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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
in order to secure the performance of in-flight image quality. 
This processing line will be implemented under the 
characteristics of the PHR system for an experimental in-flight 
commissioning checking, on a specific campaign which will 
amend by command the mechanical characteristics and generate 
vibrations. 
First, an overview of data and background will be shown. 
Second, we will explain the principles of the new local 
integration method and its results. Third, the PHR system 
characteristics for this processing application are explained. 
And fourth we will give the performance of the algorithm on 
several cases of simulation for the PHR system, which is 
broadly satisfactory. 
Image 2 :« maître » 
Image 2 :« secondaire » 
Terrain 
(MNT) 
As it will be shown further, the new integration method is 
applicable to the restitution of harmonic or quasi-harmonic 
signals, in stationary or quasi-stationary state,. It performs a 
local restitution of desired signal in temporal space, at each 
time step, using all together the different differentials measured 
around the processed time. Because signals are processed in the 
temporal space, the sampling of the measurements may be 
irregular or have some gaps. It is not necessary to observe all 
the signal : it is a local integration and hence it may be done in 
real time. 
The processing will be detailed in order to show first, the 
measurements method by colocalisation and sub pixel level 
image matching, second, the algorithm which performs the line 
by line synthesis of all the measurements of each retinas 
couples correlations, allowed thanks to the supposed quasi 
parallelism of couple arrays, third, the integration step. We will 
detailed also some further post-processes to this microvibrations 
restitution like filtering, plugging gaps and completion on the 
signal edges, eventually with correlation results between distant 
non-parallel retinas. These post-processes allow us to retrieve 
the most accurate signal over a maximum of time samples 
without extrapolation. 
2. DATA AND BACKGROUND 
This article is focused on the process of only one product of a 
pushbroom satellite. The available measurements are the results 
of the comparison between at least two images of the same 
product on the same landscape, viewed at different times with 
slightly different angles. In the following, we denote by 
“couple” one ensemble of 2 images leading to one time- 
dependant measurement of a differential of the disruptive signal. 
The comparison between the 2 images of a couple is made by 
correlation (similarity) taking into account the two images 
geometrical Models: Position of the satellite (Orbito), Line of 
sight Attitude (AOCS restitution Loop), detector viewing 
directions(DV) and terrain relief (Sensitivity depends on the B / 
H ratio). Calculated residues dc (pixel displacement in the 
swath) and dl (pixel displacement in time) from one image to 
another correspond to deviations from the assumptions of 
matching (“predicted shifts”). 
These differences have several origins: 
• Attitude inaccuracy: lack of knowledge and instability 
• Disregard Land (MNT / MNS) (effect of B / H ratio 
and the localization error) 
• viewing directions model error 
• correlation noise 
Figure 1. 2 images of the same product with disruptive 
vibrations 
In the following, we state a very low B / H ratio (and thus an 
insensitivity to DTM) and a good accuracy of the geometric 
models returned. Taking account of the focal plane rigidity, we 
can thus make a physical interpretation of dc(t) displacements 
as a sensor roll differential and dl(t) displacements as a sensor 
pitch differential. But measurements by correlation are very 
noisy. It is a major error contributor that must be taken into 
account in algorithm design, indeed, standard deviation of 
correlation noise (supposedly Gaussian) may range from. 10% 
to 20% of dc or dl. 
In 2002-2004, on SPOT5, the correction of absorbed rocking 
of the line of sight corrector mirror on the image have been 
studied, because the tranquilisation time was chosen too short 
at the beginning of the in-flight commissioning. 
First, A. Bouillon has analyzed and calibrated this instability 
phenomena by correlation between Pan HMA retina and HMB 
retina (Breton, 2003). She found a correction model 
corresponding to an extinguishing Sinus with a linear 
frequency drift. Secondly, J. Jouvray has created an image 
processing correction (for CNES during a training period in 
2004) which computes correlation between PAN / XS with 
prediction of localisation (B / H ratio ~ 0,017) and computes 
the correction by a global synthesis with least squares (on all 
points of measurement), modelising each shift with simple 
analytical formula of partial differential. 
The geometric models has been then refined with 20 
parameters: vibration roll with absorption, amplitude and chirp 
characteristic, attitude LF (polynomial degree 3), 
magnification and LF DTM errors. 
PAN XS(1 2 3.4) 
Défilement 
; \ Sat 
capteurs PAN et XS 
Visé« Visée Visé« 
oblique vertical« oblique 
Figure 2. SPOT5 characteristics 
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