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Abstract-In this letter, parameter estimation of a uniformly sampled signal that satisfies the lossy wave equation in Gaussian noise is investigated. By exploiting the linear prediction property of the noise-free signal, a maximum likelihood estimator for the parameters is first developed. Relaxation is then applied to yield a simple and accurate algorithm. It is shown that the estimation performance of the proposed method attains Cramér-Rao lower bound.

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The problem of parameter estimation of a single sinusoid with unknown offset in additive Gaussian noise is addressed. After deriving the linear prediction property of the noise-free signal, the maximum likelihood estimator for the frequency parameter is developed. The optimum estimator is relaxed according to the iterative quadratic maximum likelihood technique. The remaining parameters are then solved in a linear least squares manner. Theoretical variance expression of the frequency estimate based on high signal-to-noise ratio assumption is also derived. Simulation results show that the proposed approach can give optimum estimation performance and is superior to the nonlinear least squares.