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Uncertainty evaluation for IIR (infinite impulse response) filtering using a state-space approach

A novel method is proposed for evaluating the uncertainty associated with the output of a discrete-time IIR filter when the input signal is corrupted by additive noise and the filter coefficients are uncertain. This task arises, for instance, when the noise-corrupted output of a measurement system is compensated by a digital filter which has been designed on the basis of the characteristics of the measurement system. We assume that the noise is either stationary or uncorrelated, and we presume knowledge about its autocovariance function or its time-dependent variances, respectively. Uncertainty evaluation is considered in line with the ‘Guide to the Expression of Uncertainty in Measurement’. A state-space representation is used to derive a calculation scheme which allows the uncertainties to be evaluated in an easy way and also enables real-time applications. The proposed procedure is illustrated by an example.