ADVANCES AND LIMITATIONS IN A PARAMETRIC GEOMETRIC CORRECTION OF CHRIS/PROBA DATA Luis Alonso, José Moreno LEO Group, Dpt. de Termodinamica, Univ. Valencia, Dr. Moliner 50, 46100 Burjassot, Spain, Email:luis.alonso@uv.es ABSTRACT/RESUME The geometric correction of remote sensing images is a preprocessing step required for most applications and studies. The success of CHRIS/PROBA as scientific mission is producing a large archive of image sets that is continuously growing. Although the geometric correction problem is already solved by means of ground control points (GCP) or image corregistration techniques, these methods require intense human intervention. Therefore they are not convenient for processing large number of images. For this reason the development of a quasi-automatic parametric algorithm for geometric correction of CHRIS/PROBA data was undertaken by our group. This work has given rise to some questions about the image acquisition procedure. As a result new information about the operation of CHRIS/PROBA has recently become available for the user community, pointing out that the operation for acquisition is based on time, instead of fixed fly-by zenith angles (FZAs), as was documented previously. It also states that to determine each particular acquisition the system assumes a circular orbit with radius equal to the semi-major axis. This paper presents a study of the implication that the new information has on how the parametric algorithm must be implemented, as well as the impact on the acquisition geometry, the observation angles, and the pointing accuracy. 1. INTRODUCTION CHRIS/PROBA is the first hyperspectral sensor with pointing capabilities and high spatial resolution. Initially designed as a technology demonstrator, the uniqueness of the data obtained has probed to be very useful for scientific studies. In order to make full use of the CHRIS/PROBA multiangular capability, all five images from a given acquisition set must be accurately co-registered to make sure that the values measured from a given coordinate actually correspond to the same surface for the five angles. To achieve this, it is necessary an accurate geometric correction or geolocation algorithm. Every pixel of each image must have a geographic coordinate assigned. The current algorithms based on Ground Control Points GCP cannot assure this level of co-registration between acquisitions for different reasons: the need of a homogeneous distribution of GCPs throughout the image, the interpolation process between GCPs unable to compene the local non-linear distortions within the image, and in particular, the reduced across-track spatial resolution of the larger Fly-by Zenith Angle (FZA) images makes it more difficult to assign GCPs (subpixel precision would be required). For the Barrax test site in La Mancha (Spain), which is optimal for this type of approach due to its flatness, the number and size of fields, and landscape features that allow setting a large number of GCPs, there are portions of the images that have up to three pixels of error in the co-registration, corresponding to approximately 100m. Therefore, in those portions of the image, only fields larger than 200m will have enough number of pixels coregistered in the five observation angles. Also, the distortions introduced by the GCP correction are inhomogeneously distributed throughout the scene. This method is particularly problematic for water studies, due to the impossibility to set GCP within the water area; especially difficult is the case of coastal waters where GCP can only be assigned to a portion (sometimes small) of the image. Therefore, an algorithm for accurate geolocation is needed. Such algorithm was proposed by our group in the 2nd CHRIS/PROBA workshop [1], taking a parametric approach that would reproduce in detail the actual ellite orbit and the acquisition process, based on the knowledge available about the operation of the platform and the sensor. 2. PARAMETRIC ALGORITHM A parametric geometric correction would allow geolocation with higher accuracy, without introducing inhomogeneous distortions in the images. In flat study sites where topography has no impact in the geometry of the problem, a simple parametric method (without the use of a digital elevation model (DEM)) would provide almost direct corrections, with very little adjustments and supervision. The work done to develop this algorithm raised a number of questions about details of the operation of the Proc. of the 3rd ESA CHRIS/Proba Workshop, 21 23 March, ESRIN, Frascati, Italy, (ESA SP-593, June 2005)
ellite. These questions were answered in a recent communication by ESA to the CHRIS/PROBA users [2]. In this communication the actual acquisition procedure was detailed, and it strongly differed from what was commonly known. The algorithm was based on the assumption that the images were acquired at fixed observation angles, depicted in Figure 1. According to the documentation available at the time [3], the observation angles of each image were defined by the Fly-by Zenith Angle (FZA) and the Minimum Zenith Angle (MZA) [1,3], and the images were acquired in such a way that the centre of the images corresponded to a FZA of 0º, ±36º and ±55º; and the acquisition time was 10s for each image. According to recently released documentation it seems that this is just a simplified description of the actual procedure, which in reality operates on a time basis, instead of a fixed angles basis. FZA = +55 FZA = +36 FZA = -55 orbit FZA = -36 ground track FZA = 0 MZA N target site Figure 1. Nominal FZA and its relation to azimuth and zenith observation angles. The first documentation on CHRIS/PROBA defined the image acquisition to be angle based. To determine and program