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<p>The article considers the problem of trend detection in time series generated by technical equipment. The solution to this problem is closely related to the problem of detecting coarse measurements (outliers), which have a&#xa0;negative impact on the accuracy in estimating various physical quantities. Such quantities are obtained when solving a&#xa0;large number of applied problems in various scientific fields (space geodynamics, geodesy, etc.), where the input data are observations. Trends were plotted using a&#xa0;method previously proposed by the author, i.e., by maximizing the amount of outlier-free data used in subsequent processing. The reference values required for trend plotting are determined as a&#xa0;result of an absolutely convergent iterative process, with the minimizing set method at its core. At each step of the iterative process, the trend is approximated by a&#xa0;function from a&#xa0;predefined functional class. The aspects of trend analysis in the class of harmonic functions with unknown frequencies, phases, and amplitudes are examined. The main difficulty in solving this problem lies in the nonlinear dependence of harmonics on the target parameters, which does not allow the problem of trend analysis to be reduced to the solution of a&#xa0;system of linear equations. The conjugate gradient method generalized to nonlinear problems was used to search for harmonics approximating measurement data. The effectiveness of this method was tested using the test problem of trend plotting in computer-simulated data.</p>

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Minimizing set method for trend detection in the time series of noisy measurement data

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • Igor V. Bezmenov

摘要

The article considers the problem of trend detection in time series generated by technical equipment. The solution to this problem is closely related to the problem of detecting coarse measurements (outliers), which have a negative impact on the accuracy in estimating various physical quantities. Such quantities are obtained when solving a large number of applied problems in various scientific fields (space geodynamics, geodesy, etc.), where the input data are observations. Trends were plotted using a method previously proposed by the author, i.e., by maximizing the amount of outlier-free data used in subsequent processing. The reference values required for trend plotting are determined as a result of an absolutely convergent iterative process, with the minimizing set method at its core. At each step of the iterative process, the trend is approximated by a function from a predefined functional class. The aspects of trend analysis in the class of harmonic functions with unknown frequencies, phases, and amplitudes are examined. The main difficulty in solving this problem lies in the nonlinear dependence of harmonics on the target parameters, which does not allow the problem of trend analysis to be reduced to the solution of a system of linear equations. The conjugate gradient method generalized to nonlinear problems was used to search for harmonics approximating measurement data. The effectiveness of this method was tested using the test problem of trend plotting in computer-simulated data.