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Is there a simple to follow explanation of how to do second order motion compensation for range migration algorithm?

The one described in Carrara et al is for the ideal case. For the Extended Omega K algorithm, how does one relate the deviation in platform position to the amount of phase compensation to apply in terms of kx? Is it a scaling by $ 2\pi/\delta x $ where $ \delta x $ is the deviation along the azimuth, and the slant range deviation is assumed to have been compensated away via a mix of phase compensation and/or interpolation and/or pixel shifts?

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I have been trying to incorporate MoCo to the extended Omega-k as well following Reigbar's paper (https://ieeexplore.ieee.org/document/1648550). I understand that for the first order MoCo, the range deviation needs to be calculated from a reference range (i.e. image center) and for the second order, the differences between the deviation for all ranges and the deviation for the reference range need to be used. However, calculating the deviation in the above recommended method didn't work for me. Especially, I'm not sure if I calculated the deviation for the second order MoCo right. I used r = (c*fast_time)/2 for calculating all the range positions and then subtracted those from the non-ideal platform positions in order to know their range deviations. Is that correct?

Thank you.

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I think this is reasoned out as..: The Extended Omega-K gives the formulation with motion compensation integrated into the it. As an intermediate step, it retains the terms required for azimuth focusing, meaning data is unfocused in azimuth. However in range, the range cell migration has been solved. This allows a range variant motion compensation to be applied. However, the actual application of the motion compensation is the application of a phase term to compensate for motion errors. For the Extended Omega-K, this implies the use of a single carrier frequency, which is not the best, as the actual error is wavelength variant.

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