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Comparison of Methods for Parameter Estimating of Superimposed Sinusoids

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Recent Research in Control Engineering and Decision Making (ICIT 2020)

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 337))

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Abstract

The task of parameter estimation of signal components from a finite number of noisy discrete measurements is an active area of research. Different methods of signal components evaluation are used in practice, each of which has its own advantages and disadvantages. A new method for estimating signal components from a finite number of noisy discrete measurements based on the data matrix subfactorization is proposed. Comparison with one of the most popular methods described in IEEE-STD-1057, which presents algorithms for estimating the wave signal parameters from its noisy discrete time counts and with classic spectrum estimation method Periodogram is presented.

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References

  1. Stoica, P., Moses, R.: Introduction to Spectral Analysis, p. 427. Prentice-Hall, Upper Saddle River (1997)

    Google Scholar 

  2. Tufts, D.W., Kumaresan, R.: Estimation of frequencies of multiple sinusoids: making linear prediction perform like maximum likelihood. Proc. IEEE 70(9), 975–989 (1982)

    Article  Google Scholar 

  3. Micka, O.J., Weiss, A.J.: Estimating frequencies of exponentials in noise using joint diagonalization. IEEE Trans. Signal Process. 47(2), 341–348 (1999)

    Article  Google Scholar 

  4. Li, Y., Liu, K., Razavilar, J.: A parameter estimation scheme for damped sinusoidal signals based on low-rank hankel approximation. IEEE Trans. Signal Process. 45(2), 481–486 (1997)

    Article  Google Scholar 

  5. Roy, R., Kailath, T.: ESPRIT estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust., Speech, Signal Process. 37(7), 984–995 (1989)

    Google Scholar 

  6. Hua, Y., Sarkar, T.: Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise. IEEE Trans. Acoust., Speech, Signal Process. 38(4), 814–824 (1990)

    Google Scholar 

  7. Sarkar, T., Pereira, O.: Using the matrix pencil method to estimate the parameters of a sum of complex exponentials. IEEE Anten. Propag. Mag., vol.1, pp. 48–55 (1995)

    Google Scholar 

  8. So, H.C., Chan, K.W., Chan, Y.T., Ho, K.C.: Linerar prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses. IEEE Trans. Signal Process. 53(7), 2290–2305 (2005)

    Article  MathSciNet  Google Scholar 

  9. Linnik, Yu.V.: Metod naimen’shih kvadratov i osnovy’ teorii obrabotki nablu’deniy [The least square method and fundamentals of observation data processing theory]. GIFML, 336, (1958) (in Russian)

    Google Scholar 

  10. Bertocco, M., Offeli, C., Petri, D.: Analysis of damped sinusoidal signals via frequency-domain interpolation algorithm. IEEE Trans. Instrum. Meas. 43(2), 245–250 (1994)

    Article  Google Scholar 

  11. Wu, R.C., Chiang, C.T.: Analysis of the exponential signal by the interpolated DFT algorithm. IEEE Trans. Instrum. Meas. 59(12), 3306–3317 (2010)

    Article  Google Scholar 

  12. Moutchkaev, A.S., Kong, S.-H., L’vov, A.A.: Parameter estimation of superimposed sinusoids by data matrix subfactorization: theory and algorithm. In: Conference Proceedings International Conference on Actual Problems of Electron Devices Engineering, APEDE, vol. 2, pp. 442–447 (2016)

    Google Scholar 

  13. Moutchkaev, A.S., Kong, S.-H., L’vov, A.A.: Parameter estimation of superimposed sinusoids by data matrix subfactorization: analysis and results. In: Conference Proceedings International Conference on Actual Problems of Electron Devices Engineering, APEDE, vol. 2, pp. 448–455 (2016)

    Google Scholar 

  14. L’vov, A.A., Semenov, K.V.: A method of calibrating an automatic multi-probe measurement line. Measure. Techn. 42(4), 357–365 (1999)

    Google Scholar 

  15. Girko, V.L.: Spectrol’naya teoriya sluchayny’h matrits [Spectral theory of random matrices], Nauka, p. 376, (1988) (in Russian)

    Google Scholar 

  16. Marple, S.L.: Digital Spectral Analysis: Second Edition. Dover Publications, p. 432 (2019)

    Google Scholar 

  17. Händel, P.: Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm. IEEE Trans. Instrum. Measur. 49(6), 1189–1193 (2000)

