) rotatio matrix betwee the image coordiate system ad the object space coordiate system, time depedet dx,dy,dz GPS/IMU camera compoets of offset vector betwee IMU cetre ad projectio cetre, expressed i image coordiate system b_xoyozo d_xoyozo 2.3 Attitude equatios bias i positio (oe parameter per strip, or oe for the whole block) drift i positio (oe parameter per strip, or oe for the whole block) The third part of the model describes the pre-processed attitude observatios. I priciple, these observatios describe the rotatio betwee the IMU coordiate system (so called body system b) ad a iertial coordiate system. I strap dow avigatio, the iertial system is replaced by a local level system, the so called avigatio system (see e. g. Bäumker, Heimes 2002). The x-axis of the avigatio system poits orthwards, the z-axis dowwards alog the local plumb lie, the y-axis completes the right-haded system. Besides other correctios, the trasformatio from iertial to avigatio system requires the kowledge of Earth rotatio ad gravity parameters, ad is usually itegrated ito GPS/IMU pre-processig. Thus, the pre-processed attitude observatios describe the rotatio of b aroud. I aerial applicatios, the body system is fixed to the aircraft. b ad the related rotatio agles roll, pitch, ad yaw are defied accordig to the aviatio orm ARINC 705 (ARINC 2001). Sice the IMU measuremets refer to the local plumb lie, the avigatio system is ot a Earth-fixed system, but moves together with the IMU. A coectio to the photogrammetric rotatios is give via the Earth fixed system e. The istataeous positio of the aircraft is expressed i

3 geographic coordiates (λ i, φ i ) take from the GPS/IMU positios. A rotatio ca the be set up from to e, aother oe to the local tagetial system m cetred at the geographic coordiates (λ o, φ o ) ad used i the colliearity equatios. Additioal rotatios eed to be itroduced to take ito accout the differet axes directio of the avigatio ad the local tagetial system o the oe had, ad the body ad the image coordiate system o the other had. Fially, the misaligmet betwee the image coordiate system ad the body system must be icluded. Sice the misaligmet is cosidered as costat, it must be expressed i the body system rather tha i the image coordiate system. As i the case of the positio equatios the system is completed by bias ad drift parameters. The o-liear observatio equatios for attitude are give by roll v roll e π pitch v T [R yaw b v yaw (t) + 0 pitch = e( λi, ϕi) R ( λo, ϕo) R m( π,0, ) 0 2 m R i (t + dt) ( ) R i (,0,0) R b* ωφκ,, π ( roll, pitch, yaw) ] (3) b* b b_ roll d_ roll + b_pitch + (t + dt to) d_pitch b_yaw d_yaw b b (roll, pitch, yaw) b elemets of rotatio matrix betwee b v roll,v pitch,v yaw ad ad related residuals T fuctio to extract a vector of rotatio agles out of the rotatio matrix ω,φ,κ agles of exterior orietatio, time depedet λ i, φ i geographic coordiates of IMU at the istat of exposure λ o, φ o geographic coordiates of origi of local tagetial system roll, pitch, yaw agles of boresight misaligmet R e R e o R o m R m i R b* i R b b* rotatio matrix betwee Earth-fixed ad avigatio system rotatio matrix betwee avigatio system at the origi of the local tagetial system ad Earth-fixed frame rotatio matrix betwee local tagetial system ad fixed avigatio system rotatio matrix betwee image coordiate system ad local tagetial system rotatio matrix betwee body system altered by misaligmet ad image coordiate system rotatio matrix of boresight misaligmet b_roll, pitch, yaw bias i attitude (oe parameter per strip or oe or the whole block) d_roll, pitch, yaw drift i attitude (oe parameter per strip or oe or the whole block) t, dt, t o see above 2.4 Least-squares adjustmet Equatios (1) to (3) form the mathematical model of itegrated sesor orietatio, which is also used to determie the system calibratio parameters ecessary for direct sesor orietatio, as metioed above. Differet sets of calibratio parameters ca be chose. Besides the boresight misaligmet, the bias parameters of equatio (2) are ofte selected as calibratio parameters. Depedig o the available data ad the iteded use of the calibratio results, also the iterior orietatio parameters of the