In high-resolution methods applied to uniform linear arrays (ULA), the prep
rocessing that consists of forcing the estimated cross spectral matrix (CSM
) to be Toeplitz by averaging its elements along its diagonals is known to
increase the resolving power drastically. That is why it is always done in
practice. However, this approach is limited to linear arrays because of the
required Toeplitz structure for the CSM. This paper generalizes this techn
ique to arrays of arbitrary geometry; the developed method is referred to a
s rectification. It proceeds by searching first for a vector subspace of he
rmitian matrices that contains the manifold generated by the CSMs when the
angle of arrival (AOA) varies. This preliminary step is performed only once
for a given array geometry. Next, rectification of estimated CSMs is achie
ved by projecting them onto this subspace, resulting in denoising and incre
ased resolving power of source localization methods at a very low computati
onal cost. As a byproduct, the storage requirements for the CSMs are greatl
y reduced.