A Propagator Method like Algorithm for Estimation of Multiple Real-Valued Sinusoidal Signal Frequencies
In this paper a novel method for multiple one dimensional real valued sinusoidal signal frequency estimation in the presence of additive Gaussian noise is postulated. A computationally simple frequency estimation method with efficient statistical performance is attractive in many array signal processing applications. The prime focus of this paper is to combine the subspace-based technique and a simple peak search approach. This paper presents a variant of the Propagator Method (PM), where a collaborative approach of SUMWE and Propagator method is applied in order to estimate the multiple real valued sine wave frequencies. A new data model is proposed, which gives the dimension of the signal subspace is equal to the number of frequencies present in the observation. But, the signal subspace dimension is twice the number of frequencies in the conventional MUSIC method for estimating frequencies of real-valued sinusoidal signal. The statistical analysis of the proposed method is studied, and the explicit expression of asymptotic (large-sample) mean-squared-error (MSE) or variance of the estimation error is derived. The performance of the method is demonstrated, and the theoretical analysis is substantiated through numerical examples. The proposed method can achieve sustainable high estimation accuracy and frequency resolution at a lower SNR, which is verified by simulation by comparing with conventional MUSIC, ESPRIT and Propagator Method.
[1] D. C. Rife and R. R. Boorstyn "Multiple tone parameter estimation from discrete-time observations," Bell Syst. Tech. J., pp. 1389-1410, Nov. 1976.
[2] P. Stoica and A. Nehorai, "Statistical analysis of two nonlinear least-squares estimators of sine wave parameters in the colored noise case," in Proc. Int. Conf. Acoustic., Speech, Signal Processing, vol. 4 Apr. 1988, pp. 2408-2411.
[3] V. F. Pisarenko, The retrieval of harmonics by linear prediction," Geo-phys. J. R. Astron. Soc., vol. 33, pp.347-366, 1973.
[4] R. O. Schmidt, "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propagat., vol. 34, pp. 276-280, Mar. 1986.
[5] R. Roy and T. Kailath, ESPRIT- Estimation of signal parameter via rotational invariance techniques," IEEE Trans Acoust., Speech, Signal Processing, vol. 37, pp. 984-995, July, 1989.
[6] R. J. Mcaulay and T. F. Quateri, "Speech analysis/synthesis based on a sinusoidal representation," IEEE Trans Acoust., Speech, Signal Processing, vol. 34, PP. 744-754, Apr. 1986.
[7] T. Nakatani and M. Miyoshi, "Blind dereverberation of single channel speech signal based on harmonic structure," in Proc. IEEE Int. Conf. Acoust. Speech, Signal Processing, vol. 1, Hong Kong, China, Apr. 2003, pp. 92-95.
[8] L. Y. Ngan, Y. Wu, H. C. So, P. C. Ching, and S. W. Lee, "Joint time delay and pitch estimation for speaker localization," in Proc. IEEE Int. Symp. Circuits Systems, vol. 3, Bangkok, Thailand, May 2003, pp. 722-725.
[9] U. Kiencke and L. Nielsen, Automotive Control Systems for Engine, Driveline, and Vehicle. Berlin, Germany: Springer-Verlag, 2000.
[10] G. Simon, R. Pintelon, L. Sujbert, and J. Schoukens, "An efficient non-linear least square multi sine fitting algorithm," IEEE Trans. Instrum. Meas., vol. 45, pp. 750-755, Aug. 2002
[11] B.D.Rao and K.V.S.Hari, "Weighted Sub-space methods and spatial smoothing: Analysis and comparison", IEEE Trans. Signal processing, vol. 41,nNo.2, pp.788-803, 1993.
[12] P.Stoica, A. Eriksson and T.Soderstrom, "Optimally Weighted MUSIC for frequency Estimation", SIAm Jour. On Matrix Anal. and Appl., vol.16, no.3, pp.811-827,1995.
[13] P.Stoica and T.Soderstrom, " Statistical analysis of MUSIC and subspace rotational estimates of sinusoidal frequencies ", IEEE Trans. Signal processing, vol. 39, no.8, pp.1836-1847, 1991.
[14] P.Stoica and A.Eriksson, "MUSIC estimation of real-valued sine-wave frequencies", Signal processing, vol.42, no.2, pp.139-146, 1995.
[15] M.A.Altinkaya, H.Delic, B.Sankur and B.Anarim, "Subspace-based frequency estimation of sinusoidal signals in alpha-stable noise", Signal processing, vol.82, no.12, pp.1807-1827,2002.
[16] K.Mahata, "Subspace fitting Approaches for Frequency Estimation using Real-Valued data", IEEE Trans. Signal processing, vol.53 , no.8, pp.3099-3110, 2005.
