SELECTION OF A STATISTICALLY OPTIMAL CRITERION FOR THE AGREEMENT OF A UNIFORM DISTRIBUTION FOR RANK SIGNAL PROCESSING UNDER CONDITIONS OF A PRIORI UNCERTAINTY
Abstract
The aim of the work is to choose a statistically optimal algorithm for making a decision
about the presence or absence of a signal for rank signal processing when solving the detection
problem under conditions of a priori uncertainty. Research objectives: 1) analysis of the decisionmaking
algorithm given in open sources for ranking procedures; search for its shortcomings; 2)
selection and justification of the optimal (in the statistical sense) decision-making algorithm for
use in rank signal processing; 3) conducting an experiment to obtain the characteristics of the
selected decision-making algorithm; 4) analysis of the results obtained. A model of signal processing
against the background of interference in conditions of a priori uncertainty is proposed.
The model consists of a rank detector and a solver that compares the empirical distribution of
ranks with the theoretical one. The rank detector allows you to reduce the problem of detecting asignal against the background of interference with an unknown distribution to the problem of testing
a simple hypothesis about the distribution of ranks. The decision device is based on the use of
a nonparametric Watson Consensus criterion, which has a high power (the probability of not making
a second – kind error-skipping a signal). The use of the proposed approach to solving the detection
problem under conditions of a priori uncertainty provides the following characteristics of
the system: 1) the use of rank procedures ensures that the parameters of the detection system are
insensitive to changing parameters of signals and interference; 2) the chosen decision-making
algorithm provides acceptable characteristics of the system under conditions of significant a priori
uncertainty. The proposed approach to solving the detection problem can find a place in many
scientific fields where there is a priori uncertainty. For example, in radar, sonar, communications,
medicine and other fields of science and technology.
References
of rank information processing]. K.: Tekhnika, 1986, 120 p.
2. R 50.1.033–2001. Rekomendatsii po standartizatsii. Prikladnaya statistika. Pravila proverki
soglasiya opytnogo raspredeleniya s teoreticheskim. Ch. I. Kriterii tipa khi-kvadrat
[P 50.1.033-2001. Recommendations for standardization. Applied statistics. Rules for checking
the agreement of the experimental distribution with the theoretical one. Part I. Criteria of
the chi-square type]. Moscow: Izd-vo standartov, 2002, 87 p.
3. Lemeshko B.Yu., Blinov P.Yu. Kriterii proverki otkloneniya raspredeleniya ot ravnomernogo
zakona [Criteria for checking the deviation of the distribution from the uniform law].
ovosibirsk, 2015, 182 p.
4. Lemeshko B.yu., Blinov P.Yu., Lemeshko S.B. O kriteriyakh proverki ravnomernosti zakona
raspredeleniya veroyatnostey [On the criteria for checking the uniformity of the probability
distribution law], Avtometriya [Autometry], 2016, Vol. 52, No. 2.
5. Lemeshko B.Yu., Gorbunova A.A. O primenenii i moshchnosti neparametricheskikh kriteriev
soglasiya Kupera, Vatsona i Zhanga [On the application and power of nonparametric consent
criteria of Cooper, Watson and Zhang], Izmeritel'naya tekhnika [Measuring Technique], 2013,
No. 5, pp. 3-9.
6. Lemeshko B.Yu., Gorbunova A.A. Application of nonparametric Kuiper and Watson tests of
goodness-of-fit for composite hypotheses, Measurement Techniques, 2013, Vol. 56, No. 9,
pp. 965-973.
7. Lemeshko B.Yu., Gorbunova A.A. Application and Power of the Nonparametric Kuiper, Watson,
and Zhang Tests of Goodness-of-Fit, Measurement Techniques, 2013, Vol. 56, No. 5,
pp. 465-475.
8. Lemeshko B.Yu., Gorbunova A.A., Lemeshko S.B., Rogozhnikov A.P. Solving problems of using
some nonparametric goodness-of-fit tests, Optoelectronics, Instrumentation and Data Processing,
2014, Vol. 50, No. 1, pp. 21-35.
9. Watson G.S. Goodness-of-fit tests on a circle. I, Bio-metrika, 1961, Vol. 48, No. 1-2, pp. 109-114.
10. Watson G.S. Goodness-of-fit tests on a circle. II, Bio-metrika, 1962, Vol. 49, No. 1-2, pp. 57-63.
11. Fedosov V.P. Prikladnye matematicheskie metody v statisticheskoy radiotekhnike: ucheb.
posobie [Applied mathematical methods in statistical radio engineering: a textbook]. Taganrog:
Izd-vo TRTU, 1998, 74 p.
12. Ryzhov V.P., Fedosov V.P. Optimal'nye metody obrabotki signalov na fone pomekh: Tekst
lektsiy [Optimal methods of signal processing against the background of interference: The text
of lectures]. Taganrog: TRTI, 1990, 54 p.
13. Fedosov V.P. Radiotekhnicheskie tsepi i signaly: dlya samostoyatel'nogo izucheniya: ucheb.
posobie [Radio engineering circuits and signals: for self-study: a textbook]. Taganrog: Izd-vo
TRTU, 2004, 208 p.
14. Ryzhov V.P., Fedosov V.P. Analiz radiotekhnicheskikh ustroystv pri vozdeystvii sluchaynykh
protsessov [Analysis of radio engineering devices under the influence of random processes].
Taganrog: TRTI, 1986.
15. Ryzhov V.P., Fedosov V.P. Statisticheskie metody obrabotki signalov [Statistical methods of
signal processing]. Taganrog: TRTI, 1986.
16. Repin V.G., Tartakovskiy G.P. Statisticheskiy sintez pri apriornoy neopredelennosti i
adaptatsiya informatsionnykh system [Statistical synthesis with a priori uncertainty and adaptation
of information systems]. Moscow: Sovetskoe radio, 1977, 432 p.
17. Bogdanovich V.A., Vostretsov A.G. Teoriya ustoychivogo obnaruzheniya, razlicheniya i
otsenivaniya signalov [The theory of stable detection, discrimination and evaluation of signals].
Moscow: Fizmatlit, 2003, 320 p.
18. Gaek Ya., Shidak Z. Teoriya rangovykh kriteriev [The theory of rank criteria]: translated from
English. Moscow: Nauka, 1971.
19. Rabiner L., Gould R. Teoriya i primenenie tsifrovoy obrabotki signalov [Theory and application
of digital signal processing]. Moscow: Mir, 1978.
20. Sergienko A.B. TSifrovaya obrabotka signalov [Digital signal processing]. Saint Petersburg:
Izd-vo «Piter», 2002, 608 p.
