Skip to main content
SpringerLink
Log in

Signal Frequency Estimation via Kalman Filter and Least Squares Approach for Non-uniform Signals

  • ORIGINAL CONTRIBUTION
  • Published:
Journal of The Institution of Engineers (India): Series B Aims and scope Submit manuscript

Abstract

An innovative approach for estimating power system characteristics has been devised, and it is predicated on the Kalman filter (KF) and least squares (LS) approach. The procedure calculates an approximation of the signal’s frequency by taking three samples that are spaced equally apart. The computation of frequency requires the utilisation of the least squares method, which results in the identification of successive triples of instances. The difficulty can be solved by employing a slightly altered version of a method that calls for fewer mathematical calculations, but the resultant predictions are slightly less accurate. The strategy that has been suggested is the one that functions most effectively for predicting frequency. This is due to the fact that it has a fast response time and requires less data processing. In this work, we start by performing initial filtering using the KF before using the LS technique to estimate the frequencies. The responsiveness of the approach and its computation is precise. The discussion is on the factors that have an effect on the efficiency of such an approach, including the window size, sampling interval, distortion, harmonic components, and the filtering process. The performance results show that the suggested KF, along with the LS approach, produces a lesser estimate of the mean square error in comparison with other LS-based approaches.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. A.J. Dutra, J.F. de Oliveira, T.D.M. Prego, S.L. Netto, E.A. da Silva, High-precision frequency estimation of real sinusoids with reduced computational complexity using a model-based matched-spectrum approach. Digital Signal Process. 34, 67–73 (2014)

    Article  Google Scholar 

  2. Y.-Q. Tu, Y.-L. Shen, Phase correction autocorrelation-based frequency estimation method for sinusoidal signal. Signal Process. 130, 183–189 (2017)

    Article  Google Scholar 

  3. G. Izacard, S. Mohan, C. Fernandez-Granda, Data-driven estimation of sinusoid frequencies. Adv. Neural Inf. Process. Syst. 32 (2019)

  4. Y. Xia, Y. He, K. Wang, W. Pei, Z. Blazic, D.P. Mandic, A complex least squares enhanced smart dft technique for power system frequency estimation. IEEE Trans. Power Deliv. 32(3), 1270–1278 (2015)

    Article  Google Scholar 

  5. H. Ahmed, S.-A. Amamra, M. Bierhoff, Frequency-locked loop-based estimation of single-phase grid voltage parameters. IEEE Trans. Ind. Electron. 66(11), 8856–8859 (2018)

    Article  Google Scholar 

  6. A.B. Awoseyila, Robust synchronisation for PSK (DVBS2) and OFDM systems. University of Surrey (United Kingdom) (2008)

  7. A. Abdollahi, F. Matinfar, Frequency estimation: a least-squares new approach. IEEE Trans. Power Deliv. 26(2), 790–798 (2010)

    Article  Google Scholar 

  8. Y. Liu, D. Yan, H. Zheng, Signal frequency estimation based on Kalman filtering method, in MATEC Web of Conferences, vol. 56. EDP Sciences (2016), p. 03002

  9. R. Chudamani, K. Vasudevan, C. Ramalingam, Real-time estimation of power system frequency using nonlinear least squares. IEEE Trans. Power Deliv. 24(3), 1021–1028 (2009)

    Article  Google Scholar 

  10. A.A. Girgis, W.L. Peterson, Adaptive estimation of power system frequency deviation and its rate of change for calculating sudden power system overloads. IEEE Trans. Power Deliv. 5(2), 585–594 (1990)

    Article  Google Scholar 

  11. P.K. Dash, R. Jena, G. Panda, A. Routray, An extended complex kalman filter for frequency measurement of distorted signals. IEEE Trans. Instrum. Meas. 49(4), 746–753 (2000)

    Article  ADS  Google Scholar 

  12. L. Lai, W. Chan, C. Tse, A. So, Real-time frequency and harmonic evaluation using artificial neural networks. IEEE Trans. Power Deliv. 14(1), 52–59 (1999)

