Least-squares solution

We compare the results of the numerical inversion with the theoretical response of our target microphones for all the D directions, properly delayed, and sum the squared deviations for defining a total error:

The inversion of this matrix system is now performed adding a  regularization parameter b, in such a way to minimize the total error (Nelson/Kirkeby approach):

It revealed to be advantageous to employ a frequency-dependent regularization parameter bk.

P