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Based on the maximum likelihood method, technically simple methods are proposed for detecting and measuring the moment of appearance of a fast-fluctuating random disturbance against Gaussian white noise. For this purpose, a new asymptotic approximation of the decision-determining statistics is obtained, its maximization by the current value of the unknown parameter is carried out, and block diagrams of the corresponding detector and measurer are developed in the form of quite simple single-channel units. To determine the performance of the synthesized processing algorithms, the asymptotically accurate expressions for their characteristics, which are the false alarm and missing probabilities (when a random disturbance is detected) and the conditional bias and variance of the estimate (when measuring the moment of occurrence of a random disturbance), are found using the local Markov approximation method. Using statistical simulation methods, an experimental test of the efficiency of these algorithms is conducted. It is established that the proposed detector and measurer are operational, and the theoretical formulas for the error probabilities and the moments of the desired estimate are in good agreement with experimental data in a wide range of values of the parameters of the analyzed process. #COMESYSO1120.

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Detecting and Estimating the Moment of Appearance of an Abrupt Gaussian Random Disturbance Under Fast Fluctuations of the Realization of Observed Data

  • 会议论文

  • 发表日期：

    2025年

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  • Oleg Chernoyarov,
  • Sergey Vybornov,
  • Elena Chernoiarova,
  • Maria Kholodova

摘要

Based on the maximum likelihood method, technically simple methods are proposed for detecting and measuring the moment of appearance of a fast-fluctuating random disturbance against Gaussian white noise. For this purpose, a new asymptotic approximation of the decision-determining statistics is obtained, its maximization by the current value of the unknown parameter is carried out, and block diagrams of the corresponding detector and measurer are developed in the form of quite simple single-channel units. To determine the performance of the synthesized processing algorithms, the asymptotically accurate expressions for their characteristics, which are the false alarm and missing probabilities (when a random disturbance is detected) and the conditional bias and variance of the estimate (when measuring the moment of occurrence of a random disturbance), are found using the local Markov approximation method. Using statistical simulation methods, an experimental test of the efficiency of these algorithms is conducted. It is established that the proposed detector and measurer are operational, and the theoretical formulas for the error probabilities and the moments of the desired estimate are in good agreement with experimental data in a wide range of values of the parameters of the analyzed process. #COMESYSO1120.