A novel method is presented to estimate sinusoidal frequency from highly contaminated single channel signals by constructing multi-channel surrogates using multiple signal classification (MUSIC) method in frequency domain beam-space (FB-MUSIC). According to the comparability of sampled data in time domain and observed data in uniform linear array, the FB-MUSIC method is proposed and the explicit expressions for the covariance elements of the estimation errors associated with FB-MUSIC are derived. These expressions are then used to analyse the statistical performance of FB-MUSIC and MUSIC. These expressions for the estimation error covariance are also used to compare the theoretical results and simulation results. Monte-Carlo simulations show that the root-mean-square error of frequency estimation in simulations keep consistent with the theoretical covariance for FB-MUSIC and MUSIC, and the signal-to-noise ratio resolution threshold of FB-MUSIC with reduced dimensionality is lower than that of MUSIC. This method may provide a higher resolution of sinusoidal frequency estimation and lower computation cost as compared with the conventional MUSIC method.

References

1. 1)
  - 33. Trees, H.L.V.: ‘Optimum array processing part IV of detection, estimation and modulation’ (Wiley, New York, 2002).
2. 2)
  - 6. Stoica, P., So˝ derstro˝ m, T.: ‘Statistical analysis of MUSIC and ESPRIT estimates of sinusoidal frequencies’. Proc. IEEE ICASSP, Toronto, Canada, 1991, pp. 3273–3276.
3. 3)
  - 16. Karhunen, J.T., Joutsensalo, J.: ‘Robust MUSIC based on direct signal subspace estimation’. Proc. IEEE ICASSP, Toronto, Canada, 1991, pp. 3357–3360.
4. 4)
  - 24. Hua, Z.Z.: ‘The fourth order cumulants based modified MUSIC algorithm for DOA in colored noise’. 2010 Asia-Pacific Conf. on Wearable Computing Systems, 2010, pp. 345–347.
5. 5)
  - 18. Liu, T.H., Mendel, J.M.: ‘A subspace-based direction finding algorithm using fractional lower order statistics’, IEEE Trans. Signal Process., 2001, 49, (8), pp. 1605–1613 (doi: 10.1109/78.934131).
6. 6)
  - 32. Fuchs, J.-J.: ‘Estimating the number of sinusoids in additive white noise’, IEEE Trans. Acoust. Speech Signal Process., 1988, 36, (12), pp. 1846–1853 (doi: 10.1109/29.9029).
7. 7)
  - 15. Karhunen, J.T., Joutsensalo, J.: ‘Sinusoidal frequency estimation by signal subspace approximation’, IEEE Trans. Signal Process., 1992, 40, (12), pp. 2961–2972 (doi: 10.1109/78.175740).
8. 8)
  - 1. Ferréol, A., Larzabal, P., Viberg, M.: ‘On the asymptotic performance analysis of subspace DOA estimation in the presence of modelingerrors: case of MUSIC’, IEEE Trans. Signal Process., 2006, 54, (3), pp. 907–920 (doi: 10.1109/TSP.2005.861798).
9. 9)
  - 13. Xu, X.L., Buckley, K.M.: ‘Statistical performance comparison of MUSIC in element-space and beam-space’. Proc. IEEE ICASSP, Glasgow, UK, 1989, pp. 2124–2127.
10. 10)
  - 8. Kaveh, M., Barabell, A.J.: ‘The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise’, IEEE Trans. Acoust. Speech Signal Process., 1986, 34, (2), pp. 331–341 (doi: 10.1109/TASSP.1986.1164815).
11. 11)
  - 34. Stoica, P., Nehorai, A.: ‘MUSIC, Maximum likelihood, and Cramer-Rao bound’, IEEE Trans. Acoust. Speech Signal Process., 1989, 37, (5), pp. 720–741 (doi: 10.1109/29.17564).
12. 12)
  - 1. Brester, Y., Macovski, A.: ‘Exact maximum likelihood parameter estimation of superimposed exponential signals in noise’, IEEE Trans. Acoust. Speech Signal Process., 1986, 34, (5), pp. 1081–1089 (doi: 10.1109/TASSP.1986.1164949).
13. 13)
  - 3. Roy, R., Paulraj, A., Kailath, T.: ‘ESPRIT – a subspace rotation approach to estimation of parameters of ciscoids in noise’, IEEE Trans. Acoust. Speech Signal Process., 1986, 34, (5), pp. 1340–1342 (doi: 10.1109/TASSP.1986.1164935).
14. 14)
  - 27. Christensen, M.G., Stoica, P., Jakobsson, A., Jensen, S.H.: ‘Multi-pitch estimation’, Elsevier Signal Process., 2008, 88, (4), pp. 972–983 (doi: 10.1016/j.sigpro.2007.10.014).
15. 15)
  - 34. Zoltowski, M.D., Kautz, G.M., Silverstein, S.D.: ‘Beamspace root-MUSIC’, IEEE Trans. Signal Process., 1993, 41, (1), pp. 344–364 (doi: 10.1109/TSP.1993.193151).
16. 16)
