NDLI: MAP/ML Estimation of the Frequency and Phase of a Single Sinusoid in Noise

Content Provider	IEEE Xplore Digital Library
Author	Hua Fu Pooi Yuen Kam
Copyright Year	1991
Abstract	The problem of estimating the frequency and carrier phase of a single sinusoid observed in additive, white, Gaussian noise is addressed. Much of the work in the literature considers maximum likelihood (ML) estimation. However, the ML estimator given by the location of the peak of a periodogram in the frequency domain shown in D.C. Rife and R. R. Boorstyn, "Single-tone parameter estimation from discrete-time observations," IEEE Transactions on Information Theory, vol. IT-20, pp. 591-598, Sep. 1974, has a very high computational complexity. This paper derives the explicit structure of the ML estimator for data processing in the time domain, assuming only reasonably high signal-to-noise ratio (SNR). The result of this approximate ML estimator shows that both the phase and the magnitude of the noisy signal samples are utilized in the estimator, and the phase data alone as assumed in S. A. Tretter, "Estimating the frequency of a noisy sinusoid by linear regression", IEEE Transactions on Information Theory, vol. IT-31, pp. 832-835, Nov. 1985 and S. Kay, "A fast and accurate single frequency estimator", IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 39, pp. 1203-1205, May 1991, is not a sufficient statistic. The sample-by-sample iterative processing nature of the estimator enables us to propose a novel, recursive phase-unwrapping algorithm that allows the estimator to be implemented efficiently. To facilitate the performance analysis, a new, linearized observation model for the instantaneous signal phase that is more accurate than that of S. A. Tretter, "Estimating the frequency of a noisy sinusoid by linear regression", IEEE Transactions on Information Theory, vol. IT-31, pp. 832-835, Nov. 1985 and of S. Kay, "A fast and accurate single frequency estimator", vol. 39, pp. 1203-1205, May 1991, is proposed. This new model explains physically why the phase data are weighted by the magnitude information in the ML estimator. Moreover, by incorporating a priori knowledge via the a priori probability density function of the unknown frequency and the carrier phase, the explicit structure of the approximate maximum a posteriori probability (MAP) estimator is derived, and the Bayesian Cramer-Rao lower bound (BCRLB) on the mean-square error (mse) is obtained. Our analysis shows that the mse performance of the MAP estimator can approach the BCRLB very closely
Sponsorship	IEEE Signal Processing Society
Starting Page	834
Ending Page	845
Page Count	12
File Size	778907
File Format	PDF
ISSN	1053587X
Volume Number	55
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Frequency estimation Maximum likelihood estimation Phase estimation Phase noise Linear regression Signal processing algorithms Recursive estimation Performance analysis Additive noise phase unwrapping Cramer–Rao lower bound (CRLB)/Bayesian Cramer–Rao lower bound (BCRLB) frequency maximum a posteriori probability (MAP)/maximum likelihood (ML) estimation phase phase noise model
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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