the operation of the ellite for the acquisition procedure the system follows a series of steps: Using the ellite s position and velocity at 390s prior to acquisition start the semi-major axis of the orbit and the angular velocity are calculated. From this moment until the end of the acquisition the orbit is assumed to be circular, with radius equal to the calculated semi-major axis. Then the five acquisitions are defined to take place within a cone of 55º centred on the target. The total time of observation (the time elapsed from the start of the first image acquisition to the end of the last image acquisition) is the time that the platform needs to cross this cone. The total observation time (Tobs) is then divided into scan time (Tsc), slew time (Tsl) and margin time (Tmar). Scan time is fixed to 20s for the image acquisition, slew time is dedicated to reorient the ellite for the next acquisition in 12.5s, and margin time is added before and after scan time to damp transients and its duration is determined by the other elements of Tobs. Tobs = Tsc + Tmar + 1st acquisition Tsl + Tmar + Tsc + Tmar + 2nd acquisition Tsl + Tmar + Tsc + Tmar + 3rd acquisition Tsl + Tmar + Tsc + Tmar + 4th acquisition Tsl + Tmar + Tsc 5th acquisition Once the timing is determined, the??? and Control System calculates the necessary attitude change rates to keep the target on sight while scanning the area with a slowdown factor of 5 to increase the integration time. The actual onboard implementation of the pointing manoeuvre restricts the rotation to two axis: pitch and roll. The above procedure results in a set of different FZA angles for different altitudes of the ellite, according to Chris Data Format Issue4 [4] reflected in Table 1. Table 1. Change of FZA with ellite altitude Max altitude Min. altitude ±55 FZA angles ( ) ±49.52 ±56.18 ±36 FZA angles ( ) ±29.27 ±32.02 Inclination ( ) 97.81 97.81 Period (min) 98.33 95.596 Altitude (km) 678.8 547.4 3. NEW APPROACH FOR PARAMETRIC MODEL Then new information about the acquisition procedure implies a radical change in the whole concept of how CHRIS/PROBA works. The parametric approach is still feasible but the complete structure of the model had to be adapted to simulate the actual acquisition procedure. One advantage of the new approach is that the inputs required by the model have been r reduced to: - Satellite position ( R ) at orbit fixation time. r - Velocity vector ( V ) at orbit fixation time. - Target coordinates ( R r tgt ) These data permits to calculate all the parameters that will determine the ellite evolution with respect to the target in the following minutes [5].
One of the most relevant parameters is the semi-major axis, obtained with Eq. 1, where GM is the gravitation constant of the Earth. 1 = 2 R r V r (1) 2 GM The angular momentum H defines the orbital plane and its rotation axis: r H = R r V r (2) Using the semi-major axis a it is possible to calculate the angular velocity ω of the ellite and the φ angle, necessary to calculate the total observation time T obs and the time evolution of the platform: ω = GM 3 φ = 55º asin cos(35º) r a max R tgt (3) (4) Finally, it is possible to obtain the observation time, that determines the whole acquisition process: T obs = 2 φ ω (5) 4. TEST CASE FOR THE MODEL To test the algorithm we have focused on the acquisition of the 12th of July, 2003. For this date we have available the telemetry data and the corresponding TLE. These data allow checking the consistency of the method, as both provide the necessary information to retrieve the ellite s position and velocity at a given time, as well as other orbital parameter while they are obtained with different methods. Using both types of data we have calculated the circular orbit that corresponds to the acquisition procedure, and have found a significant difference between the actual altitude of the platform and the corresponding semimajor axis at the moment of orbit fixation, shown in Table 2; obtaining similar results from telemetry and TLE propagation. Table 2. Difference between actual ellite height from Earth centre and calculated semi-major axis at the moment of orbit fixation, derived by the two methods. Units are in kilometers. Sat. height Difference: Telemetry 7019.9 6970.0 49.9 TLE Estimation 7020.0 6972.4 47.6 Difference: -0.1-2.4 Ground height: 6378.8 The difference is of 49.9km in the case of telemetry data, and 47.6km in the case of TLE propagation. This difference that might seem small in comparison to the distance of the ellite to the Earth s centre turns very significant with respect to the altitude of the platform over the Earth s surface. In this test case it represents a decrement of 7.8% on the altitude above ground of the ellite, see Fig. 3. Because the whole determination of the ellite pointing and imaging programming depends on the assumption of a circular orbit of radius equal to the semi-major axis the difference between and the actual altitude can have a big impact in the accurate determination of the observation angles. 7075 6975 6875 6775 6675 6575 6475 6375 Altitude from Earth centre [km] actual altitude estimated Ground 1 3 5 7 9 11 13 15 17 19 21 23 25 27 Telemetry sample Figure 2. Actual altitude of the ellite and the altitude of the corresponding semi-major axis. The vertical lines indicate the instants of orbit fixation (yellow), image acquisition start (green) and end (red). The situation worsens when we look at the evolution of the actual altitude of the ellite, which increases as it overpasses the target area, as illustrated in Fig. 3; the increment of altitude, with respect to the altitude at the moment of orbit fixation, is 15km at the start of image acquisition and 20km at the end of the acquisition process.
