Methods of enhancing the estimation efficiency of the number of signal harmonic components by using the surrogate data technology

Authors

DOI:

https://doi.org/10.3103/S073527271410001X

Keywords:

surrogate data, information criterion, signal-to-noise ratio, Gaussian noise

Abstract

The problem of enhancing the estimation efficiency of the number of harmonic components of signal based on its observation in the presence of additive white Gaussian noise using the surrogate data technology has been considered. The results of simulation modeling are presented. The application of this technology was shown to be effective at small and large values of the signal-to-noise ratio (SNR), when the frequencies of signal components were a multiple of the observation sampling frequency in the frequency domain.

References

MARPLE Jr., S.L. Digital Spectral Analysis with Applications. New Jersey: Prentice-Hall, 1986, 584 p.

STOICA, P.; MOSES, R.L. Introduction to Spectral Analysis. Prentice-Hall, 1997.

VASYLYSHYN, V.I. Direction finding of noise radiation sources with superresolution based on centrosymmetrical phased-array antenna by using modified unitary algorithm ESPRIT. Prikladnaya Radioelektronika, v.5, n.2, p.230-237, 2006.

VASYLYSHYN, V.I.; GRUSHENKO, M.V.; KOLESNIKOV, A.N. Efficiency of the modified spatial smoothing method. Zbirnyk Naukovykh Prats KhUPS, n.1, p.89-93, 2005.

EFRON, B. Nonconventional Methods of Multivariate Statistical Analysis. Moscow: Finansy i Statistika, 1988 [in Russian, translation from English of articles collection] 263 p.

ORLOV, A.I. Econometrics. Moscow: Ekzamen, 2002 [in Russian] 576 p.

SHITIKOV, V.K.; ROZENBERG, G.S. Randomization, Bootstrap, and Monte-Carlo Methods. Examples of the Statistical Analysis of Data in the Field of Biology and Ecology. Tolyatti, 2012 [in Russian] 290 p.

ZOUBIR, A.M.; BOASHASH, B. The bootstrap: signal processing applications. IEEE SP Magazine (Signal Processing), v.15, p.56-6, 1998.

GERSHMAN, A.B.; BOHME, J.F. A pseudo-noise approach to direction finding. Signal Processing, v.71, p.1-13, May 1998, DOI: http://dx.doi.org/10.1016/S0165-1684(98)00130-3.

VASYLYSHYN, V.I. Improved beamspace ESPRIT-based DOA estimation via pseudo-noise resampling. Proc. of 9th European Radar Conf., Oct. 31–Nov. 2, 2012, Amsterdam, Netherlands. IEEE, 2012, p.238-241, INSPEC: 13290424.

VASYLYSHYN, V. Removing the outliers in root-MUSIC via pseudo-noise resampling and conventional beamformer. Signal Processing, v.93, n.12, p.3423-3429, 2013, DOI: http://dx.doi.org/10.1016/j.sigpro.2013.05.026.

GERSHMAN, A.B. Pseudo-randomly generated estimator banks: A new tool for improving the threshold performance of direction finding. IEEE Trans. Signal Process., v.46, n.5, p.1351-1364, May 1998, DOI: http://dx.doi.org/10.1109/78.668797.

VASYLYSHYN, V.I. Direction finding with superresolution using root implementation of eigenstructure techniques and joint estimation strategy. Proc. of European Conf. on Wireless Technology, 11–12 Oct. 2004, Amsterdam, Netherlands. Amsterdam, 2004, p.101-104.

THEILER, JAMES S.; EUBANK, STEPHEN; LONGTIN, ANDRE; GALDRIKIAN, BRYAN; FARMER, J. DOYNE. Testing for nonlinearity in time series: The method of surrogate data. Physica D: Nonlinear Phenomena, v.58, n.1-4, p.77-94, Sept. 1992, DOI: http://dx.doi.org/10.1016/0167-2789(92)90102-S.

SMALL, M. Applied Nonlinear Time Series Analysis Applications in Physics, Physiology and Finance. World Scientific Publishing Co. Pte. Ltd., 2005, 245 p.

KANTZ, H.; SCHREIBER, T. Nonlinear Time Series Analysis. Cambridge: CUP, 2004, 369 p.

KOSTENKO, P.Y.; VASIUTA, K.S.; SYMONENKO, S.N.; BARSUKOV, A.N. Nonparametric BDS detector of chaotic signals against the background of white noise. Izv. Vyssh. Uchebn. Zaved., Radioelektron., v.54, n.1, p.23-31, 2011, http://radio.kpi.ua/article/view/S0021347011010031; Radioelectron. Commun. Syst., v.54, n.1, p.19-25, 2011, DOI: http://dx.doi.org/10.3103/S0735272711010031.

