"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 9, 2016

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The presence of periodicity detection in a random stream in terms of prior uncertainty


F. V. Golik

Yaroslav-the-Wise Novgorod State University

The paper is received on September 17, 2016

Abstract: The article is devoted to the development of the method of periodic component detection in a random stream in the terms of prior uncertainty regarding stream parameters and impossibility of multiple observations of stream realizations. Available for observation stream realization is the superposition of decimated periodic stream with interval wobbulation and Poisson arrival.

To enhance the periodic component of the stream a method of point stream conversion into delta function is proposed. The amplitude spectrum of the converted stream is the spectral function (SF) of the original stream.

It is shown that the density of the probability distribution of the global maximum of Poisson arrival SF is well approximated by an alpha distribution. The relations of quantiles of this distribution to the number of points of Poisson arrival are found by the method of statistical simulation in software MathCad. This allowed to reducĺ the problem of detecting periodicity to the verification of statistical hypotheses that the observed realization of the stream is Poisson, i.e. contains no periodicity.

To illustrate the potential application of the proposed method in solving practical tasks, probabilistic characteristics of detection of periodicity have been calculated.

The proposed procedure for the periodicity detection may be used in passive radar systems and radio observations systems, as well as in practical tasks related to the random streams properties research.

Key words: random stream, decimation, wobble, superposition of streams, acquisition probability, false-alarm probability, detection performances, passive radiolocation, radio tracking.


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