665 Sat height above ground 660 655 Height [km] 650 645 640 elliptical circular ~55º 55º 635 630 5km between 1st and 5th image 20km between orbit fix and acquisition Φ 625 1 3 5 7 9 11 13 15 17 19 21 23 25 27 Telemtry Sample Figure 3. Variation in altitude of the ellite during the orbit determination and imaging process. These results are particular to this test case, but it is possible to determine how the situation would be for the extreme cases of the orbit in that date, that is, if the acquisition occurs at perigee or apogee. The orbit of PROBA had an excentricity of 0.0083543 and a semimajor axis of 6972.4km according to TLE, which has results in a perigee radius of 6914km, and an apogee radius of 7031km. In these cases the error in the orbit height would be of ±58km. This difference in height has a direct impact on the accuracy of the programmed observation angles, and could produce pointing problems during image generation, as can be seen in Fig. 4. Further analysis of archived telemetry will produce sounder results about the magnitude of the effects derived from the difference in the actual height and the estimated height used for operation. 5. ANALYSIS OF POINTING ACCURACY With the aim of checking if these differences in altitude were due to some computation error or they actually represent the present situation of CHRIS/PROBA acquisition the pointing accuracy was analyzed over whole collection of acquisitions over Barrax by determining the coordinates of the centre pixel of each image and their distance to the programmed target coordinates. Figure 4. Impact of using a circular orbit of radius for acquisition determination in an elliptical orbit of higher altitude. Diagram not at scale. We restricted the analysis to those acquisitions performed during 2004, after the enhancement in the pointing accuracy with the star-trackers, in order to include only those images with the best attitude control, i.e. highest pointing capability. We have also included in this analysis the images acquired over Rosarito test site (also in Spain) to increase the significance of the results. Fig. 6 (left) shows the position of the images centres acquired the 16/07/2004 over the test site Barrax; the blue circle indicates the programmed image centre, and the blue crosses indicate de limit of a ±0.01º area (the precision of the centre coordinates). In Fig. 6 (right) a graph shows the position of the image centers for all the Barrax acquisitions during 2004. The programmed centre is the red cross, the image centre of the FZA 0º acquisitions are distinguished by symbols with an outer frame, the ±36 are filled symbols, and the ±55 are empty symbols. The inclination of the orbit at the given latitude is displayed as a black dashed line as reference of the along-track direction. The centre image pixel coordinates of the Rosarito test site have been provided by the Center for Hydrographic Studies (CEDEX) to improve the analysis. These data are plotted in Fig. 7 in a similar way than the data from Barrax.
