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Determination of Probabilistic Characteristics of Random Values of Estimates of the Lyapunov Function for Description of a Physical Process

Application of the Lyapunov characteristic function is determined by the means for estimating it. The probabilistic characteristics of estimates of the Lyapunov characteristic function are described for the first time. The probabilistic characteristics of random values of estimates of the Lyapunov function are estimated empirically by statistical methods. A model of a special device for producing estimates of the characteristic function by a direct method is developed in the Matlab package. A quasi-deterministic signal is delivered to the input of the model for which the instantaneous values are distributed according to an arcsine law and at the output a set of values of estimates of the Lyapunov function is obtained which is used to evaluate the probabilistic characteristics of these estimates. Statistical evaluation is carried out by an indirect method. It is found that the values of the estimates of the Lyapunov characteristic function are distributed according to a normal law. The results of these studies will be of use for engineering calculations, e.g., in identifying the errors in transfer of messages in modems with a modulated characteristic function.

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Correspondence to D. A. Titov.

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Translated from Metrologiya, No. 4, pp. 53–67, October–December, 2021.

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Veshkurtsev, Y.M., Titov, D.A. Determination of Probabilistic Characteristics of Random Values of Estimates of the Lyapunov Function for Description of a Physical Process. Meas Tech 64, 1010–1015 (2022). https://doi.org/10.1007/s11018-022-02037-0

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  • DOI: https://doi.org/10.1007/s11018-022-02037-0

Keywords

  • estimates of probabilistic characteristics
  • random process
  • Lyapunov characteristic function
  • estimate measurement device