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The set of velocities used is chosen to cover the 
expected span of velocities, and the velocity step is chosen 
according to the accuracy with which the velocity has to be 
known in order to obtain an output image with satisfactory 
quality. 
The appropriate step size in time direction is 
determined by several factors. The minimum step length is 
approximately equal to the length of the reference filter 
used. In case of velocity variations on a shorter time scale 
than the filter length, the filter will average out the 
velocity variations, and the estimate will be an average of 
the actual velocities. For velocity variations on a longer 
time scale than the processing vector length, which 
typically is several times the length of the reference 
filter, the velocity can be considered constant for one 
processing block, and the problem with varying platform 
velocity will appear only when combining several images. 
This is the typical situation for satellite borne SAR's. For 
velocities that vary on a time scale between reference 
filter length and processing vector length the method 
described here is applicable. 
When the platform velocity as a function of time 
has been estimated, the recorded data must be compressed 
according to this velocity history. As mentioned above, this 
corresponds to applying a time-varying filter to the 
original data. To avoid this problem the approach chosen 
here is to correct the uncompressed data according to the 
set of velocities to make the samples equally spaced, and 
then compress the corrected data with a time-invariant 
filter. This actually corresponds to the feedback loop from 
the navigation system to the pulse repetition frequency of 
the radar, but in our case we achieve equally spaced samples 
by interpolating in the recorded data in the along-track 
direction. Since this is independent of range, the inter- 
polation is identical for all range bins. 
An additional benefit of this correction method is 
that it performs automatic geometric correction of the image 
in the along-track direction, since it results in equally 
spaced samples. 
Up to- this ^point only variations in platform 
velocity in the along-track direction have been considered. 
The recorded target phase histories are, however, highly 
sensitive to platform movements in the cross-track 
direction. Such irregularities will introduce phase errors 
similar to the ones mentioned above, but in this case it is 
not caused by unequally spaced samples. If the sum of these 
Cross-track deviations over the length of the synthetic 
aperture is well below one range bin, however, the same 
correction method can be used to produce an improved output 
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