Iterative quadratic maximum likelihood based estimator for a biased sinusoid

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.