Abstract
One of the main challenges in the analysis of dynamic measurements is the estimation of the timedependent value of the measurand and the corresponding propagation of uncertainties. In this paper we outline the design of appropriate digital compensation filters as a means of estimating the quantity of interest. For the propagation of uncertainty in the application of such digital filters we present online formulae for finite impulse response and infinite impulse response filters. We also demonstrate a recently developed efficient Monte Carlo method for uncertainty propagation in dynamic measurements which allows calculating point-wise coverage intervals in real-time.
Highlights
The "Guide to the Expression of Uncertainty in Measurement" (GUM) [1] provides a framework for harmonized evaluation and the interpretation of measurement uncertainty
For the propagation of uncertainty in the application of such digital filters we present sequential formulae for finite impulse response (FIR) and infinite impulse response (IIR) filters [8,9]
The analysis of dynamic measurements and in particular the corresponding evaluation of uncertainties is a topic of growing importance in metrology
Summary
The "Guide to the Expression of Uncertainty in Measurement" (GUM) [1] provides a framework for harmonized evaluation and the interpretation of measurement uncertainty. We assume that the continuous time-dependent functions ܺሺݐሻ and ܻሺݐሻ can be represented by discrete-time sequences ࢄ ൌ ሺܺଵǡ ǥ ǡ ܺேሻ் and ࢅ ൌ ሺܻଵǡ ǥ ǡ ܻேሻ் with ܺ ൌ ܺሺݐሻ and ܻ ൌ ܻሺݐሻ for equidistant ݐ with a sampling interval length ܶ௦. This can be assumed when, for instance, the length of the sampling interval ܶௌ in the analogue-todigital conversion satisfies the Nyquist criterion [6]. We demonstrate a recently developed efficient Monte Carlo method for uncertainty propagation in dynamic measurements which, in principle, allows calculating point-wise coverage intervals in real-time [10]
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