Abstract
Accuracy and resistance to noise are two important aspects of time delay estimation algorithms. The cross power-spectrum phase algorithm is a classic time delay estimation algorithm. It is accurate but not robust to noise. Its performance deteriorates or even fails under impulsive noise. The improved cross power-spectrum phase algorithms based on fractional lower-order statistics rely on a priori knowledge of impulsive noise. In this paper, we propose a novel time delay estimation algorithm based on the weighted correntropy spectral density. The proposed method works well under impulsive noise because it is based on correntropy theory and its resistance to noise is further strengthened by the weighting process in the frequency domain. Our theoretical analysis and simulations demonstrate that the proposed method is very accurate in the presence of Gaussian or impulsive noise with a low generalized signal-to-noise ratio.
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P.G. Georgiou, P. Tsakalides, C. Kyriakakis, Alpha-stable modeling of noise and robust time-delay estimation in the presence of impulsive noise. IEEE Trans. Multimed. 1(3), 291–301 (1999)
A. Hojjati, A.G. Kim, E.V. Linder, Robust strong lensing time delay estimation. Phys. Rev. D 87(12), 123512 (2013)
F.Y. Jiang, Y.B. Kuang, K. Aström, Time delay estimation for TDOA self-calibration using truncated nuclear norm, in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, BC, Canada, pp. 3885–3889 (2013), 26–31 May 2013
J. Lee, M. Jin, K.K. Ahn, Precise tracking control of shape memory alloy actuator systems using hyperbolic tangential sliding mode control with time delay estimation. Mechatronics 23(3), 310–317 (2013)
J.S. Lim, H.S. Pang, Time delay estimation method based on canonical correlation analysis. Circuits Syst. Signal Process. 32(5), 2527–2538 (2013)
W.F. Liu, P.P. Pokharel, J.C. Príncipe, Correntropy: properties and applications in non-Gaussian signal processing. IEEE Trans. Signal Process. 55(11), 5286–5298 (2007)
X.H. Ma, L.L. Liang, F.L. Yin, Generalized crosspower-spectrum phase method, in 2004 International Conference on Communications, Circuits and Systems (ICCCAS 2004), Chengdu, Sichuan, China, pp. 826–829 (2004), 27–29 June 2004
X.Y. Ma, C.L. Nikias, Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics. IEEE Trans. Signal Process. 44(11), 2669–2687 (1996)
R.S. Marinescu, A. Buzo, H. Cucu, C. Burileanu, Fast accurate time delay estimation based on enhanced accumulated cross-power spectrum phase, in 2013 Proceedings of the 21st European Signal Processing Conference (EUSIPCO), Marrakech, Morocco, pp. 1–5 (2003), 9–13 Sept 2013
M. Matassoni, P. Svaizer, Efficient time delay estimation based on cross-power spectrum phase, in European Signal Processing Conference (EUSIPCO) Florence, Italy, pp. 1–5 (2006), 4–8 Sept 2006
C.L. Nikias, M. Shao, Signal Processing with Alpha-Stable Distributions and Applications (Wiley-Interscience, New York, NY, 1995)
M. Omologo, P. Svaizer, Acoustic event localization using a crosspower-spectrum phase based technique, in 1994 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-94), Adelaide, SA, Australia, pp. II/273–II/276 (1994), 19–22 April 1994
I. Santamaría, P.P. Pokharel, J.C. Principe, Generalized correlation function: definition, properties, and application to blind equalization. IEEE Trans. Signal Process. 54(6), 2187–2197 (2006)
S. Shaltaf, M. Abdallah, An enhanced technique for online discrete cosine transform-based time-varying delay estimation. Circuits Syst. Signal Process. 19(6), 501–515 (2000)
M. Shen, H. Liu, A modified cross power-spectrum phase method based on microphone array for acoustic source localization, in IEEE International Conference on Systems, Man and Cybernetics (SMC 2009), San Antonio, USA, pp. 1286–1291 (2009), 11–14 Oct 2009
H.Z. Wang, P.X. Xu, A.Q. Bi, A new adaptive time delay estimation using fourth-order cumulants based on polarity iterative, in 2014 International Conference on Information Science, Electronics and Electrical Engineering (ISEEE), pp. 257–259 (2014)
D. Ying, Y. Yan, Robust and fast localization of single speech source using a planar array. IEEE Signal Process. Lett. 20(9), 909–912 (2013)
W.J. Zeng, H. So, A.M. Zoubir, An \(\ell \)p-norm minimization approach to time delay estimation in impulsive noise. Digit Signal Process 23(4), 1247–1254 (2013)
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This work was partly supported by National Natural Science Foundation of China (61172108, 61139001, and 81241059) and the Science and Technology Support Program (2012BAJ18B06).
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Yu, L., Qiu, Ts. & Song, Am. A Time Delay Estimation Algorithm Based on the Weighted Correntropy Spectral Density. Circuits Syst Signal Process 36, 1115–1128 (2017). https://doi.org/10.1007/s00034-016-0347-y
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DOI: https://doi.org/10.1007/s00034-016-0347-y