# Maximum cross-correlation coefficient value for time delay estimation

I am using cross-correlation for time delay estimation of two synchronized recordings ($$x_1$$ and $$x_2$$) of a fixed sound source from two different locations.

I understand that the delay is associated with the maximum cross-correlation coefficient.

My question: should I use the maximum of the cross-correlation coefficient vector or absolute cross-correlation coefficient vector?

This

$$\Delta t \approx \tau_{peak} = \underset{\tau}{\arg\max} (\rho_{x_1 x_2}(\tau))$$

or this

$$\Delta t \approx \tau_{peak} = \underset{\tau}{\arg\max} (|\rho_{x_1 x_2}(\tau)|)$$

As your plot shows, the second form allows for the correlation peak to be negative. Now, what does a strong negative cross correlation mean? It means the signals are very similar, except one has a negative sign in front of it, i.e., $$x_1 \approx -x_2$$. Whether or not this makes sense depends a lot on the actual application.