Differentiator for Noisy Sampled Signals with Best Worst-Case Accuracy

HAIMOVICH, HERNAN; SEEBER, RICHARD; ALDANA-LOPEZ, RODRIGO; GOMEZ-GUTIERREZ, DAVID

IEEE Control Systems Letters

Institute of Electrical and Electronics Engineers Inc.

Año: 2022 vol. 6 p. 938 - 943

This letter 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.