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<p>Based on observations of the realization of a non-stationary random process on a finite interval and at discrete points, the authors analyze the problem of estimating linear functionals of spectral functions of signals that are included in the mean values of such processes. Under the conditions that the correlation function of the random process and the spectral function of the signal are unknown and belong to certain bounded sets, expressions for guaranteed mean square linear estimates of a set of linear functionals of spectral functions are found. In a special case, such estimates are shown to be expressed in terms of solutions to certain linear integral and linear algebraic equations. Test examples illustrate the use of a guaranteed approach to finding linear mean square estimates of the corresponding linear functionals.</p>

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Linear Mean Square Estimates of the Spectral Functions of Mean Values of Nonstationary Random Processes Under Uncertainty

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • O. G. Nakonechnyi,
  • P. M. Zinko,
  • T. P. Zinko

摘要

Based on observations of the realization of a non-stationary random process on a finite interval and at discrete points, the authors analyze the problem of estimating linear functionals of spectral functions of signals that are included in the mean values of such processes. Under the conditions that the correlation function of the random process and the spectral function of the signal are unknown and belong to certain bounded sets, expressions for guaranteed mean square linear estimates of a set of linear functionals of spectral functions are found. In a special case, such estimates are shown to be expressed in terms of solutions to certain linear integral and linear algebraic equations. Test examples illustrate the use of a guaranteed approach to finding linear mean square estimates of the corresponding linear functionals.