KOSTENKO, P.Y.; VASIUTA, K.S.; SLOBODYANYUK, V.V.; YAKOVENKO, D.S. The use of surrogate signals for enhancing the estimation quality of parameters of regular and chaotic signals observed against the background of additive noise. Systems of Control, Navigation and Communications, n.4, p.28-32, 2010.

KOSTENKO, P.Y.; VASYLYSHYN, V.I.; SYMONENKO, S.N.; VYSOTSKII, O.V.; YAKOVENKO, D.S. Enhancing the efficiency of coherent processing of chaotic signals during the transmission of binary messages using surrogate signals. Izv. Vyssh. Uchebn. Zaved., Radioelektron., v.55, n.7, p.24-33, 2012, http://radio.kpi.ua/article/view/S0021347012070035; Radioelectron. Commun. Syst., v.55, n.7, p.307-314, 2012, DOI: http://dx.doi.org/10.3103/S0735272712070035.

KOSTENKO, P.Y.; VASYLYSHYN, V.I. Enhancing the efficiency of spectral analysis of signals by the Root-MUSIC method using surrogate data. Izv. Vyssh. Uchebn. Zaved., Radioelektron., v.57, n.1, p.31-39, 2014, http://radio.kpi.ua/article/view/S0021347014010026; Radioelectron. Commun. Syst., v.57, n.1, p.31-38, 2014, DOI: http://dx.doi.org/10.3103/S0735272714010026.

VASYLYSHYN, V.I. Adaptive correction of preliminary processing of signals using the technology of surrogate data in spectral analysis problems. Syst. Obrob. Inf., n.2, p.15-20, 2013.

VASYLYSHYN, V.I. Enhancing the spectral analysis efficiency by the ESPRIT method using the technology of surrogate data. Prikladnaya Radioelektronika, v.12, n.3, p.412-418, 2013.

VASYLYSHYN, V.I. Enhancing the spectral analysis efficiency by eigenstructure methods using the surrogate data technology for eigenvectors of the covariance observation matrix. Radiotekhnika (Kharkiv), n.174, p.66-72, 2013.

VASYLYSHYN, V.I. Analysis of the spectral analysis procedure error using the surrogate data technology. Syst. Obrob. Inf., n.1, p.3-7, 2014.

WAX, M.; KAILATH, T. Detection of signals by information theoretic criteria. IEEE Trans. Acoust., Speech, Signal Process., v.33, n.2, p.387-392, Apr. 1985, DOI: http://dx.doi.org/10.1109/TASSP.1985.1164557.

WILLIAMS, D.B. Detection: determining the number of source. Digital Signal Processing Handbook. Boca Raton: CRC Press LLC, 1999 [ed. by V. K. Madisetti and D. B. Williams].

CHEN, P.; WU, TIEE-JIAN; YANG, J. A comparative study of model selection criteria for the number of signals. IET Radar, Sonar and Navigation, v.2, n.3, p.180-188, Jun. 2008, DOI: http://dx.doi.org/10.1049/iet-rsn:20070102.

GORBUNOVA, A.A.; KUZNETSOV, Y.V. Determination of the model order of the Doppler target spectrum. Proc. of 12th Int. Conf. and Exhib. on Digital Signal Processing and Applications, DSPA-2010, Moscow, Russia. Moscow, 2010.

KONOVALOV, L.N. Determination of the number of signals by the method of complex hypotheses testing using the likelihood ratio criterion. Izv. Vyssh. Uchebn. Zaved., Radioelektron., v.31, n.7, p.18-25, 1988; Radioelectron. Commun. Syst., v.31, n.7, p.16, 1988.

FAL’KOVICH, S.E.; KONOVALOV, L.N.; OLEINIKOV, S.Y. Foundations of the Radio System Theory. Kharkov: KhAI, 1990 [in Russian] 77 p.

ABRAMOV, A.D.; NEZHAL’SKII, R.V. Experimental investigation of the detector of the number of simultaneously observed components with unknown parameters. Radioelektronni i Kompyuterni Systemy, n.2, p.27-31, 2004, http://www.khai.edu/csp/nauchportal/Arhiv/REKS/2004/REKS204/pdf/Abramov.pdf.

LU, ZHIHUA; ZOUBIR, ABDELHAK M.; ROEMER, FLORIAN; HAARDT, MARTIN. Source enumeration using the bootstrap for very few samples. Proc. of 19th European Conf. on Signal Processing, EUSIPCO 2011, 29 Aug.–2 Sept. 2011, Barcelona, Spain. EURASIP, 2011, p.976-979, http://www.eurasip.org/Proceedings/Eusipco/Eusipco2011/papers/1569429813.pdf.

STOICA, PETRE; ERIKSSON, ANDERS. MUSIC estimation of real-valued sine-wave frequencies. Signal Processing, v.42, n.2, p.139-146, Mar. 1995, DOI: http://dx.doi.org/10.1016/0165-1684(94)00123-H.

Published

2014-10-11

Issue

Section

Research Articles