camera, ad the sychroisatio offset dt ca be cosidered as ukows. Of course, it must be esured that the selected parameters ca be computed i a umerically stable way from the provided iformatio. For istace, assumig a flat test field a correctio to the calibrated focal legth ad a bias parameter i Z ca oly be determied if imagery from at least two differet flyig heights is available, ad a correctio to the pricipal poit i flight directio together with a bias i flight directio requires at least two strips flow i opposite directios. Also, the sychroisatio offset dt is highly correlated with the correctio for the pricipal poit i flight directio, a separatio eeds agai two differet flyig heights. Fially, i order to iterpolate the corrected exterior orietatio parameters at the istat of image exposure after havig estimated dt at the ed of each adjustmet iteratio, high resolutio iformatio for positio ad attitude must be available. The ukows of the approach are computed i a leastsquares adjustmet, based o the priciple v T Pv -> miimum (4) As usual, P is the weight matrix of the observatios. It should be oted that ofte o stochastic iformatio is available for the GPS/IMU measuremets after the Kalma filterig if commercial software is used for GPS/IMU pre-processig. 2.5 GPS etwork solutio We ow address the GPS etwork solutio. It is well kow, that the observatio quality i differetial GPS depeds o the legth of the baselie (Seeber 2003). I other applicatios GPS etwork solutios, i.e. solutios ivolvig more tha oe referece statio, have foud major iterest ad are icreasigly also used i practical applicatios. I photogrammetry, such possibilities have ot yet bee exploited. Based o the described formulae, we ca create a etwork solutio i two differet ways: first, we ca cosider each available referece statio idividually ad set up equatios (2) ad (3) for each image as ofte as there are referece statios. A alterative is to combie the observatios of the differet referece statios durig GPS/IMU pre-processig, ad to subsequetly set up equatios (2) ad (3) oly oce per image. The first possibility has the advatage of simplicity, sice pre-processig ca be doe i the covetioal way. The secod possibility has the advatage of beig able to aalyse i detail the differet high frequecy GPS/IMU observatios, ad to elimiate ay error at a early stage. Also, differet sets of calibratio parameters ca be take ito accout for the differet referece statios. Sice at preset we do ot have the possibility to do GPS/IMU preprocessig, we have decided to use this first possibility for our studies.

4 The characteristics of the etwork solutio are as follows: (1) if there are multiple baselies of similar legth, the differet referece statios have the effect of repeated measuremets. (2) if the baselies are differet i legth, ad thus the quality of the GPS/IMU observatios differs, the etwork solutio yields a average result, which is obviously ot as accurate as the oe for the shortest baselie, but better tha the oe for the logest baselie. (3) if there are short term errors i ay of the baselies, the etwork solutio is able to reduce, ad perhaps to elimiate, the effect of these errors. I ay case, multiple baselies lead to a larger redudacy of the adjustmet system, ad thus to a icreased possibility for detectig gross errors, ad to a more reliable solutio for the parameters of exterior orietatio. Of course, ay problems coected to the GPS receiver i the aircraft caot be detected, either ca the stadard deviatio of computed object space coordiates be improved, if the limitig factor is the measuremet accuracy of the correspodig image coordiates, ad ot the exterior orietatio. - Torp (20-50 km baselie), - Soer (25-60 km baselie), - Stavager (baselie approx. 