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<p>The article considers the correction of dynamic measurement error through sensor input signal restoration in the presence of additive noise at the sensor output. A&#xa0;review of publications on the application of the Savitzky-Golay filter in dynamic measurements is provided. Also, a&#xa0;diagram is presented for an adaptive dynamic measurement system based on a&#xa0;Savitzky-Golay discrete differentiation filter. It is proposed to reduce the transfer function of the sensor to its minimal form, an integrating element, whose order is equal to the order difference between the denominator and numerator of the transfer function. The proposed reduction consists in processing a&#xa0;sequence of discrete samples of the sensor output signal by means of a&#xa0;reduction block, whose output signal is equivalent to that of the sensor’s reduced transfer function. The dynamic error in input signal restoration is analyzed, along with estimation of its components, which are associated with the difference between the sensor’s transfer function and ideal function, as well as with additive noise at its output. The differentiation filter’s parameter is adapted to noise using the minimum standard deviation of the dynamic error estimate. A&#xa0;computer simulation of the developed measurement system was performed in the presence of additive random noise at the output of a&#xa0;second-order sensor. By means of the measurement system based on a&#xa0;Savitzky-Golay differentiation filter, the waveform and amplitude of the sensor input signal were effectively restored. The developed model of a&#xa0;dynamic measurement system can be used to process the results of measuring such rapidly varying quantities as temperature, pressure, velocity, and acceleration, whose measurement errors are dominated by the dynamic component due to sensor response time, as well as additive noise at the sensor output.</p>

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Application of the Savitzky-Golay differentiation filter in restoring the sensor input signal

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • Andrei S. Volosnikov

摘要

The article considers the correction of dynamic measurement error through sensor input signal restoration in the presence of additive noise at the sensor output. A review of publications on the application of the Savitzky-Golay filter in dynamic measurements is provided. Also, a diagram is presented for an adaptive dynamic measurement system based on a Savitzky-Golay discrete differentiation filter. It is proposed to reduce the transfer function of the sensor to its minimal form, an integrating element, whose order is equal to the order difference between the denominator and numerator of the transfer function. The proposed reduction consists in processing a sequence of discrete samples of the sensor output signal by means of a reduction block, whose output signal is equivalent to that of the sensor’s reduced transfer function. The dynamic error in input signal restoration is analyzed, along with estimation of its components, which are associated with the difference between the sensor’s transfer function and ideal function, as well as with additive noise at its output. The differentiation filter’s parameter is adapted to noise using the minimum standard deviation of the dynamic error estimate. A computer simulation of the developed measurement system was performed in the presence of additive random noise at the output of a second-order sensor. By means of the measurement system based on a Savitzky-Golay differentiation filter, the waveform and amplitude of the sensor input signal were effectively restored. The developed model of a dynamic measurement system can be used to process the results of measuring such rapidly varying quantities as temperature, pressure, velocity, and acceleration, whose measurement errors are dominated by the dynamic component due to sensor response time, as well as additive noise at the sensor output.