Jacek Grodecki , jgrodecki@spaceimaging.com
James Lutes , jlutes@spaceimaging.com
Space Imaging
12076 Grant Street, Thornton, CO 80241
Since its launch in September of 1999, the IKONOS satellite has undergone a series of geometric calibrations. The IKONOS geometric sensor model includes the interior orientation parameters, i.e. the
Field Angle Map (FAM), and the elements of the exterior orientation parameter set, namely the interlock angles. The initial values of the interlock angles and the FAM parameters were determined by pre-launch measurements. They were subsequently refined by a series of on-orbit geometric calibrations. This paper presents the results of the most recent on-orbit geometric calibration and describes a prototype offline system developed for that purpose.
Dial and Grodecki [2002 & 2003] presented results of accuracy tests of monoscopic and stereoscopic images, which demonstrated excellent absolute and relative accuracy within an IKONOS image. Good long term stability of the exterior orientation is shown in [Grodecki and Dial, 2002] by comparing the interlock angle errors over a period of a few years. IKONOS geometric accuracy has also been verified empirically against various test ranges by Grodecki and Dial [2002], Ager [2003], and Fraser and Hanley [2004].
High absolute and relative geometric accuracy of IKONOS reported by these various authors is due to a stable thermal-mechanical environment inside the spacecraft, sophisticated ephemeris and attitude determination, and advanced ground processing.
IKONOS geometric accuracy has been continuously improved by a series of on-going geometric calibrations. The present paper describes methodology and the results of the most recent on-orbit geometric calibration.
The IKONOS satellite orbits the earth in a sun synchronous orbit at an altitude of about 680 km. It simultaneously collects imagery in four multispectral bands with a ground sampling distance (GSD) of 3.28 m at nadir, and a panchromatic band with a GSD of 0.82 m. The nominal IKONOS swath width is 13 km.
All five bands are collected at an 11-bit radiometric resolution. The spectral characteristics of the IKONOS multispectral bands are approximately the same as the LANDSAT TM bands 1 through 4.
IKONOS is a fully agile satellite, i.e. it can be pitched and rolled to any off-nadir angle to acquire an image. The revisit time depends on the magnitude of the off-nadir acquisition angle. For example, at 26 degrees off-nadir (equivalent to approximately 1m GSD) the revisit time is about 3 days.
The IKONOS physical camera model comprises the interior orientation parameters, i.e. the Field Angle
Map (FAM), and the exterior orientation parameters. The FAM provides a functional relationship between the pixel location on the focal plane and the unit vector defining the ray direction out of the camera. The exterior orientation parameters include satellite attitude and position. Satellite position is determined using
GPS. Satellite attitude is measured by on-board star trackers and gyros. Interlock angles relate the satellite attitude to the camera orientation.

Additional information on the IKONOS satellite can be found in [Grodecki and Dial, 2001].
The initial IKONOS interior and exterior orientation parameters were determined by pre-launch assembly measurements. The post-launch IKONOS geometric accuracy was subsequently verified during the On-
Orbit Acceptance Test (OOAT) [Grodecki and Dial, 2001]. The OOAT showed that the absolute horizontal and vertical accuracy of uncontrolled IKONOS stereo images was better than 6 meters.
The original geometric calibration parameters were subsequently refined by a series of in-flight calibrations. The 2001 in-flight calibration is described in [Grodecki and Dial, 2002]. The reported geometric accuracy of the 2001 calibration over a large stereo image block was 4.4 m CE90 and 2.7 m
LE90 for an uncontrolled case, and 2.7 m CE90 and 2.5 m LE90 with a single GCP.
The most recent on-orbit geometric calibration was conducted in 2004. The calibration methodology, data and software used for the 2004 calibration, and the FAM validation process and results are described below.
The motivation for the 2004 geometric calibration was twofold. The first objective was to remove residual imperfections in the Field Angle Map. The second objective was to test and validate a prototype system that had been developed for the purpose of calibrating the upcoming IKONOS Block 2 satellite.
A prototype offline engineering system was developed to support both the forthcoming calibrations of the
IKONOS Block 2 satellite and the independent verification and validation of the future Block 2 production system. To support these activities, the system had to satisfy the following objectives:
• It had to be physically separate from the current production system so it would not interfere with production operations.
• The camera model and image generation had to be developed independently of the current ground station implementation to support validation of the production system.
• The system had to be able to generate the current and future mix of image products.
• It needed to be modular in design, i.e. it had to have the ability to easily plug-in additional sensor models.
• Large degree of automation was required to ensure high throughput for quick turnaround.
• The system had to be inexpensive and easy to maintain.
To fulfill these requirements, a system utilizing generic PC hardware running a Linux operating system has been developed. The system uses CORBA for communication between various software modules and mySQL for database tasks.
The system architecture is based on a distributed processing paradigm. Distributed processing ensures scalability of the system, i.e. the ability to easily add image processing CPUs to increase throughput as required. Using a distributed architecture also provides for high robustness of the system and improves its fault-tolerance. For example, if any of the image processing CPUs becomes inoperative, the processing task is simply reassigned to another CPU.
The software has been written entirely in C++ using object oriented design principles, which makes it easy to modify and maintain.