307 km). The differet values for the baselies are caused by the flight patter, for Stavager this effect amouts to oly 10 % of the legth ad is egligible. Figure 1 shows the accuracy of the GPS-positio for the referece statio Raade for the various strips of the project flight. I the upper part of the figure, the PDOP (positio dilutio of precisio), a commo descriptor for GPS positio accuracy (Seeber 2003) ca be see as the straight lie, the baselie legth is the more udulated lie. It is clearly visible that the PDOP icreases sharply durig the first strip idicatig some problem i the GPS sigal, ad oly decreases after the fourth strip. I the lower part, the resultig GPS accuracies i X, Y, ad Z derived from processig differet satellites (but o IMU data) are show. The correlatio betwee the large PDOP value ad the large stadard deviatios for the GPS positio ca clearly be see. 3 Test data I order to aalyse our model we used the data of the OEEPE test Itegrated sesor orietatio (see Heipke et al. 2002a; b ad Nilse 2002). For this paper we used oly a subset of the test data. The test was flow over the test field Fredrikstad i Souther Norway. The test field has a size of approximately 4,5*6 km 2 ad cotais about 50 sigalised GCP with object space coordiates kow to sub-cetimetre accuracy. The aircraft was flow at a altitude of meters above groud resultig i a image scale of approximately 1: Two flights were selected: the calibratio flight icluded four strips, two strips i west-east ad east-west directio ad two further strips i orth-south ad southorth directio; ad a project flight with five strips i orthsouth ad south-orth directio. I order to achieve a good iitial aligmet for the IMU axes with the gravity field, the aircraft made a S-like tur before the first flight strip. Image coordiates of a sufficiet umber of tie poits ad of all GCP were measured maually o a aalytical plotter. The selected GPS/IMU aircraft equipmet was a POS/AV 510-DG from Applaix, cosistig of a high quality off-theshelf avigatio grade IMU as typically used i precise airbore positio ad attitude determiatio. The POS/DG equipmet was tightly coupled to a wide agle Leica RC30, the latter mouted o the gyro-stabilised platform PAV30. The PAV30 data ad thus rotatios of the camera ad the IMU relative to the plae body were recorded at 200 Hz ad itroduced ito further processig. The claimed accuracy is better tha 0.1 m for the IMU positio, ad better tha degree i roll ad pitch, ad better tha degree i yaw (Applaix 1999). Durig data acquisitio several GPS referece statios were used ad the GPS equipmet i the aircraft ad o the referece statios cosisted of dual frequecy receivers performig differetial carrier phase measuremets at 2 Hz. The followig referece statios were used for the results reported i this paper: - Raade (baselie 8 30 km), - Moss (baselie km), Figure 1: Accuracy of GPS positio, referece statio Raade The small peaks i the X,Y ad Z accuracies i the lower part of figure 1 ca be smoothed whe itroducig IMU data durig Kalma filterig. It is ot possible, however, to compesate the weaker accuracy over the loger time period i the same way. Oly a etwork solutio or additioal GCP ca overcome this problem. 4 Sesor calibratio Based o the model explaied i sectio 2 ad the calibratio flight data described i sectio 3 we performed a calibratio of the equipmet used i the test. The displacemet vector betwee the GPS atea ad the IMU cetre of mass was determied before the flight missio usig covetioal surveyig techiques ad was used as a costat lever arm correctio. Sice we oly had oe flyig height, we selected the six stadard parameters (boresight misaligmet ad GPS offset parameters). I additio, we solved for a time sychroisatio offset. I the adjustmet, we itroduced twelve GCP, together with sufficiet, well distributed image coordiates of tie poits together with the pre-processed positio ad attitude data. Iitial values for all ukows could also be made available.

5 The stadard deviatios used for the weight matrix were as follows (see table 1): image coordiates object space coords. of GCP GPS/IMU positio GPS/IMU roll, pitch GPS/IMU yaw ± 6 µm ± 0.01 m i X,Y ad Z ± 0.1 m ± 5 deg * 10-3 ± 8 deg * 10-3 Table 1: Stadard deviatios of observatios used for sesor calibratio All observatios were cosidered as ucorrelated, because o other iformatio was available. The values for the positio ad attitude data are those reported by Applaix. I the adjustmet, all seve parameters could be determied with high sigificace. Whereas the results for the six covetioal parameters were relatively small, the time offset was foud to be 5.3 msec with stadard deviatio of 0.3 msec, ad thus approximately oe cycle of the 200 Hz data set. As metioed before, however, this value must be iterpreted as a combiatio of time offset ad correctio to the pricipal poit i flight directio. 