Fast rational approximation algorithms of signal and noise subspaces

Fast methods for approximating the dominant and subdominant subspaces have been developed. These methods offer a computational benefit in that subspaces are computed without the costly eigendecomposition or singular value decomposition. More generally we provided a way of splitting an L-dimensional space into several complementary invariant subspaces of the sample covariance matrix, without actually computing any eigenvalues. Frequency estimators such as MUSIC-, minimum-norm-, and ESPRIT-type are then derived using these approximated subspaces. The computation of obtaining these approximate subspaces and estimators are shown to be less than the standard techniques. Through several examples it is demonstrated that these methods have a performance comparable to that of MUSIC yet will require fewer computation to obtain the signal subspace projection.