Compensate delay of non-symmetric (non-linear phase) filter
If your filters have a low pass characteristic (which at least the one in your example appears to have), then a possibly useful measure for the delay is the center of gravity of the impulse response:

$$\hat{\tau}=\frac{\displaystyle\sum_nnh[n]}{\displaystyle\sum_nh[n]}\tag{1}$$

For more general impulse responses, other than low pass, you can modify $(1)$ by either taking magnitudes or squares of $h[n]$. Note that $(1)$ is the filter's group delay evaluated at DC.