    Article  ADS  Google Scholar 

  13. M. Morelli, M. Moretti, A.A. D’Amico, Single-tone frequency estimation by weighted least-squares interpolation of fourier coefficients. IEEE Trans. Commun. 70(1), 526–537 (2021)

    Article  Google Scholar 

  14. S.-R. Nam, S.-H. Kang, S.-H. Kang, Real-time estimation of power system frequency using a three-level discrete fourier transform method. Energies 8(1), 79–93 (2014)

    Article  Google Scholar 

  15. C. Hu, Y. Wu, L. Huang, G. Yan, Unitary root-music based on tensor mode-r algorithm for multidimensional sinusoidal frequency estimation without pairing parameters. Multidimension. Syst. Signal Process. 31, 491–501 (2020)

    Article  MathSciNet  Google Scholar 

  16. L.-M. Zhu, H.-X. Li, H. Ding, Estimation of multifrequency signal parameters by frequency domain nonlinear least squares. Mech. Syst. Signal Process. 19(5), 955–973 (2005)

    Article  ADS  Google Scholar 

  17. P.J. Teunissen, O. Montenbruck, Springer Handbook of Global Navigation Satellite Systems, vol. 10 (Springer, 2017)

    Book  Google Scholar 

  18. H. Hafedh, N. Hamdi, N. Sboui, Optimising computing time in the wave iterative method by rls and sftf algorithms. Int. J. Numer. Model. Electron. Netw. Dev. Fields 32(6), e2645 (2019)

    Article  Google Scholar 

  19. A. Pradhan, A. Routray, A. Basak, Power system frequency estimation using least mean square technique. IEEE Trans. Power Deliv. 20(3), 1812–1816 (2005)

    Article  Google Scholar 

  20. M.A. Majidi, C.-S. Hsieh, H.S. Yazdi, Kalman filter reinforced by least mean square for systems with unknown inputs. Circuits Syst. Signal Process. 37, 4955–4972 (2018)

    Article  MathSciNet  Google Scholar 

  21. T. Nizampatnam, P. Kumar, Frequency estimation using kls technique, in 2022 OPJU International Technology Conference on Emerging Technologies for Sustainable Development (OTCON) (IEEE, 2023), pp. 1–6

  22. L. Stanković, I. Djurović, S. Stanković, M. Simeunović, S. Djukanović, M. Daković, Instantaneous frequency in time–frequency analysis: enhanced concepts and performance of estimation algorithms. Digital Signal Process. 35, 1–13 (2014)

    Article  Google Scholar 

  23. M.D. Kusljevic, J.J. Tomic, L.D. Jovanovic, Frequency estimation of three-phase power system using weighted-least-square algorithm and adaptive fir filtering. IEEE Trans. Instrum. Meas. 59(2), 322–329 (2009)

    Article  ADS  Google Scholar 

  24. H. Sepahvand, M. Saniei, S.S. Mortazavi, S. Golestan, Performance improvement of single-phase plls under adverse grid conditions: an fir filtering-based approach. Electric Power Syst. Res. 190, 106829 (2021)

    Article  Google Scholar 

  25. M. Karimi-Ghartemani, M.R. Iravani, A nonlinear adaptive filter for online signal analysis in power systems: applications. IEEE Trans. Power Deliv. 17(2), 617–622 (2002)

    Article  Google Scholar 

Download references

Funding

Authors state there is no funding involved in this study.

Author information

Authors and Affiliations

  1. School of Electronics Engineering, VIT-AP University, Amaravathi, Andhra Pradesh, 522237, India

    Thirumalesh Nizampatnam & Neeraj Kumar Misra

Authors
  1. Thirumalesh Nizampatnam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Neeraj Kumar Misra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Neeraj Kumar Misra.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nizampatnam, T., Misra, N.K. Signal Frequency Estimation via Kalman Filter and Least Squares Approach for Non-uniform Signals. J. Inst. Eng. India Ser. B (2024). https://doi.org/10.1007/s40031-024-01020-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40031-024-01020-3

Keywords

Search

Navigation