Skip to main content
Log in

Square Root Unscented Digital Phased-locked Loop

  • Technical Notes and Correspondence
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

Digital phase-locked loops (DPLLs) are widely used for synchronizing and estimating phase information. In DPLLs, the state estimator is a powerful method to estimate unknown phase information accurately. The Kalman filter (KF) is a well-known state estimator and has been employed to design DPLLs. However, the KF-based DPLL limited as it rsults in inaccurate modeling, including nonlinear effects (e.g., quantization error). The particle filter (PF) is a useful state estimator, but it incurs a large computation burden. In this paper, we propose a novel approach to design the square root unscented DPLL (SRUDPLL) in order to overcome the defects of the existing DPLLs. Through simulations, we demonstrate that the proposed method shows better performance than the existing approach in terms of nonlinear effects.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. W. C. Lindsey and C. M. Chie, “A survey of digital phaselocked loops,” Proc. IEEE, vol. 69, no. 4, pp. 410–431, Apr. 1981.

    Article  Google Scholar 

  2. S. R. Al-araji, Z. M. Hussain, and M. A. Al-qutayri, Digital Phase Lock Loops: Architectures and Applications. Springer, 2006.

    Book  Google Scholar 

  3. M. H. Izadi and B. Leung, “PLL-based frequency discriminator using the loop filter as an estimator,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process, vol. 49, no. 11, pp. 721–727, Nov. 2002.

    Article  Google Scholar 

  4. J. Hakkinen and J. Kostamovaara, “Speeding up an integer-N PLL by controlling the loop filter charge,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process, vol. 50, no. 7, pp. 343–354, Jul. 2003.

    Article  Google Scholar 

  5. R. B. Staszewski and P. T. Balsara, “All-digital PLL with ultra fast settling,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 54, no. 2, pp. 181–185, Feb. 2007. [click]

    Article  Google Scholar 

  6. C. K. Ahn, S. Han, and W. H. Kwon, “H FIR filters for linear continuous-time state-space systems,” IEEE Signal Process. Lett., vol. 13, no. 9, pp. 557–560, Sep. 2006. [click]

    Article  Google Scholar 

  7. C. K. Ahn, “Robustness bound for receding horizon finite memory control: Lyapunov-Krasovskii approach,” International Journal of Control, vol. 85, no. 7, pp. 942–949, Mar. 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  8. Y. S. Shmaliy, S. Zhao, and C. K. Ahn, “Unbiased finite impluse response filtering: an iterative alternative to Kalman filtering ignoring noise and initial conditions,” IEEE Control Systems Magazine, vol. 37, no. 5, pp. 70–89, Oct. 2017. [click]

    Article  Google Scholar 

  9. C. K. Ahn, “A new solution to the induced l finite impulse response filtering problem based on two matrix inequalities,” International Journal of Control, vol. 87, no. 2, pp. 404–409, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. C. K. Ahn, P. Shi, and M. V. Basin, “Two-dimensional dissipative control and filtering for Roesser model,” IEEE Transactions on Automatic Control, vol. 60, no. 7, pp. 1745–1759, Jul. 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  11. C. K. Ahn, P. Shi, and M. V. Basin, “Deadbeat dissipative FIR filtering,” IEEE Transactions on Circuits and Systems I-Regular Paper, vol. 63, no. 8, pp. 1210–1221, Aug. 2016. [click]

    Article  MathSciNet  Google Scholar 

  12. J. M. Pak, C. K. Ahn, Y. S. Shmaliy, and M. T. Lim, “Improving reliability of particle filter-based localization in wireless sensor networks via hybrid particle/FIR filtering,” IEEE Transactions on Industrial Informatics, vol. 11, no. 5, pp. 1089–1098, Oct. 2015. [click]

    Article  Google Scholar 

  13. J. M. Pak, C. K. Ahn, Y. S. Shmaliy, P. Shi, and M. T. Lim, “Switching extensible FIR filter bank for adaptive horizon state estimation with application,” IEEE Transactions on Control Systems Technology, vol. 24, no. 3, pp. 1052–1058, May. 2016. [click]

    Article  Google Scholar 

  14. S. Zhao, Y. S. Shmaliy, P. Shi, and C. K. Ahn, “Fusion kalman/UFIR filter for state estimation with uncertain parameters and noise statistics,” IEEE Trans. Industrial Electronics, vol. 64, no. 4, pp. 3075–3083, 2017. [click]

