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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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DOI: https://doi.org/10.15866/iremos.v12i5.17839

Abstract


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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Keywords


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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References


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