Please use this identifier to cite or link to this item:
|Title:||MAP/ML estimation of the frequency and phase of a single sinusoid in noise||Authors:||Fu, H.
|Keywords:||Cramer-Rao lower bound (CRLB)/Bayesian Cramer-Rao lower bound (BCRLB)
Maximum a posteriori probability (MAP)/maximum likelihood (ML) estimation
Phase noise model
|Issue Date:||Mar-2007||Citation:||Fu, H., Kam, P.Y. (2007-03). MAP/ML estimation of the frequency and phase of a single sinusoid in noise. IEEE Transactions on Signal Processing 55 (3) : 834-845. ScholarBank@NUS Repository. https://doi.org/10.1109/TSP.2006.888055||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 CramerRao 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. © 2007 IEEE.||Source Title:||IEEE Transactions on Signal Processing||URI:||http://scholarbank.nus.edu.sg/handle/10635/56582||ISSN:||1053587X||DOI:||10.1109/TSP.2006.888055|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Jun 25, 2022
WEB OF SCIENCETM
checked on Jun 17, 2022
checked on Jun 23, 2022
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.