Adaptive spectral estimation using the conjugate gradient algorithm

A method for spectral estimation is presented, using the modified conjugate gradient (CG) algorithm. It implements an adaptive version of Pisarenko's harmonic retrieval method, where the estimates are updated sample-by-sample. First, a constrained unit norm CG algorithm is formulated, then it is recast into an unconstrained minimization problem. The resulting algorithms can be extended to solve the generalized eigensystem problem, when the noise covariance matrix is known a priori. It is shown that the proposed algorithms convergence rate is comparable to that of a least-squares type algorithm, while being computationally more efficient. Performance simulations are shown, and comparisons with some existing methods are provided.