Abstract
A comparative analysis of two methods of estimating the observation correlation matrix (CM) based on obtaining an ensemble of its segments and a pseudo-ensemble obtained by applying the technology of surrogate data. It was shown that in the range of small values of the signal-to-noise ratio the error of CM estimation using the pseudo-ensemble was less than that of the CM estimation using the observation segmentation. Since the CM estimation is a basic procedure in advanced methods of spectral analysis, this study showed (by using simulation) that the application of observation pseudo-ensemble made it possible to avoid the segmentation of observations, which causes the reduction of spectral analysis resolution.
Similar content being viewed by others
References
B. Efron, Nonconventional Methods of Multivariate Statistical Analysis (Finansy i Statistika, Moscow, 1988) [in Russian, translation from English of articles collection], 263 p.
A. I. Orlov, Econometrics (Ekzamen, Moscow, 2002) [in Russian], 576 p.
V. K. Shitikov and G. S. Rozenberg, Randomization and Bootstrap: Statistical Analysis of Data in the Field of Biology and Ecology Using R (Tolyatti, 2013) [in Russian].
A. M. Zoubir, B. Boashash, “The bootstrap: Signal processing applications,” IEEE SP Magazine (Signal Processing) 15, 56 (1998).
James S. Theiler, Stephen Eubank, Andre Longtin, Bryan Galdrikian, J. Doyne Farmer, “Testing for nonlinearity in time series: the method of surrogate data,” PhysicaD 58, Nos. 1–4, 77 (Sept. 1992), PII: 016727899290102S.
M. Small, Applied Nonlinear Time Series Analysis Applications in Physics, Physiology and Finance (World Scientific Publishing Co. Pte. Ltd., 2005), 245 p.
P. Yu. Kostenko, K. S. Vasiuta, V. V. Slobodyanyuk, D. S. Yakovenko, “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, No. 4, 28 (2010).
P. Yu. Kostenko, V. I. Vasylyshyn, S. N. Symonenko, O. V. Vysotskii, D. S. Yakovenko, “Enhancing the efficiency of coherent processing of chaotic signals during the transmission of binary messages using surrogate signals,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 55(7), 24 (2012), http://radio.kpi.ua/article/view/S0021347012070035 [Radioelectron. Commun. Syst. 55(7), 307 (2012), DOI: 10.3103/S0735272712070035].
A. B. Gershman, J. F. Bohme, “A pseudo-noise approach to direction finding,” Signal Processing 71, 1 (May 1998), DOI: 10.1016/S0165-1684(98)00130-3.
V. Vasylyshyn, “Removing the outliers in root-MUSIC via pseudo-noise resampling and conventional beamformer,” Signal Processing 93, No. 12, 3423 (2013), DOI: 10.1016/j.sigpro.2013.05.026.
Enno Mammen, Swagata Nandi, Thomas Maiwald, Jens Timmer, “Effect of jump discontinuity for phase-randomized surrogate data testing,” Int. J. Bifurcation Chaos 19, No. 1, 403 (Jan. 2009), DOI: 10.1142/S0218127409022968.
Alex B. Gershman, “Pseudo-randomly generated estimator banks: a new tool for improving the threshold performance of direction finding,” IEEE Trans. Signal Process. 46, No. 5, 1351 (May 1998), DOI: 10.1109/78.668797.
V. I. Vasylyshyn, “Direction finding with superresolution using root implementation of eigenstructure techniques and joint estimation strategy,” in Proc. of European Conf. on Wireless Technology, 11–12 Oct. 2004, Amsterdam, Netherlands (Amsterdam, 2004), pp. 101–104.
V. I. Vasylyshyn, “Enhancing the spectral analysis efficiency by eigenstructure methods using the surrogate data technology for eigenvectors of the covariance observation matrix,” Radiotekhnika (Kharkiv), No. 174, 66 (2013).
P. Yu. Kostenko, V. I. Vasylyshyn, “Enhancing the efficiency of spectral analysis of signals by the Root-MUSIC method using surrogate data,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 57(1), 31 (2014), http://radio.kpi.ua/article/view/S0021347014010026 [Radioelectron. Commun. Syst. 57(1), 31 (2014), DOI: 10.3103/S0735272714010026].
V. I. Vasylyshyn, “Adaptive correction of preliminary processing of signals using the technology of surrogate data in spectral analysis problems,” Syst. Obrob. Inf., No. 2, 15 (2013).