5 3D poit determiatio 5.1 Poit determiatio with a sigle baselie I the ext step, we computed object space coordiates for those GCP which had ot bee used i the calibratio. We used the images from the project flight ad oly two rays per poit ad computed the 3D coordiates via forward itersectio. I this step the calibratio parameters were used as costat values 1. The project flight was covered by approximately 50 stereo models. All computatios were carried out for each of the available five referece statios. The results are show i table 2. For each baselie the mea accuracy of the GPS/IMU observatios are give. The positio values come from differetial GPS solutios ad represet more or less the accuracy of the GPS geometric cofiguratio (satellite visibility ad legth of baselie). The attitude values had to be take from the compay iformatio sice o other iformatio was available. I the right colum the RMS differeces betwee the computed object space coordiates ad the kow values for the 41 idepedet cotrol poits (most of them were ot itroduced i the calibratio phase) are give. Ref. statio (legth of baselie) Raade (8-30 km) Moss (15-38 km) Torp (20-50 km) Soer (25-60 km) Stavager (307 km) Table 2: Mea accuracy of GPS/IMU positio ad attitude positio [cm] attitude [deg * 10-3 ] Xo Zo roll, Yo pitch RMS differeces at ICP [cm] yaw X,Y Z 2,5 6,7 ~ 5 ~ 8 8,0 14,5 3,1 7,1 ~ 5 ~ 8 8,1 14,8 3,5 8,2 ~ 5 ~ 8 8,3 15,1 3,5 8,1 ~ 5 ~ 8 8,5 15,4 4,5 11,5 ~ 5 ~ 8 10,2 19,1 Results of direct 3D poit determiatio at idepedet check poits (ICP) usig two-ray poits ad sigle referece statios, image scale 1: GPS etwork solutio We ow tur to the GPS etwork solutio. I order to better demostrate the effects of this approach we select oly two strips, oe with good overall GPS data, ad aother oe with somewhat worse data. Figure 2 shows the same iformatio for the referece statio Torp as figure 1 does for Raade. It ca be see that strip 1 has a small ad thus a good PDOP value for both referece statios. Strip 2 has a small PDOP for Torp, but a higher oe for Raade. The graphs for the referece statios Moss ad Soer are similar to those for Raade. We therefore expect, that the results of strip 1 will be good overall, ad will ot be effected by the etwork solutio. Strip 2, o the other had, should show good results whe computed with statio Torp, but worse results whe computed from Raade. Oe of the questios was i how far a etwork solutio would be able to improve the results obtaied with the Raade statio. The results are show i table 3. The expected tedecy ca be observed whe ispectig the values i the table, The results are i the rage of 8 cm i plaimetry ad 15 cm i height at idepedet check poits for short baselie (util 60 km). For the loger baselie at Stavager (approximately 300 km) we obtaied RMS values i the rage of 10 cm i X, Y ad 19 cm i Z. The differeces represet the weaker geometric GPS cofiguratio ad possibly differet atmospheric coditios betwee the test field ad Stavager, which ca ot be compesated by differetial GPS strategies. It should be metioed that these results, obtaied with imagery of scale 1: compare very favourable to the results obtaied i the OEEPE test (Heipke et al. 2002b). 1 Note that separate sets of calibratio parameters were computed for each referece statio, ad these were used i all followig computatios. Figure 3: Accuracy of GPS positio, referece statio Torp

