The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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M - (Rp). (Rm)- (Ra)- (Ro), (2) 
where ‘Ro’ is orbit rotation matrix, ‘R A ’ is attitude rotation 
matrix, ‘R M ’ for spacecraft master reference to payload cube 
and ‘R P ’ payload cube to optical axis of the sensor(device). 
The above relation is used by both DP s/w and SST s/w for 
Cartosat-1 and Cartosat-2 data products generation and this 
forms the major mathematical model for adjustment of interior 
and exterior parameters for Cartosat-1 and Cartosat-2. Details 
of the in-flight geometric calibration exercises carried for 
Cartosat-1 and Cartosat-2 are briefly discussed in the following 
sections. 
3. EXPERIMENTS WITH CARTOSAT-1 
One of the tasks taken up during post-launch scenario as part of 
initial phase activities is to monitor the overall system 
performance and assess the geometric quality of Cartosat-1 
data products. Initial evaluation carried out by Data Quality 
Evaluation (DQE) team on Cartosat-1 data products confirmed 
that location accuracy of the data products was high and large 
systematic differences in errors between Fore and Aft cameras 
in both scan and pixel directions (both mean and standard 
deviation) were observed. Relative scale error was also found 
to be high apart from Fore Camera results showing yaw effect. 
In fact, the location accuracy was poorer for Fore data set than 
Aft because of large view angle (26 deg.). The outputs of 
Stereo Strip Triangulation(SST) s/w in the form of GCPs’ 
residuals before and after adjustment from both cameras, for 
various dates on full pass basis, strengthened the analysis. 
Reference for the geometric in-flight calibration is the test bed 
areas, where a large number of GCPs are available with high 
accuracy. These data points (test bed GCPs) were used to 
derive alignment angles and re-estimate camera parameters 
from the initial values. Significant improvements in the 
location accuracy and internal distortion of Cartosat data 
products have been achieved after incorporating various in 
flight parameters estimated from Cartosat-1 imagery. However, 
the final accuracy of the re-estimated parameters using in-flight 
calibration procedures depend on the (i) accuracy of the 
reference data, (ii) the models used for the characterisation of 
the parameters and (iii) knowledge on the various input 
parameters. Major activities carried out as part of in-flight 
geometric calibration are described below. 
3.1 Correct usage of payload parameters 
DP and SSTS s/w use photogrammetric collinearity condition 
model to establish a precise relation between image and ground 
for products generation and DEM generation respectively. It 
was found that the values being used during initial operations 
required changes to meet the performance demands of mission. 
Analysis of location errors evaluated using a large number of 
GCP points for image products generated and SSTS results 
over test bed areas indicated that in both Fore and Aft cases 
pixel differences versus pixel number was very high and this 
was attributed to using payload cube axis as optical axis instead 
of optical axis as reference in the Cartsoat-1 camera model. 
Incorporation of correction for this - a two level transformation 
from spacecraft master reference(MRC) to payload cube (PLC) 
and then PLC to camera optical axis, brought down the error 
substantially leading to improvement of standard deviation at 
both pre(system) and post resection results of SSTS. 
3.2 Estimation of platform biases 
As mentioned earlier, location accuracy of data products were 
found to be of the order of 500m and 100m for Aft camera and 
700m and 400m for Fore camera in along and across directions 
respectively. Analysis of outputs of SSTS s/w with optimum 
GCP configurations over a segment for 8 data sets confirmed 
the presence of large errors at model as well as check points. 
Residuals at each GCP and thus mean, standard deviation and 
root mean square(RMS) were calculated at pre-resection level 
for both along and across track directions. The evaluation of 
Hyderabad (08th June ‘05) and Bangalore (28th May ‘05) test 
bed data sets for which a substantial number of accurate GCPs 
were available, indicated that there is common bias angle in 
pitch and yaw directions, which if incorporated would bring 
down the location errors observed in the data products. The 
angles estimated were about 0.04 degree in pitch and -0.06 
degree in yaw as platform attitude angles by using scan 
differences and pixel differences against time. Figure 1.0 gives 
a typical example for Fore camera for bias estimation. By 
incorporating 0.04 degrees in pitch and -0.06 degrees in yaw as 
the angle between star sensor and MRC, the location errors in 
image products were brought down. 
3.3 Estimation of Camera bias angle 
Further analysis of location error data (scan line error as a 
function of pixel number) after incorporation of above biases 
indicated that for Fore camera there is a yaw angle of about - 
0.146 degrees. While Aft showed that the yaw estimated was 
within measurement errors. This yaw angle was incorporated in 
the payload model for Fore camera (Figure 2.0). Upon using - 
0.146 deg yaw value between payload cube normal and optical 
axis of Fore camera, standard deviation at system level has 
improved. A comparative results at system level with and 
without biases is given in Table 1. 
3.4 Adjustment of focal length 
Accuracy inconsistencies between Fore & Aft seen in 
individual SST segments over test bed areas at pre-resection 
level (system level) even after accounting for all biases, 
prompted further scrutiny of systematic errors. By using error 
values and analyzing them as delta pixel as a function of pixel 
number and delta scan as a function of pixel number, one could 
obtain the corrections in focal length and residual yaw for Fore 
and Aft cameras. This exercise and analysis indicated that focal 
length numbers used for both Fore and Aft needed correction 
factor of 1.0072 and 1.00024 respectively. With adjusted focal 
length, scale variation came down from eight to maximum 
three pixels for 12000-detector array of Fore camera (Figure 3). 
For Aft camera, the effect was very negligible. 
3.5 Re-estimation of platform biases 
Though all the above exercises resulted in meeting the 
Cartosat-1 overall system level accuracy, recent evaluation of 
products confirm that there is still some residual error of 
around 150m common to both Fore and Aft being observed in 
along track direction and relative error of 100m between Fore 
and Aft in across direction. Sensitivity analysis carried