1. bookVolume 19 (2019): Issue 6 (December 2019)
Journal Details
License
Format
Journal
eISSN
1335-8871
First Published
07 Mar 2008
Publication timeframe
6 times per year
Languages
English
access type Open Access

Measuring the Moment and the Magnitude of the Abrupt Change of the Gaussian Process Bandwidth

Published Online: 21 Nov 2019
Volume & Issue: Volume 19 (2019) - Issue 6 (December 2019)
Page range: 250 - 256
Received: 12 Jul 2019
Accepted: 07 Nov 2019
Journal Details
License
Format
Journal
eISSN
1335-8871
First Published
07 Mar 2008
Publication timeframe
6 times per year
Languages
English
Abstract

The maximum likelihood algorithm is introduced for measuring the unknown moment of abrupt change and bandwidth jump of a fast-fluctuating Gaussian random process. This algorithm can be technically implemented much simpler than the ones obtained by means of common approaches. The technique for calculating the characteristics of the synthesized measurer is presented and the closed analytical expressions for the conditional biases and variances of the resulting estimates are found using the additive local Markov approximation of the decision statistics. By statistical simulation methods, it is confirmed that the presented measurer is operable, while the theoretical formulas describing its performance well approximate the corresponding experimental data in a wide range of the parameter values of the analyzed random process.

Keywords

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

[2] Kligene, N., Tel'ksnis, L. (1983). Methods to determine the times when the properties of random processes change. Automation and Remote Control, 41 (10), 1241-1283.Search in Google Scholar

[3] Basseville, M., Nikiforov, I.V. (1993). Detection of Abrupt Changes: Theory and Application. Prentice-Hall.Search in Google Scholar

[4] Konev, V., Vorobeychikov, S. (2017). Quickest detection of parameter changes in stochastic regression: Nonparametric CUSUM. IEEE Transactions on Information Theory, 63 (9), 5588-5602.10.1109/TIT.2017.2673825Search in Google Scholar

[5] Hanus, R., Kowalczyk, A., Chorzȩpa, R. (2018). Application of conditional averaging to time delay estimation of random signals. Measurement Science Review, 18 (4), 130-137.10.1515/msr-2018-0019Search in Google Scholar

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

[7] Van Trees, H.L., Bell, K.L., Tian, Z. (2013). Detection, Estimation, and Modulation Theory: Part I - Detection, Estimation, and Filtering Theory. Wiley.Search in Google Scholar

[8] Chernoyarov, O.V., Shahmoradian, M.M., Kalashnikov, K.S. (2016). The decision statistics of the Gaussian signal against correlated Gaussian interferences. In 2016 International Conference on Mathematical, Computational and Statistical Sciences and Engineering, 30-31 October 2016, Shenzhen, China. DEStech Publications, 426-431.Search in Google Scholar

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

[10] Chernoyarov, O.V., Sai Si Thu Min, Salnikova, A.V., Shakhtarin, B.I., Artemenko, A.A. (2014). Application of the local Markov approximation method for the analysis of information processes processing algorithms with unknown discontinuous parameters. Applied Mathematical Sciences, 8 (90), 4469-4496.10.12988/ams.2014.46415Search in Google Scholar

[11] Kailath, T. (1966). Some integral equations with nonrational kernals. IEEE Transactions on Information Theory, 12 (4), 442-447.10.1109/TIT.1966.1053925Search in Google Scholar

[12] Chernoyarov, O.V., Salnikova, A.V., Rozanov, A.E., Marcokova, M. (2014). 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, 8 (147), 7341-7357.10.12988/ams.2014.49740Search in Google Scholar

[13] Zakharov, A.V., Pronyaev, E.V., Trifonov, A.P. (2001). Detection of step random disturbance. Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, (6), 29-37.Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo