Multiple-tone estimation by IEEE standard 1057 and the expectation-maximization algorithm

The aim of this paper is to present an efficient algorithm for multiple-tone parameter estimation. The algorithm is inspired by the expectation-maximization algorithm, and it utilizes the IEEE standard 1057 for single-tone parameter estimation. In the derivation of the algorithm, it is assumed that the number of tones are known and that the frequencies are well separated. The algorithm is evaluated using noisy data consisting of multiple real-valued tones. The performance of the frequency estimator is studied and compared with the asymptotic Cramer-Rao bound (CRB). It is shown that the algorithm produces statistically efficient frequency estimates at high signal-to-noise ratios (SNRs), that is the variance of the estimates reaches the CRB. Finally, it is illustrated that the algorithm can produce efficient estimates independent of the number of tones in the input signal.