  - 7. Tichavský, P.: ‘High-SNR asymptotics for signal-subspace methods in sinusoidal frequency estimation’, IEEE Trans. Signal Process., 1993, 41, (7), pp. 2448–2460 (doi: 10.1109/78.224253).
17. 17)
  - 9. Li, F., Liu, H.: ‘Statistical analysis of beam-space estimation for direction-of-arrivals’, IEEE Trans. Signal Process., 1994, 42, (3), pp. 604–610 (doi: 10.1109/78.277852).
18. 18)
  - 14. Stoica, P., Nehorai, A.: ‘Comparative performance study of element-space and beam-space MUSIC estimators’, Circuits Syst. Signal Process, 1991, 10, (3), pp. 285–292 (doi: 10.1007/BF01187547).
19. 19)
  - 19. Weng, B., Barner, K.E.: ‘TR-MUSIC – a robust frequency estimation method in impulsive noise’, Signal Process., 2006, 86, pp. 1477–1487 (doi: 10.1016/j.sigpro.2005.08.006).
20. 20)
  - 26. Zhang, J.X., Christensen, M.G., Dahl, J., Jensen, S.H., Moonen, M.: ‘A robust and computationally efficient subspace-based fundamental frequency estimator’, IEEE Trans. Audio. Speech Lang. Process., 2010, 18, (3), pp. 487–497 (doi: 10.1109/TASL.2010.2040786).
21. 21)
  - 36. Janssen, P., Stoica, P.: ‘On the expectation of the product of four matrix-valued Gaussian random variables’, IEEE Trans. Autom. Control, 1988, 33, pp. 867–870 (doi: 10.1109/9.1319).
22. 22)
  - 17. Tsakalides, P., Nikias, C.L.: ‘The robust covariation-based MUSIC (ROC-MUSIC) algorithm for bearing estimation in impulsive noise environments’, IEEE Trans. Signal Process., 1996, 44, (7), pp. 1623–1633 (doi: 10.1109/78.510611).
23. 23)
  - 30. Bienvenu, G., Tufts, D.W.: ‘Decreasing high-resolution method sensitivity by conventional beamformer preprocessing’. Proc. ICASSP, 1984, pp. 33.2.1–4.
24. 24)
  - 21. Viberg, M., Lundgren, A.: ‘Array interpolation based on local polynomial approximation with application to DOA estimation using weighted MUSIC’. Proc. IEEE ICASSP, Taiwan, China, 2009, pp. 2145–2148.
25. 25)
  - 20. Christensen, M.G., Jakobsson, A., Jensen, S.H.: ‘Joint high-resolution fundamental frequency and order estimation’, IEEE Trans. Audio. Speech Lang. Process., 2007, 15, (5), pp. 1635–1644 (doi: 10.1109/TASL.2007.899267).
26. 26)
  - 25. Zhang, J.X., Christensen, M.G., Dahl, J., Jensen, S.H., Moonen, M.: ‘Robust implementation of the MUSIC algorithm’. Proc. IEEE ICASSP 2009, Taiwan, China, 2009, pp. 3037–3040.
27. 27)
  - 10. Kristensson, M., Jansson, M., Ottersten, B.: ‘Further results and insights on subspace based sinusoidal frequency estimation’, IEEE Trans. Signal Process., 2001, 49, (12), pp. 2962–2974 (doi: 10.1109/78.969505).
28. 28)
  - 5. Stoica, P., So˝ derstro˝ m, T.: ‘Statistical analysis of MUSIC and subspace rotation estimates of sinusoidal frequencies’, IEEE Trans. Signal Process., 1991, 39, (8), pp. 1836–1846 (doi: 10.1109/78.91154).
29. 29)
  - 35. Stoica, P., So˝ derstro˝ m, T., Ti, F.N.: ‘Over determined Yule-Walker estimation of the frequencies of multiple sinusoids: accuracy aspects’, Signal Process., 1989, 16, pp. 155–174 (doi: 10.1016/0165-1684(89)90094-7).
30. 30)
  - 28. Zhang, H., Wu, H.-C., Chang, S.Y.: ‘Novel fast MUSIC algorithm for spectral estimation with high subspace dimension’. Proc. IEEE ICNC 2013, San Diego, USA, 2013, pp. 474–478.
31. 31)
  - 29. Christensen, M.G.: ‘An exact subspace method for fundamental frequency estimation’. Proc. IEEE ICASSP 2013, Vancouver, Canada, 2013, pp. 6802–6806.
32. 32)
  - 23. Lobos, T., Leonowicz, Z., Rezmer, J., Schegner, P.: ‘High-resolution spectrum-estimation methods for signal analysis in power systems’, IEEE Trans. Instrum. Meas., 2006, 55, (1), pp. 219–225 (doi: 10.1109/TIM.2005.862015).
33. 33)
  - 2. Schmidt, R.O.: ‘Multiple emitter location and signal parameter estimation’. Proc. RADC Spectral Estimation Workshop, Rome, NY, 1979, pp. 243–258.
34. 34)
  - 31. War, M., Kailath, T.: ‘Detection of signals by information theoretic criteria’, IEEE Trans. Acoust. Speech Signal Process., 1985, 33, (3), pp. 387–392.
35. 35)
  - 11. Swindlehurst, A.L., Kailath, T.: ‘A performance analysis of subspace-based methods in the presence of model errors, part I: the MUSIC algorithm’, IEEE Trans. Signal Process., 1992, 40, (7), pp. 1758–1774 (doi: 10.1109/78.143447).

Sinusoidal frequency estimation by multiple signal classification in frequency domain beam-space

References

Related content