Estimating small time shift between two time series

Question

I have two time series, and i suspect that there is a time shift between them, and i want to estimate this time shift.

This question has been asked before in: Find phase

Answer 1

I've successfully used (in awgn channel) matched filter approach, that gives peak energy m[n] at index n; then fitting a 2nd degree polynomial f(n) to m[n-1], m[n], m[n+1] and finding the minimum by setting f'(n)==0.

The response is not necessarily absolutely linear, especially if the autocorrelation of the signal doesn't vanish at m[n-1], m[n+1].