Improved Pisarenko´s sinusoidal spectrum estimate via SVD subspace approximation methods

This paper presents two numerically stable Pisarenko type spectrum estimators based on a subspace approximation approach. A sinusoidal signal plus noise model is assumed. By using the singular value decomposition, the covariance matrix is decomposed into a signal subspace which represents the signal component; and a noise subspace which represents the noise contributions. The first method makes use of a signal subspace structure which characterizes the signal covariance matrix by a linear system triple (A, b, c). Then the frequencies of the signal sinusoids are solved as the eigenvalues of the A matrix. The second method utilizes a Toeplitz structure of the noise subspace. Then a subspace approximation procedure is taken to find an estimate of this noise subspace. The frequency estimates are then solved as the roots of the defining sequence of this Toeplitz noise subspace matrix. Simulation results are furnished to illustrate the advantages of these proposed new methods.