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.
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.
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.
illustrate the potential application of the proposed method in solving
practical tasks, probabilistic characteristics of detection of periodicity have
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.
1. Lyubushin A.A. Analiz dannyh sistem geofizicheskogo
i ehkologicheskogo monitoringa. [Analysis of data from
geophysical and ecological monitoring systems]. Moscow. Nauka Publ. 2007. 228 p. (In Russian).
2. Golik F.V. Characteristics of Periodic Stream Detection with
Independent Decimation in Superposition with a Simple Stream. Zhurnal
Radioelektroniki - Journal of Radio Electronics, 2015, No. 8. Available at
http://jre.cplire.ru/jre/aug15/4/text.pdf (In Russian).
3. Serebryakov M.G., Pervozvanskij A.A. Vyyavlenie skrytyh periodichnostej.
[Detection of hidden periodic behavior]. Moscow. Nauka Publ. 1965. 244 p. (In Russian).
Lidbetter M., Lindgren G., Rotsen X. Ehkstremumy sluchajnyh posledovatel'nostej
i processov. [Extremum of random sequences and
processes]. Moscow. Mir Publ. 1989. 392 p. (In Russian).
E.S. Sluchajnye processy v parametricheskih modelyah nadezhnosti. [Random processes in parametric models of
reliability]. Kiev. Nauk. dumka Publ.
1987. 240 p. (In Russian).