[17] Shigeru Ando, Takaaki Nara ," An Exact Direct Method of Sinusoidal Parameter Estimation Derived From Finite Fourier Integral of Differential Equation" IEEE transactions on signal processing, vol. 57, no. 9, pp3317-3329.
[18] K.W.Chan and H.C.So, "Accurate Frequency Estimation for Real Harmonic Sinusoids'; IEEE signal processing Lett., vol.11, no.7, pp.609-612, 2004.
[19] H. Shatnawi, Qasaymeh M. M, Gami Hiren, M.E. Sawan "An Improved Frequency Estimator" Proceedings of the 5th Annual GRASP Symposium, Wichita State University, 2009.
[20] Kaushik Mahata and Torsten Soderstrom, "ESPRIT-Like Estimation ofReal-Valued Sinusoidal Frequencies", IEEE transactions on signal processing, vol. 52, NO. 5, pp-1161-1170 May-2004.
[21] P.Palanisamy, Sambit Prasad Kar , "Estimation of Real-Valued Sinusoidal Signal Frequencies based on ESPRIT and Propagator methods", in proc IEEE-International Conf on Recent Trends in Information Technology, ICRTIT 2011. pp.69-73 June-2011.
[22] Jingmin Xin, Akira Sano, "Computationally Efficient Subspace-Based Method for Direction-of-Arrival Estimation Without Eigen decomposition" IEEE transactions on signal processing, vol. 52, No. 4,
,April 2004.
[23] Guangmin Wang, Jingmin Xin, Nanning Zheng, Akira Sano, "Computationally Efficient Subspace-Based Method for Two-Dimensional Direction Estimation With L-Shaped Array", ieee transactions on signal processing, vol. 59, no. 7, pp-3197-3212 July 2011
[24] S. Marcos, A. Marsal, and M. Benidir, "The propagator method for source bearing estimation," Signal Process. vol. 42, no. 2, pp. 121-138, 1995.
[25] H. L. Van Trees, Optimum Array Processing, Part IV of Detection, Estimation, and Modulation Theory. New York: Wiley, 2002.
[26] S. M. Kay, Modem Spectral Estimation. Upper Saddle River, NJ: Prentice-Hall, 1988
[1] D. C. Rife and R. R. Boorstyn "Multiple tone parameter estimation from discrete-time observations," Bell Syst. Tech. J., pp. 1389-1410, Nov. 1976.
[2] P. Stoica and A. Nehorai, "Statistical analysis of two nonlinear least-squares estimators of sine wave parameters in the colored noise case," in Proc. Int. Conf. Acoustic., Speech, Signal Processing, vol. 4 Apr. 1988, pp. 2408-2411.
[3] V. F. Pisarenko, The retrieval of harmonics by linear prediction," Geo-phys. J. R. Astron. Soc., vol. 33, pp.347-366, 1973.
[4] R. O. Schmidt, "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propagat., vol. 34, pp. 276-280, Mar. 1986.
[5] R. Roy and T. Kailath, ESPRIT- Estimation of signal parameter via rotational invariance techniques," IEEE Trans Acoust., Speech, Signal Processing, vol. 37, pp. 984-995, July, 1989.
[6] R. J. Mcaulay and T. F. Quateri, "Speech analysis/synthesis based on a sinusoidal representation," IEEE Trans Acoust., Speech, Signal Processing, vol. 34, PP. 744-754, Apr. 1986.
[7] T. Nakatani and M. Miyoshi, "Blind dereverberation of single channel speech signal based on harmonic structure," in Proc. IEEE Int. Conf. Acoust. Speech, Signal Processing, vol. 1, Hong Kong, China, Apr. 2003, pp. 92-95.
[8] L. Y. Ngan, Y. Wu, H. C. So, P. C. Ching, and S. W. Lee, "Joint time delay and pitch estimation for speaker localization," in Proc. IEEE Int. Symp. Circuits Systems, vol. 3, Bangkok, Thailand, May 2003, pp. 722-725.
[9] U. Kiencke and L. Nielsen, Automotive Control Systems for Engine, Driveline, and Vehicle. Berlin, Germany: Springer-Verlag, 2000.
[10] G. Simon, R. Pintelon, L. Sujbert, and J. Schoukens, "An efficient non-linear least square multi sine fitting algorithm," IEEE Trans. Instrum. Meas., vol. 45, pp. 750-755, Aug. 2002
[11] B.D.Rao and K.V.S.Hari, "Weighted Sub-space methods and spatial smoothing: Analysis and comparison", IEEE Trans. Signal processing, vol. 41,nNo.2, pp.788-803, 1993.
