IF Estimation of Overlapped Multicomponent Signals Based on Viterbi Algorithm

  • Po LiEmail author
  • Qing-Hai Zhang


Viterbi algorithm (VA) on time frequency (TF) distribution is a highly performed instantaneous frequency (IF) estimator. However, inaccurate IFs may be tracked due to switch problem in VA when signal components are overlapped on the TF plane. In order to address the problem, this paper first assumes the IF linearity in the overlapped TF regions should not change much, then, a new penalty function describing the variation of IF linearity based on the linear least square fitting technique is developed, and finally, a novel algorithm composed of two IF estimates is introduced. In the first coarse IF estimation, original VA is applied to determine the TF overlapped regions. In the second fine IF estimation, a modified VA employing the new penalty function is applied in the overlapped regions, while the original VA still functions in the non-overlapped regions. Simulations indicate the proposed algorithm can effectively suppress the switch problem and thus can achieve accuracy improvement especially for non-monotonous IF curves compared to other VA-based estimators.


Viterbi algorithm Instantaneous frequency estimator Multicomponent signals Time–frequency analysis 



This work is supported by The Natural Science Foundation of the Jiangsu Higher Education Institutions of China (17KJB510027).


  1. 1.
    X. Bai, M. Xing, F. Zhou et al., Imaging of micromotion targets with rotating parts based on empirical-mode decomposition. IEEE Trans. Geosci. Remote Sens. 46(11), 3514–3523 (2008)CrossRefGoogle Scholar
  2. 2.
    B. Boashash, Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals. Proc. IEEE 80(4), 520–538 (1992)CrossRefGoogle Scholar
  3. 3.
    S. Chen, X. Dong, G. Xing et al., Separation of overlapped non-stationary signals by ridge path regrouping and intrinsic chirp component decomposition. IEEE Sens. J. 17(18), 5994–6005 (2017)CrossRefGoogle Scholar
  4. 4.
    S. Chen, Y. Yang, K. Wei et al., Time-varying frequency-modulated component extraction based on parameterized demodulation and singular value decomposition. IEEE Trans. Instrum. Meas. 65(2), 276–285 (2016)CrossRefGoogle Scholar
  5. 5.
    V.C. Chen, F. Li, S.S. Ho et al., Micro-Doppler effect in radar: phenomenon, model, and simulation study. IEEE Trans. Aerosp. Electron. Syst. 42(1), 2–21 (2006)CrossRefGoogle Scholar
  6. 6.
    I. Djurović, L.J. Stanković, An algorithm for the Wigner distribution based instantaneous frequency estimation in a high noise environment. Sig. Process. 84(3), 631–643 (2004)CrossRefGoogle Scholar
  7. 7.
    I. Djurović, Estimation of sinusoidal frequency-modulated signal parameters in high-noise environment. SIViP 11(8), 1537–1541 (2017)CrossRefGoogle Scholar
  8. 8.
    I. Djurović, QML-RANSAC instantaneous frequency estimator for overlapping multicomponent signals in the time–frequency plane. IEEE Signal Process. Lett. 25(3), 447–451 (2018)CrossRefGoogle Scholar
  9. 9.
    N.A. Khan, M. Mohammadi, I. Djurović, A modified Viterbi algorithm-based IF estimation algorithm for adaptive directional time–frequency distributions. Circuits Syst. Signal Process. 38(5), 2227–2244 (2019)CrossRefGoogle Scholar
  10. 10.
    P. Li, D.C. Wang, J.L. Chen, Parameter estimation for micro-Doppler signals based on cubic phase function. SIViP 7(6), 1239–1249 (2013)CrossRefGoogle Scholar
  11. 11.
    P. Li, D.C. Wang, L. Wang, Separation of micro-Doppler signals based on time frequency filter and Viterbi algorithm. SIViP 7(3), 593–605 (2013)CrossRefGoogle Scholar
  12. 12.
    P. Li, Q.H. Zhang, An improved Viterbi algorithm for IF extraction of multicomponent signals. SIViP 12(1), 171–179 (2018)CrossRefGoogle Scholar
  13. 13.
    M. Mohammadi, A.A. Pouyan, N.A. Khan, A highly adaptive directional time–frequency distribution. SIViP 10(7), 1369–1376 (2016)CrossRefGoogle Scholar
  14. 14.
    H.J. Motulsky, L.A. Ransnas, Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB J. 1(5), 365–374 (1987)CrossRefGoogle Scholar
  15. 15.
    S.T.N. Nguyen, S. Kodituwakku, R. Melino et al., Wavelet-based sparse representation for helicopter main rotor blade radar backscatter signal separation. IEEE Trans. Aerosp. Electron. Syst. 53(6), 2936–2949 (2017)CrossRefGoogle Scholar
  16. 16.
    E. Sejdić, I. Orović, S. Stanković, Compressive sensing meets time–frequency: an overview of recent advances in time–frequency processing of sparse signals. Digit. Signal Proc. 77, 22–35 (2018)MathSciNetCrossRefGoogle Scholar
  17. 17.
    P. Suresh, T. Thayaparan, T. Obulesu et al., Extracting micro-Doppler radar signatures from rotating targets using Fourier–Bessel transform and time–frequency analysis. IEEE Trans. Geosci. Remote Sens. 52(6), 3204–3210 (2014)CrossRefGoogle Scholar
  18. 18.
    Y. Yang, X. Dong, Z. Peng et al., Component extraction for non-stationary multi-component signal using parameterized de-chirping and band-pass filter. IEEE Signal Process. Lett. 22(9), 1373–1377 (2015)CrossRefGoogle Scholar
  19. 19.
    Y. Yang, Z.K. Peng, G. Meng et al., Characterize highly oscillating frequency modulation using generalized Warblet transform. Mech. Syst. Signal Process. 26, 128–140 (2016)CrossRefGoogle Scholar
  20. 20.
    H. Zhang, G. Bi, W. Yang et al., IF estimation of FM signals based on time–frequency image. IEEE Trans. Aerosp. Electron. Syst. 51(1), 326–343 (2015)CrossRefGoogle Scholar
  21. 21.
    Q. Zhang, T.S. Yeo, H.S. Tan et al., Imaging of a moving target with rotating parts based on the Hough transform. IEEE Trans. Geosci. Remote Sens. 46(1), 291–299 (2008)CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Electrical EngineeringNanjing Institute of Industry TechnologyNanjingChina

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