V. I. Vasylyshyn, “Enhancing the spectral analysis efficiency by the ESPRIT method using the technology of surrogate data,” Prikladnaya Radioelektronika 12, No. 3, 412 (2013).
V. I. Vasylyshyn, “Estimating the number of harmonic components of a signal with using surrogate data technology,” Prikladnaya Radioelektronika 12, No. 4, 542 (2013).
V. I. Vasylyshyn, “Analysis of the spectral analysis procedure error using the surrogate data technology,” Syst. Obrob. Inf., No. 1, 3 (2014).
P. Yu. Kostenko, V. I. Vasylyshyn, “Signal processing correction in spectral analysis using the surrogate autocovariance observation functions obtained by the ATS-algorithm,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 57(6), 3 (2014), http://radio.kpi.ua/article/view/S0021347014060016 [Radioelectron. Commun. Syst. 57(6), 235 (2014), DOI: 10.3103/S0735272714060016].
S. L. Marple Jr., Digital Spectral Analysis with Applications (Prentice-Hall, New Jersey, 1986).
P. Stoica and R. L. Moses, Introduction to Spectral Analysis (Prentice-Hall, 1997).
V. I. Vasylyshyn, A. N. Kolesnikov, “Uniform linear antenna array in superresolution mode by the modified unitary ESPRIT algorithm,” in Proc. of III Int. Conf. on Antenna Theory and Techniques, 8–11 Sept. 1999, Sevastopol, Ukraine (Sevastopol, 1999), pp. 254–255, http://icatt.org.ua/proc/article/view/ICATT.1999.1236181 .
V. I. Vasylyshyn, “High-resolution phased array signal processing via DFT beamspace TLS-ESPRIT with structure weighting,” in Proc. IEEE Int. Symp. on Phased Array Systems and Technology, 14–17 Oct. 2003, Boston, Massachusetts, USA (IEEE, 2003), pp. 605–610, DOI: 10.1109/PAST.2003.1257049.
M. Wax, Tie-Jun Shan, T. Kailath, “Spatio-temporal spectral analysis by eigenstructure methods,” IEEE Trans. Signal Process. 32, No. 4, 817 (Aug. 1984), DOI: 10.1109/TASSP.1984.1164400.
Petre Stoica, Anders Eriksson, “MUSIC estimation of real-valued sine-wave frequencies,” Signal Processing 42, No. 2, 139 (Mar. 1995), DOI: 10.1016/0165-1684(94)00123-H.
V. I. Vasylyshyn, M. V. Grushenko, A. N. Kolesnikov, “Efficiency of the modified spatial smoothing method,” Zbirnyk Naukovykh Prats KhUPS, No. 1, 89 (2005).
A. B. Gershman, V. T. Ermolaev, “Optimal subarray size for spatial smoothing,” IEEE Signal Process. Lett. 2, No. 2, 28 (Feb. 1995), DOI: 10.1109/97.365531.
A. V. Tarakanov, “Analysis of the possible increase of digital radar resolution,” in Proc. of Int. Conf. on Digital Signal Processing and Applications, DSPA-2009, Russia (2009), pp. 359–362.
Pierre Borgnat, Patrick Flandrin, “Stationarization via surrogates,” J. Stat. Mech., P01001 (2009), DOI: 10.1088/1742-5468/2009/01/P01001.
A. J. Barabell, “Improving the resolution performance of eigenstructure based direction-finding algorithms,” in Proc. of IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, ICASSP’83, Apr. 1983, Boston, MA (IEEE, 1983), Vol. 8, pp. 336–339, DOI: 10.1109/ICASSP.1983.1172124.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © P.Yu. Kostenko, V.I. Vasylyshyn, 2015, published in Izv. Vyssh. Uchebn. Zaved., Radioelektron., 2015, Vol. 58, No. 2, pp. 36–47.
ORCID: 0000-0002-3382-0684
ORCID: 0000-0002-5461-0125
About this article
Cite this article
Kostenko, P.Y., Vasylyshyn, V.I. Enhancing the spectral analysis efficiency at low signal-to-noise ratios using the technology of surrogate data without the segmentation of observation. Radioelectron.Commun.Syst. 58, 75–84 (2015). https://doi.org/10.3103/S0735272715020041
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0735272715020041