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arXiv · 2106.05320

Differentiator for Noisy Sampled Signals with Best Worst-Case Accuracy

Hernan Haimovich·Richard Seeber·Rodrigo Aldana-López·David Gómez-Gutiérrez
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Abstract

This paper proposes a differentiator for sampled signals with bounded noise and bounded second derivative. It is based on a linear program derived from the available sample information and requires no further tuning beyond the noise and derivative bounds. A tight bound on the worst-case accuracy, i.e., the worst-case differentiation error, is derived, which is the best among all causal differentiators and is moreover shown to be obtained after a fixed number of sampling steps. Comparisons with the accuracy of existing high-gain and sliding-mode differentiators illustrate the obtained results.

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Hernan Haimovich, Richard Seeber, Rodrigo Aldana-López, David Gómez-Gutiérrez. 2021-06-09. Differentiator for Noisy Sampled Signals with Best Worst-Case Accuracy. https://doi.org/10.1109/lcsys.2021.3087542

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