    Article  Google Scholar 

  15. S. Zhao, Y. S. Shmaliy, C. K. Ahn, and P. Shi, “Real-time optimal state estimation of multi-DOF industrial systems using FIR filtering,” IEEE Trans. on Industrial Informatics, vol. 13, no. 3, pp. 967–975, 2017. [click]

    Article  Google Scholar 

  16. D. Song, J. Yang, M. Dong, and Y. H. Joo, “Kalman filterbased wind speed estimation for wind turbine control,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1089–1096, 2017. [click]

    Article  Google Scholar 

  17. P. F. Driessen, “DPLL bit synchronizer with rapid acquisition using adaptive Kalman filtering techniques,” IEEE Trans. Commun., vol. 42, no. 9, pp. 2673–2675, Sep. 1994.

    Article  Google Scholar 

  18. A. Patapoutian, “On phase-locked loops and Kalman filters,” IEEE Trans. Commun., vol. 47, no. 5, pp. 670–672, May. 1999. [click]

    Article  Google Scholar 

  19. A. Patapoutian, “Application of Kalman filters with a loop delay in synchronization,” IEEE Trans. Commun., vol. 50, no. 5, pp. 703–706, May. 2002. [click]

    Article  Google Scholar 

  20. A. V. Oppenheim and R. W. S. J. Buck, Discrete Time Signal Processing, Prentice Hall, 1999.

    Google Scholar 

  21. D. S. K. Chan and L. R. Rabiner, “Analysis of quantization errors in the direct form for finite impulse response digital filters,” IEEE Trans. Audio Electroacoust., vol. AU-21, Aug 1973.

    Google Scholar 

  22. B. Widrow and I. Koll, Quantization Noise, Cambridge Univ. Press, 2008.

    Book  Google Scholar 

  23. S. H. You, J. M. Pak, and J. H. Kim, “Optimal horizon size for unbiased finite memory digital phase-locked loop,” IEICE Electronics Express, vol. 14, no. 3, p. 20161184, Feb. 2017.

    Article  Google Scholar 

  24. C. K. Ahn, P. Shi, and S. H. You, “Optimal memory size formula for moving-average digital phase-locked loop,” IEEE Signal Processing Letters, vol. 23, no. 12, pp. 1844–1847, Dec. 2016. [click]

    Article  Google Scholar 

  25. C. K. Ahn, P. Shi, and S. H. You, “A new approach on design of a digital phase-locked loop,” IEEE Signal Processing Letters, vol. 23, no. 5, pp. 600–604, May. 2016. [click]

    Article  Google Scholar 

  26. S. H. You, J. M. Pak, C. K. Ahn, P. Shi, and M. T. Lim, “Unbiased finite memory digital phase locked loop,” IEEE Transactions on Circuits and Systems II, vol. 63, no. 8, pp. 798–802, Aug. 2016. [click]

    Article  Google Scholar 

  27. J. H. Chung, S. H. You, J. M. Pak, J. H. Kim, M. T. Lim, and M. K. Song, “A novel particle filter-based digital phase-locked loop robust against quantization error,” International Journal of Control, Automation and Systems, vol. 15, no. 1, pp. 457–461, Feb. 2017. [click]

    Article  Google Scholar 

  28. Y. Zhao, S. Gao, J. Zhang, and Q. Sun, “Robust predictive augmented unscented kalman filter,” International Journal of Control, Automation and Systems, vol. 12, no. 5, pp. 996–1004, 2014. [click]

    Article  Google Scholar 

  29. R. V. d. Menve and E. A. Wan, “The squre-root unscented kalman filter for state and parameter-estimation,” Oregon Graduate Institute of Science and Technology, Oregon 97006, USA, pp. 3461–3464, May 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Moon Kyou Song.

Additional information

Recommended by Associate Editor Choon Ki Ahn under the direction of Editor Myo Taeg Lim. This research was supported by Wonkwang University in 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

You, S.H., Kang, H.H. & Song, M.K. Square Root Unscented Digital Phased-locked Loop. Int. J. Control Autom. Syst. 16, 387–391 (2018). https://doi.org/10.1007/s12555-017-0394-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-017-0394-6

Keywords

Navigation