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In this paper, the problem of fundamental frequency estimation for real harmonic sinusoids is addressed. By making use of the subspace technique and Markov-based eigenanalysis, an optimally weighted harmonic multiple signal classification (OW-HMUSIC) estimator is devised. The fundamental frequency estimates are computed in an iterative manner. The performance of the proposed method is derived. Computer simulations are performed to compare the proposed approach with nonlinear least squares and HMUSIC methods as well as Cramér-Rao lower bound.