Rational invariant subspace approximations with applications

Subspace methods such as MUSIC, Minimum Norm, and ESPRIT have gained consid erable attention due to their superior performance in sinusoidal and direct ion-of-arrival (DOA) estimation, but they are also known to be of high comp utational cost, In this paper, new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are p resented. These algorithms approximate the required subspace using rational and power-like methods applied to the direct data or the sample covariance matrix. Several ESPRIT- as well as MUSIC-type methods are developed based on these approximations. A substantial computational saving can be gained c omparing with those associated with the eigendecomposition-based methods. T hese methods are demonstrated to have performance comparable to that of MUS IC yet will require fewer computation to obtain the signal subspace matrix.