6 especially i height. The RMS values i Z of strip 2 for Raade, Moss ad Soer are larger tha the oe for Torp. It ca also be see that the etwork solutio yields slightly better results especially compared to those statios with a larger PDOP. While the improvemets i accuracy are ot very large i this example, it should be kept i mid, that potetial GPS errors occurrig at a particular referece statio caot be detected if oly oe statio is used. Therefore, the reliability of a solutio based o a sigle referece statio is ot very high. By usig the suggested etwork solutio, which has already foud wide applicability i other GPS applicatios, the reliability of the results ca be sigificatly improved. Havig said this, it should also be metioed that problems cocerig the GPS receiver i the aircraft ca of course oly be detected ad elimiated by usig multiple GPS equipmet o board the plae. RMS differeces at Used ref. Strip PDOP ICPs (two-ray-poits) Statio sxy [cm] SZ [cm] Raade Strip 1 1,8 7,8 13,7 (8 30 km) Strip 2 3,3 8,3 14,8 Moss Strip 1 1,8 8,1 14,1 (15 38 km) Strip 2 3,2 8,4 14,5 Torp Strip 1 1,7 8,1 14,0 (20 50 km) Strip 2 1,9 7,9 13,9 Soer Strip 1 1,9 8,2 14,6 (35 60 km) Strip 2 3,3 8,9 15,8 Network solutio (8 60 km) Network solutio (8 60 km) Table 3: 6 Coclusio Strip 1-7,9 13,8 Strip 2-8,0 14,0 Results of direct 3D poit determiatio at idepedet check poits (ICP) usig two-ray poits ad sigle referece statios ad the etwork solutio, idividual strips, image scale 1: Direct sesor orietatio has prove to be a serious alterative to aerial triagulatio. I this paper, a solutio for direct sesor orietatio based o sigle referece statios ad o a GPS etwork was described, test results based o the OEEPE test Itegrated sesor orietatio were reported. Our work resulted i RMS differeces of 8 cm i plaimetry ad 14 cm i height at idepedet check poits obtaied with two-ray poits a image scale 1: for sigle, short baselies. The etwork solutio was show to be slightly more accurate tha the sigle baselie solutio, moreover the reliability of the results is sigificatly higher. 7 Refereces Ackerma, F. 1994: O the status ad accuracy performace of GPS photogrammetry. I: Proceedigs, ASPRS Workshop "Mappig ad remote sesig tools for the 21st Cetury, Washigto D.C., USA, pp Applaix 1999: POS/DG POS/AV 510-DG Specificatios, Otario, Caada (May 6, 2004). ARINC : (May 6, 2004). Bäumker, M.; Heimes, F. J. 2002: New Calibratio ad Computig Method for Direct Georeferecig of Image ad Scaer Data Usig the Positio ad Agular Data of a Hybrid Itertial Navigatio System i: Itegrated Sesor Orietatio, OEEPE Official Publicatio No. 43, Budesamt für Kartographie ud Geodäsie, Frakfurt/Mai, pp Cramer, M. 1999: Direct geocodig - is aerial triagulatio obsolete? I: Photogrammetric Week 99; Fritsch/Spiller (Ed.), Herbert Wichma Verlag, Heidelberg, pp Grewal, M. S.; Adrews A. P., 2001:Kalma Filterig Theory ad Practice Usig Matlab; Wiley-Itersciece Publicatio, New York (USA). pp Heipke, C.; Jacobse, K.; Wegma, H.; Aderse O.; Nilse Jr. B (a): Test goals ad test set up for the OEEPE test "Itegrated Sesor Orietatio". I: Itegrated Sesor Orietatio, OEEPE Official Publicatio No. 43, Budesamt für Kartographie ud Geodäsie, Frakfurt/Mai, pp Heipke, C.; Jacobse, K.; Wegma, H (b): Aalysis of the results of the OEEPE test "Itegrated Sesor Orietatio". I: Itegrated Sesor Orietatio, OEEPE Official Publicatio No. 43, Budesamt für Kartographie ud Geodäsie, Frakfurt/Mai, pp Jacobse, K. 1991: Treds i GPD photogrammetry, ASPRS Aual Covetio 1991, Baltimore, Vol. 5, pp Jacobse, K. 2002: Trasformatios ad computatio of orietatio data i differet coordiate systems. I: Itegrated Sesor Orietatio, OEEPE Official Publicatio No. 43, Budesamt für Kartographie ud Geodäsie, Frakfurt/Mai, Germay, pp Nilse Jr., B. 2002: Test field Frederikstad ad data acquisitio for the OEEPE test "Itegrated Sesor Orietatio" i: Itegrated Sesor Orietatio, OEEPE Official Publicatio No. 43, Budesamt für Kartographie ud Geodäsie, Frakfurt/Mai, Germay, pp Ressl, C., 2002: The impact of coformal map projectios o direct georeferecig. Iteratioal Archives of Photogrammetry ad Remote Sesig, Vol. 34, Part 3A, pp ISPRS Commissio III Symposium 2002, Sept. 9-13, Graz, Austria. Schwarz, K. P.; Fraser, C.; Gustafso, P. 1984: Aerotriagulatio without Groud Cotrol, Iteratioal Archives of Photogrammetry ad Remote Sesig, Vol. 25, Part A1, pp Schwarz K.-P.; Chapma M.E.; Cao E., Gog P. 1993: A itegrated INS/GPS approach to the georeferecig of remotely sesed data, Photogrammetric Egieerig & Remote Sesig Vol. 59, No. 11, pp Seeber, G. 2003: Satellite Geodesy 2d Editio. Foudatios, Methods ad Applicatios; Walter de Gruyter, Berli. Skaloud, J. 1999: Optimizig Georeferecig of Airbore Survey Systems by INS/DGPS. Ph. D. Thesis, UCGE Report Uiversity of Calgary, Alberta, Caada. pp. 160.