    Article  Google Scholar 

  18. Ramos Pedro, M., Silva, F., Cruz Serra, A.: Improving sine-fitting algorithms for amplitude and phase measurements. In: Proceedings XVII IMEKO World Congress, Croatia, pp. 614–619 (2003)

    Google Scholar 

  19. Li, L., Hong, H.: Research on power spectrum estimation based on periodogram and burg algorithm. In: International Conference on Computer Application and System Modeling Taiyuan: ICCASM2010, vol. 3, pp. 695–698 (2010)

    Google Scholar 

  20. Wang, G., Wang, X., Zhao, X.: Speech enhancement based on a combined spectral subtraction with spectral estimation in various noise environment. In: International Conference on Audio, Language and Image Processing, Shanghai: ICALIP2008, pp. 1424–1429 (2008)

    Google Scholar 

  21. Musson, J., Jiang, L.: A Comparative Survey of PSD Estimation Method for EEG Signal Analysis

    Google Scholar 

  22. Proakis, J.G., Manolakis, D.G.: Digital Signal Processing: Principles, Algorithms, and Applications. Prentice Hall, Englewood Cliffs (1996)

    Google Scholar 

  23. Seranova, A.A., Abakumov, A.V., Gutsevich, D.E., Ermakov, R.V., Livshits, D.Yu., Romadin, S.N., Sergushov, I.V., Skripal’, E.N.: Design aspects of flight and navigation systems for small UAVs of different types. In: Proceedings 24th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2017, pp. 208–217 (2017)

    Google Scholar 

  24. Ermakov, R.V., Popov, A.N., Scripal E.N., Kalikhman D.M., Kondratov D.V., L’vov A.A.: Methods for testing and test results of inertial sensors intended for operation in helicopter-type aircraft. In: Proceedings 24th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2017, pp. 335–338 (2017)

    Google Scholar 

  25. Ermakov, R.V., Seranova, A.A., L’vov, A.A., Kalikhman, D.M.: Optimal estimation of the motion parameters of a precision rotating stand by maximum likelihood method. Measure. Techniques 62(2), 139–146 (2019). https://doi.org/10.1007/s11018-019-01598-x

    Article  Google Scholar 

  26. Gulevich, S.P., Sergushov, I.V., Skripal, E.N., Abakumov, A.V., Kuzmenko, I.K., Livshits, D.Yu., Shapovalova, K.D.: Aircraft high accuracy positioning during approach to a platform using laser system with the GNSS signals outage. In: Proceedings 25th Anniversary Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018, pp. 213–220 (2018)

    Google Scholar 

  27. Andersson, T., Hndel, P.: Toward a standardized multi-sinewave fit algorithm. In: Proceedings 9th European Workshop ADC Modelling Test, pp. 337–342 (2001)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Yuri Gagarin State Technical University of Saratov, Saratov, Russian Federation

    Alexey L’vov, Anna Seranova, Roman Ermakov & Alexandr Sytnik

  2. Martec Corporation, Las-Vegas, USA

    Artem Muchkaev

Authors
  1. Alexey L’vov
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  2. Anna Seranova
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  3. Roman Ermakov
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  4. Alexandr Sytnik
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  5. Artem Muchkaev
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Corresponding author

Correspondence to Anna Seranova .

Editor information

Editors and Affiliations

  1. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Olga Dolinina

  2. ITMO University, Saint Petersburg, Russia

    Igor Bessmertny

  3. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Alexander Brovko

  4. University of Texas at El Paso, El Paso, USA

    Vladik Kreinovich

  5. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Vitaly Pechenkin

  6. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Alexey Lvov

  7. Novosibirsk State Technical University, Novosibirsk, Russia

    Vadim Zhmud

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L’vov, A., Seranova, A., Ermakov, R., Sytnik, A., Muchkaev, A. (2021). Comparison of Methods for Parameter Estimating of Superimposed Sinusoids. In: Dolinina, O., et al. Recent Research in Control Engineering and Decision Making. ICIT 2020. Studies in Systems, Decision and Control, vol 337. Springer, Cham. https://doi.org/10.1007/978-3-030-65283-8_12

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