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Signal-subspace approximation for line spectrum estimation

The Toeplitz form for an observed covariance matrix is investigated. A least-squares solution is found with respect to a given inner product space. The use of this form as a means for enhancing the Pisarenko Harmonic Decomposition method of estimating the location of line components in a spectrum is reported. The more general problem of finding a rank-p Toeplitz form for an observed covariance matrix is reviewed and an iterative solution is proposed. MUSIC-based estimates of line components are improved at lower SNRs by using the rank-p Toeplitz form instead of the original rank-p covariance matrix.