A novel method of estimating dynamic measurement errors

Abstract

A general method for estimating an upper bound of the dynamic measurement error in the time domain is derived, assuming that the complex-valued frequency response function of the system is known. This dynamic error bound related to the dynamic response of the system can be included in the measurement uncertainty as an uncorrected systematic error. The only restriction in the analysis is on linearity of the system, which can include electrical filters, mechanical sensors, amplifiers and similar subsystems. Calculations are verified by simulations for two example systems. The results for one of the most commonly used models of force and pressure transducers and accelerometers are presented emphasizing the main differences to a common estimate. For signals with well-confined spectra the linear dynamic error arises for two reasons: varying amplification and delay with frequency. The latter is analogous to the well-known bandwidth limiting dispersion of signals. For extended spectrum signals/simple pulses the asymptotic tails of the spectra may generate the major part of the error. No widespread robust, general and systematic method of quantifying the measurement error caused by these effects exists, despite that they may generate signal distortion far beyond the common prediction.