4331000 4329000 UTM Y [m] 4327000 4325000 4323000 Programmed Centre 16/07/2004 MZA= -8º 15/07/2004 MZA= 19º 30/06/2004 MZA=-17º 27/05/2004 MZA= 14º 23/03/2004 MZA= 10º 4321000 16/07/2004 4319000 4319000 574500 576500 578500 580500 582500 584500 586500 UTM X [m] Figure 6. Center of image position: Estimation of pointing accuracy. Barrax test site (Spain). 4446000 4444000 4442000 4440000 4438000 20May MZA=14 15Jun MZA=-20 27Aug MZA=4 23Oct MZA=19 26Nov MZA=-4 FZA=0 FZA=±55 Target 20/05/2004 4436000 4434000 300500 302500 304500 306500 308500 310500 312500 UTM Easting [m] Figure 7. Center of image position: Estimation of pointing accuracy. Rosarito test site (Spain). As with all ellite imaging instruments, sources of uncertainty in CHRIS/PROBA pointing exist and lead to misalignments of the images with respect programmed pointing [4]. Typical sources of error include: Alignment (instrument and spacecraft) Datation, i.e. timing (error in time translate into errors on the computed earth rotation, hence on pointing) Limitation in the PROBA on-board feedback loop used to maintain maximum pointing accuracy during the acquisition (residual calibration errors on wheel axis and inertia ratio) The image centers alignment follow the orbit inclination rather well indicating a good across-track pointing, although they present a systematic deviation eastwards of the orbit track; this could be due to a problem of instrument alignment or a timing shift. It has also been detected a large along-track dispersion of the five images of each acquisition (FZA = 0º, ±36º
and ±55º), in some cases more than 7km, that is, more than half the size of the image. This result would be consistent with the effect of a large difference between the operational orbit height and the actual orbit height. It is also interesting to note that in many cases the centers of the ±55º images fall to the north of the 0º centre while the ±36º images centers are located to the south. This distribution cannot be explained with the arguments expressed before, which would produce an ordered dispersion. Data from other test sites would increase statistical significance of this problem, also allowing a thorough analysis of image centre coordinates, which can provide a deeper insight to improve PROBA s pointing accuracy. 6. ACTUAL TIME OF OBSERVATION Up to now we have only considered changes in altitude, in orbital mechanics a change in altitude implies a change in angular velocity, and this would affect the T obs required. It is possible to find a relationship between the observation time (T o obs) of a circular orbit that fits the actual orbit and the calculated T obs for image acquisition, using Eqs. 3 and 5 where T o obs m = = m T (6) R o implying that the time required in the actual orbit to travel an arc of 2 φ is larger than the T obs used for imaging. Hence the angular distance covered by PROBA in its orbit 2 φ in a time T obs would be obs 3/2 (7) 2 φ' = 2 φ / m (8) which is shorter than the distance needed to point the target correctly. This implies that the estimated attitude for the acquisition based on the reference orbit will be performed on an orbit that is actually at a different altitude, and which requires an observation time to cross the 55º cone that is different from the calculated T obs, illustrated in Fig.8. These two mis-estimations add up to produce an error in the pointing of the five angles that could be not necessarily consecutive (e.g. image centers located from north to south in a ±55º, 0º, ±36º, instead of -55º, -36º, 0º, +36º, +55º), contrary to the case of and appropriate T obs with wrong altitude, that would produce ordered pointing errors. circular estimated circular approximated R o 2 φ 55º Φ Figure 8. Diagram on the effect of an understimation of ellite height and time of observation. 7. CONCLUSIONS Image acquisition based on fixed time instead of fixed FZAs has serious implications in observation geometry assumptions, especially in the determination of observation angles. Parametric correction needs accurate information about location and velocity of the ellite at the orbit fixation before the image acquisition. Inputs can be retrieved from telemetry or from TLE (orbit propagation). It has been found that the assumption of a circular orbit with radius the semi-major axis could be inappropriate even for a near circular orbit like PROBA s, producing a mis-estimation of observation angles during the determination of the image acquisition procedure. Satellite pointing errors have been noticed with some systematic deviations consistent with the misestimation of the acquisition process. Further analysis could help to improve PROBA performance. Geometric correction and per pixel observation angles, our main goal, are still possible with the new approach. Despite the fact that the objective of our work is to obtain an algorithm for quasi-automatic geometric correction these results on the performance of CHRIS/PROBA acquisition procedure could be relevant for the improvement of the ellite. For this reason it now our intention to include in the model the possibility to allow changes in different parameters: - From the orbit (circular, elliptical) - From the Earth (rotation, oblanteness, etc) - From the procedure (integration time, slowdown factor, )
The nominal model could become a useful tool for sensitivity analysis on acquisition performance, or as simulator of alternative acquisition procedures. ACKNOWLEDGEMNT The authors want to thank R. Peña, J. A. Dominguez and A. Verdú for kindly providing the pointing data from the Rosarito CHRIS/PROBA test site. REFERENCES 1. Alonso L. and Moreno J., Quasi-Automatic Geometric Correction and Related Geometric Issues in the Exploitation of CHRIS/Proba Data, Proceedings of the second CHRIS/Proba Workshop, 28-30 April 2004, ESA/ESRIN, Frascati, Italy (ESA SP-578, July 2004) 2. Davidson M. and Vuilleumier P., Note on CHRIS Acquisition Procedure and Image Geometry revision 1.3, ESA, Noordwijk, The Netherlands, 2005. 3. Cutter M. A., CHRIS Data Format revision 2, SIRA, Kent, U.K., 2002. 4. Cutter M. A., CHRIS Data Format revision 4, SIRA, Kent, U.K., 2004. 5. Wertz J. R. and Larson W. J., Space mission analysis and design 3 rd ed., Dordrecht: Kluwer Academic Publishers, 1999