We used the IKONOS sensor model to prototype and test the system. Work on the prototype started with the development of an IKONOS camera model object. The IKONOS camera model object provided us with the capability to perform rigorous image-to-ground and ground-to-image transformations, and could thus serve as the basis for further work, i.e. development of image rectification and block adjustment software.
Image rectification was tackled next. The image rectification software takes as input the “raw” IKONOS images and attitude and ephemeris data to produce various rectified products including radiometrically corrected synthetic array (Level 1) products, georectified (Level 2 & 3) products, and orthorectified (Level
4) products. The software also performs pan-sharpening and estimation of the Rational Polynomial Camera
(RPC) coefficients.
Block adjustment software was designed in such a way that it would have an inherent multisource capability, i.e. images described by different camera models could be block adjusted together. The prototype was implemented with two camera models: the IKONOS physical camera model and the RPC model. Different camera models are implemented as derived objects which facilitates adding new sensors.
Partitioning algorithms have been implemented to minimize memory requirements and speed up computations. This allows accommodating a large number of tie points. Tie points can be either picked manually or can be generated automatically using image-to-image correlation over features identified using the Förstner interest operator [Förstner and Gülch, 1987].
Finally, system management software that automates product ordering and processing tasks was put together. It has the ability to distribute product orders to different processing units based on their workload, and uses CORBA and a mySQL database for progress monitoring and reporting.
Generic off-the-shelf Intel based PCs were used to put together the prototype system. Six PCs in total were used for the prototype. Each unit runs a Pentium4 3.2GHz CPU, has 1 GB of RAM and two 160GB IDE hard drives. A Gigabit Ethernet local network was put in place to connect all units.
Using low cost generic hardware minimized the initial set up cost and made the system easy to expand and upgrade in the future.
Despite using inexpensive generic hardware, the prototype system achieved respectable throughput rates.
The sustained throughput of the system was clocked at 300 GB per day, which translates to 1,600 standard
10 km by 10 km IKONOS images in a 24 hour period.
IKONOS scenes and ground control from two separate test ranges were used for FAM recalibration: the
San Diego test range with 147 ground control points (GCPs), and the Thornton test range with 45 GCPs.
Two reverse scan scenes covering the San Diego test range were used for FAM calibration. Figure 1 shows
the layout of scenes and ground control points used in the analysis. Of the 147 GCPs available in the San
Diego area, 43 fell within the scene footprints and were identifiable.

Figure 1. San Diego scenes and GCP layout
Figure 2. Thornton scenes and GCP layout

Six scenes covering the Thornton test range, comprising three reverse and three forward scans, were also used. 45 GCPs from the 128 th
Street test range were used as well. Figure 2 shows the layout of scenes and
GCPs.
All identifiable ground control points were measured in the panchromatic band of each source image.
Automated image correlation software was used to add a large number of tie points between all the panchromatic (Pan) bands and all the multispectral (MSI) bands. Tie points were identified both between bands and between scenes; that is, a tie point could have been identified in all 5 bands of each scene. On average, each tie point was identified in approximately 6 scenes. Initial tie point locations were selected in one of the pan scenes by using the Förstner operator [Förstner and Gülch, 1987] to find areas of interest.
This generated a large number of points, and a total of 13719 tie points were eventually measured in the images, which allowed for aggressive outlier detection and removal in the least squares estimation process.
The Thornton test range provides a good illustration of the resulting FAM accuracy, because the east-west line of control points captures a good snapshot of sensor geometry that is largely independent of any changes in motion or attitude of the satellite.
The following figures show the image space residuals for Thornton GCPs plotted against their east-west extents. It is seen that no obvious trends are present, and all residuals are below one pixel.
Image residuals (Sample)
3
2
-2
-3
1
0
0
-1
2000 4000 6000 8000 10000 12000
Sample (west-east) [m]
Figure 3. Sample residuals vs. West-East extents (all Thornton images)
14000

