Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses

Based on the linear prediction property of sinusoidal signals, two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed. In order to achieve accurate frequency estimation, the first algorithm uses a generalized unit-norm constraint, while the second method employs a monic constraint. The weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner. For the case of a single real tone with sufficiently large data samples, both estimators provide nearly identical frequency estimates and their performance approaches Crame/spl acute/r-Rao lower bound (CRLB) for white Gaussian noise before the threshold effect occurs. Algorithms for closed-form single-tone frequency estimation are also devised. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the CRLB for different frequencies, observation lengths and signal-to-noise ratio (SNR) conditions.