Hi AdamRex, your first three three steps - i am slightly tweaking...

1. Setup ADC1 and ADC2 to sample at Fs1 and Fs2. Fs1 != Fs2
2. Collect N1 samples from ADC1 and N2 samples ADC2 as x1 and x2. Fs1/N1 = Fs2/N2
3. Calculate N1 pt DFT of x1 and N2 pt DFT of x2 as X1 and X2.
   The rest you are more or less right and can work it through. (polyphase filterbank is not essential. It is just a good way to cut the spectrum up). The key bit is at step 3 the DFT bins are of the same size.
   Also when you expand the spectrum, spectral flips are required for even Nyquist zones. These will become apparent when you work it out.

Mr. Pathikulangara,

Is this general understanding of your method correct?:

1. Setup ADC1 and ADC2 to sample at Fs1 and Fs2. Fs1 != Fs2
2. Collect N samples from ADC1 and ADC2 as x1 and x2.
3. Calculate DFTs of x1 and x2 as X1 and X2.
4. Separate X1 and X2 in to M partitions using polyphase filterbanks. The result, X1p and X2p are arrays of N/M DTF samples.
5. Construct expanded versions of X1p and X2p that hold data of consecutive nyquist zones. Expanded spectrums are X1pe and X2pe. Kind of like making Kirigami paper dolls by cutting folded paper:)
6. Divide each partition of X1pe by it's norm and multiply the result element-wise by X2pe.

If not, could you show me where I went wrong?

Thanks for your interest. I had left it as an exercise for the listener!
One method would be to do two sets of computations.
First set – convert the first signal into a unit vector, cross correlate and accumulate.
Second set – convert the second signal into a unit vector, cross correlate and accumulate.
Pick the smallest!

Hello Mr Pathikulangara,
Your research is very interesting. Thank you for the presentation.
In your presentation you mention:

There are many ways to reconstruct the signal so that the spurious artifacts does not appear

Can you share some more details about this ?
Kind regards