On the estimation of the parameters of sinusoidal signals in noise.

摘要

In this dissertation the problem of estimating the parameters (frequencies, phases, and amplitudes) of sinusoidal signals from a collection of noisy data samples is studied. The Cramer-Rao bounds (CRB) to the estimation accuracy are derived and their properties are examined for both large and finite sample cases. The maximum likelihood estimator (MLE) for the estimation problem is investigated. Large signal (i.e., when the signal-to-noise ratio (SNR) is large) and large sample properties of the MLE are established. The probability density function of the MLE of a single frequency in the large SNR case is derived.;Due to the relationship between the MLE and the periodogram, the performance of the periodogram frequency estimator is studied. The mean-square convergence of the periodogram frequency estimates is proved. The performance of the periodogram for finite sample sizes is examined through simulation studies.;Analogous to the definition of periodogram, the biperiodogram is defined in terms of the instantaneous estimate of the bispectrum. The use of the biperiodogram in estimation of the frequencies of phase coupled sinusoids is studied. The mean-square convergence of the biperiodogram frequency estimates is proved. The asymptotic (large sample) variances of the biperiodogram estimates are shown to be of the same order as the corresponding CRB; however, do not achieve the asymptotic CRB. The finite sample properties of the biperiodogram estimates are studied through simulations.;The performances of the two estimators (the periodogram and the biperiodogram) are compared. It is found that the biperiodogram gives superior performance in all the cases considered.