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Detection and Measurement of the Unknown Moment and Magnitude of the Gaussian Random Process Energy Parameter Abrupt Change

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Synthesis, analysis, and simulation of the algorithms for detecting and measuring the abrupt change in the unknown mathematical expectation and dispersion of a fast fluctuating Gaussian random process at an unknown point in time are carried out in this paper. These algorithms can be technically implemented in a simpler way than the ones obtained by means of the common approaches. New asymptotic expressions are proposed for the logarithm of the functional of the likelihood ratio and its adaptive versions obtained after maximization by the unknown regular parameters under various hypotheses. By applying the joint application of the small parameter method and the local Markov approximation method, the closed asymptotically exact expressions are found for the characteristics of the performance of the synthesized detector and measurer. Both the procedure for determining the distribution law and the error moments of the estimate of the discontinuous parameter (abrupt change point) are illustrated, with an allowance of anomalous effects. By means of the statistical computer simulation, a satisfactory agreement is established between the obtained theoretical results and the corresponding experimental data.
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Abrupt Change of Random Process; Mathematical Expectation; Dispersion; Maximum Likelihood Method; Discontinuous Parameter; Small Parameter Method; Local Markov Approximation Method; False-Alarm Probability; Missing Probability; Statistical Simulation

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Kanaan Kadhim, Q., Yusof, R., Sadeq Mahdi, H., Rahayu Selamat, S., The Effectiveness of Random Early Detection in Data Center Transmission Control Protocol-Based Cloud Computing Networks, (2017) International Journal on Communications Antenna and Propagation (IRECAP), 7 (5), pp. 357-363.

Okoyeigbo, O., Okokpujie, K., Noma-Osaghae, E., Ndujiuba, C., Shobayo, O., Jeremiah, A., Comparative Study of MIMO-OFDM Channel Estimation in Wireless Systems, (2018) International Review on Modelling and Simulations (IREMOS), 11 (3), pp. 158-165.

A.A. Zhigljavsky, A.E. Krasnovsky, Detection of the Abrupt Change of Random Processes in Radio Engineering Problems [in Russian] (Leningrad State University, 1988).

N. Kligene, L. Tel'ksnis, Methods to Determine the Times when the Properties of Random Processes Change, Automation and Remote Control, Vol. 41 (Issue 10): 1241-1283, October 1983.

M. Basseville, I.V. Nikiforov, Detection of Abrupt Changes: Theory and Application (Prentice-Hall, 1993).

V. Konev, S. Vorobeychikov, Quickest Detection of Parameter Changes in Stochastic Regression: Nonparametric CUSUM, IEEE Transactions on Information Theory, Vol. 63 (Issue 9): 5588-5602, September 2017.

J. Song, J. Kang, Parameter change tests for ARMA-GARCH models, Computational Statistics and Data Analysis, Vol. 121: 41-56, May 2018.

J. Song, Robust Test for Dispersion Parameter Change in Discretely Observed Diffusion Processes, Computational Statistics and Data Analysis, Vol. 142, February 2020.

Y. Yu, X. Liu, L. Liu, P. Zhao, Detection of Multiple Change Points for Linear Processes under Negatively Super-Additive Dependence, Journal of Inequalities and Applications, Vol. 2019 (Issue 1), December 2019.

O.V. Chernoyarov, A.V. Salnikova, D.S. Rozhkova, Abrupt Change of the Mathematical Expectation of the Random Process with Unknown Intensity, Applied Mathematical Sciences, Vol. 9 (Issue 138): 6891-6908, November 2015.

O.V. Chernoyarov, M. Vaculik, A.V. Salnikova, L.A. Golpayegani, Detection and Measurement of the Fast-fluctuating Gaussian Random Process Dispersion Abrupt Change, International Journal of Control Theory and Applications, Vol. 10 (Issue 32): 261-276, July 2017.

A.P. Trifonov, Yu.S. Shinakov, Joint Discrimination of Signals and Estimation of their Parameters against Background [in Russian] (Radio i Svyaz', 1986).

A.P. Trifonov, E.P. Nechaev, V.I. Parfenov, Detection of Stochastic Signals with Unknown Parameters [in Russian] (Voronezh State University, 1991).

H.L. van Trees, K.L. Bell, Z. Tian, Detection, Estimation, and Modulation Theory. Part I. Detection, Estimation and Filtering Theory (Wiley, 2013).

O.V. Chernoyarov, M.M. Shahmoradian, K.S. Kalashnikov, The Decision Statistics of the Gaussian Signal against Correlated Gaussian Interferences, 2016 International Conference on Mathematical, Computational and Statistical Sciences and Engineering (MCSEE2016), pp. 426-431, Shenzhen, China, October, 2016.

A.P. Trifonov, O.V. Chernoyarov, Probability Characteristics of the Absolute Maximum of Generalized Rayleigh Stochastic Process, Radiophysics and Quantum Electronics, Vol. 42 (Issue 12): 1070-1079, December 1999.

O.V. Chernoyarov, Sai Si Thu Min, A.V. Salnikova, B.I. Shakhtarin, A.A. Artemenko, Application of the Local Markov Approximation Method for the Analysis of Information Processes Processing Algorithms with Unknown Discontinuous Parameters, Applied Mathematical Sciences, Vol. 8 (Issue 90): 4469-4496, July 2014.

J. Noonan, A. Zhigljavsky, Approximating Shepp's Constants for the Slepian Process, Statistics and Probability Letters, Vol. 153: 21-31, October 2019.

O.V. Chernoyarov, A.V. Salnikova, A.E. Rozanov, M. Marcokova, Statistical Characteristics of the Magnitude and Location of the Greatest Maximum of Markov Random Process with Piecewise Constant Drift and Diffusion Coefficients, Applied Mathematical Sciences, Vol. 8 (Issue 147): 7341-7357, October 2014.

M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (National Bureau of Standards, Applied Mathematics Series 55, 1964).

L. Ji, P. Liu, S. Robert, Tail asymptotic behavior of the supremum of a class of chi-square processes, Statistics and Probability Letters, Vol. 154: paper number 108551, November 2019.

A.P. Trifonov, Y.E. Korchagin, M.B. Bespalova, M.V. Trifonov, Amplitude Estimation of Rectangular Narrow-band Radio Pulse with Unknown Duration and Initial Phase, Radioelectronics and Communications Systems, Vol. 60 (Issue 12): 519-527, December 2017.

Baqqal, Y., El Hammoumi, M., Modelling and Optimization Techniques for Maintenance Systems Using Simulation: a Systematic Literature Review, (2019) International Review on Modelling and Simulations (IREMOS), 12 (3), pp. 152-162.

Chernoyarov, O., Trifonov, A., Salnikova, A., Zakharov, A., Probability Characteristics of the Absolute Maximum of the Discontinuous Homogeneous Gaussian Random Field, (2018) International Review on Modelling and Simulations (IREMOS), 11 (5), pp. 267-276.


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