[12] P.Stoica, A. Eriksson and T.Soderstrom, "Optimally Weighted MUSIC for frequency Estimation", SIAm Jour. On Matrix Anal. and Appl., vol.16, no.3, pp.811-827,1995.
[13] P.Stoica and T.Soderstrom, " Statistical analysis of MUSIC and subspace rotational estimates of sinusoidal frequencies ", IEEE Trans. Signal processing, vol. 39, no.8, pp.1836-1847, 1991.
[14] P.Stoica and A.Eriksson, "MUSIC estimation of real-valued sine-wave frequencies", Signal processing, vol.42, no.2, pp.139-146, 1995.
[15] M.A.Altinkaya, H.Delic, B.Sankur and B.Anarim, "Subspace-based frequency estimation of sinusoidal signals in alpha-stable noise", Signal processing, vol.82, no.12, pp.1807-1827,2002.
[16] K.Mahata, "Subspace fitting Approaches for Frequency Estimation using Real-Valued data", IEEE Trans. Signal processing, vol.53 , no.8, pp.3099-3110, 2005.
[17] Shigeru Ando, Takaaki Nara ," An Exact Direct Method of Sinusoidal Parameter Estimation Derived From Finite Fourier Integral of Differential Equation" IEEE transactions on signal processing, vol. 57, no. 9, pp3317-3329.
[18] K.W.Chan and H.C.So, "Accurate Frequency Estimation for Real Harmonic Sinusoids'; IEEE signal processing Lett., vol.11, no.7, pp.609-612, 2004.
[19] H. Shatnawi, Qasaymeh M. M, Gami Hiren, M.E. Sawan "An Improved Frequency Estimator" Proceedings of the 5th Annual GRASP Symposium, Wichita State University, 2009.
[20] Kaushik Mahata and Torsten Soderstrom, "ESPRIT-Like Estimation ofReal-Valued Sinusoidal Frequencies", IEEE transactions on signal processing, vol. 52, NO. 5, pp-1161-1170 May-2004.
[21] P.Palanisamy, Sambit Prasad Kar , "Estimation of Real-Valued Sinusoidal Signal Frequencies based on ESPRIT and Propagator methods", in proc IEEE-International Conf on Recent Trends in Information Technology, ICRTIT 2011. pp.69-73 June-2011.
[22] Jingmin Xin, Akira Sano, "Computationally Efficient Subspace-Based Method for Direction-of-Arrival Estimation Without Eigen decomposition" IEEE transactions on signal processing, vol. 52, No. 4,
,April 2004.
[23] Guangmin Wang, Jingmin Xin, Nanning Zheng, Akira Sano, "Computationally Efficient Subspace-Based Method for Two-Dimensional Direction Estimation With L-Shaped Array", ieee transactions on signal processing, vol. 59, no. 7, pp-3197-3212 July 2011
[24] S. Marcos, A. Marsal, and M. Benidir, "The propagator method for source bearing estimation," Signal Process. vol. 42, no. 2, pp. 121-138, 1995.
[25] H. L. Van Trees, Optimum Array Processing, Part IV of Detection, Estimation, and Modulation Theory. New York: Wiley, 2002.
[26] S. M. Kay, Modem Spectral Estimation. Upper Saddle River, NJ: Prentice-Hall, 1988
@article{"International Journal of Electrical, Electronic and Communication Sciences:53377", author = "Sambit Prasad Kar and P.Palanisamy", title = "A Propagator Method like Algorithm for Estimation of Multiple Real-Valued Sinusoidal Signal Frequencies", abstract = "In this paper a novel method for multiple one dimensional real valued sinusoidal signal frequency estimation in the presence of additive Gaussian noise is postulated. A computationally simple frequency estimation method with efficient statistical performance is attractive in many array signal processing applications. The prime focus of this paper is to combine the subspace-based technique and a simple peak search approach. This paper presents a variant of the Propagator Method (PM), where a collaborative approach of SUMWE and Propagator method is applied in order to estimate the multiple real valued sine wave frequencies. A new data model is proposed, which gives the dimension of the signal subspace is equal to the number of frequencies present in the observation. But, the signal subspace dimension is twice the number of frequencies in the conventional MUSIC method for estimating frequencies of real-valued sinusoidal signal. The statistical analysis of the proposed method is studied, and the explicit expression of asymptotic (large-sample) mean-squared-error (MSE) or variance of the estimation error is derived. The performance of the method is demonstrated, and the theoretical analysis is substantiated through numerical examples. The proposed method can achieve sustainable high estimation accuracy and frequency resolution at a lower SNR, which is verified by simulation by comparing with conventional MUSIC, ESPRIT and Propagator Method.
", keywords = "Frequency estimation, peak search, subspace-based
method without eigen decomposition, quadratic convex function.", volume = "6", number = "2", pages = "177-5", }
