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I have $N$ time series which have unknown time offsets relative to each other. I want to estimate the $(N - 1)$ time offsets, $\tau_{i,i+1}$, which maximise the sum of the cross-correlations between the time series. How should I do this?

Notes:

The MathWorks documentation provides an example of this. However, this example aligns the time series one-by-one, and does not make use of the redundant information from the $N(N - 1)/2$ cross-correlations, so it is not the best possible solution.

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  • $\begingroup$ The example you linked seems to be the best way to do this. The only improvement computationally would be to use a tree structured approach to comparing the relative delays of various signals, but you already seem aware of this from your notes. What criteria are you using to judge what is good or bad about a solution? $\endgroup$ – hops Feb 15 '17 at 22:08
  • $\begingroup$ I think this may help you, as the delay of the equalizer would be the time delay between your series once they are equalized (and specifically would provide the delay that may be different at different frequencies, and hence optimized as you suggested: dsp.stackexchange.com/questions/31318/… $\endgroup$ – Dan Boschen Feb 16 '17 at 2:06

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