Covariance Matrix C2 for Sentinel-1 - Algorithm details

[ricvo]

Apologies if the question might seem obvious, I looked in the help of the filters but could not find the exact algorithm used to compute the C2 matrix, for Sentinel1 for example, hence a dual pol SAR.

Theory says we need to compute

but the ensemble is done spatially on a local window? Could this ensemble be done also in time if for example we have few maps on the same season in which we do not expect big variability? and if yes, is there any support for this currently?
If I understand correctly S_vv = q_vv + j * i_vv (analogously for the other term S_hv),
where q and i are exactly what we get from the raw maps of Sentinel1 SLC.

I saw that exists also a filter Radar → Polarimetric → Polarimetric Speckle Filter, which does both speckle filter and subsequent computation of C2.
Is it a good idea to make the speckle filter before C2 computation? I read on other posts in this forum that speckle filters might change the phases, but I see this as a big deal if is done before the computation of the S2 matrix, is my interpretation wrong?

Can someone point me to the right reference for the C2 computation algorithm used in SNAP?
Thanks

[grshennan]

Old question by now, I know, but I would also like to know about the relationship between speckle filtering and C2 matrices, and the exact computational method of the C2 matrix in SNAP.

From my beginner understanding, dual co-pol is required for the C2 matrix to not have two elements that are zero. However, this is fixed in the notation above by not including the HH and HV channels. So, which one is SNAP computing?

Regarding speckle filtering, I have been performing this after C2 matrix calculation, but not sure if this is right, or distorting my results (which don’t seem to be useful - I’ll try not speckle filtering and see what happens).

[grshennan]

It occurs to me that SNAP will probably simply calculate C2 with the available bands, so will should cross- or co-pol the same?