Linear programming in spectral estimation. Application to array processing

We address the narrow-band source localization problem for arbitrary arrays with known geometry in the presence of arbitrary noise of unknown spatial spectral density. Very few methods are able to handle this problem. We present a very unsophisticated approach whose algorithmic part relies on a standard linear programming algorithm (such as the simplex algorithm available in any scientific program library). The computational complexity of the method is reasonable, the performance appear to be remarkable on simulations. The justification of the procedure and the asymptotic analysis is more complex and much work remains to be done