Image residuals (Line)
3
2
1
0
0
-1
2000 4000 6000 8000 10000 12000 14000
-2
-3
Sample (west-east) [km]
Figure 4. Line residuals vs. West-East extents (all Thornton images)
A test range in Mississippi, consisting of 6 stereo pairs and 40 GCPs, was used for validating the results of
FAM calibration.
Figure 5. Mississippi test block layout

As shown by Grodecki [2001] and Lutes [2004], RPCs accurately represent the IKONOS physical camera model (to better than 0.05 pixels) and thus could be used for the FAM validation in lieu of the physical camera model. Georectified (Level 2) scenes, whose imaging geometry is described by RPC models, were thus generated for all 12 source images using the new FAM.
Image space locations of the ground control points and tie points were identified in the Level 2 scenes.
Figure 5 illustrates the layout of ground control and tie points. In the overlap between stereo pairs, tie
points were measured in all four images.
The Level 2 images were block adjusted using the RPC block adjustment model, given in [Grodecki and
Dial, 2003] as:
L = R
L
( φ , λ , h ) + a o
+ a
L
L n
+ ε
L
(1)
S = R
S
( φ , λ , h ) + b o
+ b
L
L n
+ ε
S
(2) where
( φ , λ , h) are the latitude, longitude, and height,
L, S are the measured image line and sample coordinates,
L n
is the approximate fixed value for the true image line coordinate,
R
L
, R
S
are the nominal ground to image RPC functions for line and sample, provided with the
IKONOS images, a o
, b o
= adjustable bias parameters for line and sample, a
L
, b
L
= adjustable drift parameters for line and sample, and
ε
L
, ε
S
= random unobservable line and sample errors.
To quantify block adjustment accuracy as a function of a number and distribution of ground control points,
GCPs were selectively changed to check points.
The block adjustment was run once using all tie points and ground control, and then the average line and sample bias terms ( a o
, b o
) were used to estimate corrections to the interlock angles. Using the new interlock angles, the Level 2 scenes were regenerated and the block adjustment was repeated. It should be noted that Space Imaging has an ongoing process to monitor and refine interlock angles using the MTF target (cf. [Grodecki and Dial, 2002]). The goal is to monitor interlock stability and ensure continuity between consecutive calibration campaigns.
In the second run, the ground control was used as checkpoints only. Figure 6 shows the distribution of
residual errors at the checkpoints, where red vectors illustrate horizontal errors and green vectors are vertical errors. The results indicate 1.5 m CE90 horizontal and 2.2 m LE90 vertical accuracy.

Lon Lat Ht
----- ----- -----
Average 0.19 -0.08 1.32
Std Dev 0.74 0.67 1.06
CE90/LE90 1.53 2.19
(computed at checkpoints only)
Figure 6. Ground space checkpoint residuals, tie point-only block adjustment
Looking at the checkpoint errors in image space rather than ground space, similar numbers are seen, as
depicted in Figure 7.
When all ground control points are added to the block, the accuracy further improves, to 0.89 m CE90 (see
Figure 8).
It is seen that in either of the block adjustment cases no systematic residual error trends can be observed, thus validating the new FAM.

Samp Line
----- -----
Average 0.04 -0.03
Std Dev 0.91 0.93
CE90 1.97
(computed at checkpoints only)
Figure 7. Image space checkpoint residuals, tie point-only block adjustment

Samp Line
----- -----
Average 0.00 0.00
Std Dev 0.39 0.44
CE90 0.89
(computed at GCPs only)
Figure 8. Image space GCP residuals, block adjustment with all GCPs and tiepoints
To visually inspect accuracy of the interior orientation, a stereo pair over a flat area was reprocessed using the new FAM and a DEM was extracted. The DEM elevations were scaled by a factor of 10 to accentuate any potential anomalies in the shaded relief. The resulting shaded relief (see Figure 9) shows no trace of any DEM anomalies.
Figure 9. DEM created using new FAM

For testing Pan-MSI registration, Pan-MSI bundle products were generated for all six Thornton scenes. For each scene, the misregistration of each MSI band with respect to the Pan band was measured using automated image correlation. In all cases the Pan-MSI registration was better that 0.25 MSI pixel, well within specification. As the next step, a sample pan-sharpened image (see Figure 10 below) was generated to make sure that no image artifacts due to Pan-MSI misregistration were seen in the image.
Figure 10. Sample pan-sharpened image.
In summary, the 2004 in-flight calibration achieved all of its objectives. As demonstrated by the validation tests, the new FAM has excellent accuracy and the resulting images are free of any perceptible artifacts.
We also successfully tested and validated our prototype off-line production/calibration system that has since been used for troubleshooting various production issues and resulted in improvements to our main production system, has supported ongoing radiometric calibration activities, and is currently being used for prototyping a range of IKONOS and other image products.
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