Improved Newton-type algorithm for adaptive implementation of Pisarenko´s harmonic retrieval method and its convergence analysis

Pisarenko´s harmonic retrieval (PHR) method is probably the first eigenstructure based algorithm for estimating the frequencies of sinusoids corrupted by additive white noise. To develop an adaptive implementation of the PHR method, one group of authors has proposed a least-squares type recursive algorithm. In their algorithm, they made approximations for both gradient and Hessian. The authors derive an improved algorithm, where they use exact gradient and a different approximation for the Hessian and analyze its convergence rigorously. Specifically, they provide a proof for the local convergence and detailed arguments supporting the local instability of undesired stationary points. Computer simulations are used to verify the convergence performance of the new algorithm. Its performance is substantially better than that exhibited by its counterpart, especially at low SNR´s