Papers › HOUND: High-Order Universal Numerical Differentiator for a Parameter-free Polynomial...

HOUND: High-Order Universal Numerical Differentiator for a Parameter-free Polynomial Online Approximation

18 Oct 2024arXiv:2411.00794archive 2025-07-28

Igor Katrichek

This paper introduces a scalar numerical differentiator, represented as a system of nonlinear differential equations of any high order. We derive the explicit solution for this system and demonstrate that, with a suitable choice of differentiator order, the error converges to zero for polynomial signals with additive white noise. In more general cases, the error remains bounded, provided that the highest estimated derivative is also bounded. A notable advantage of this numerical differentiation method is that it does not require tuning parameters based on the specific characteristics of the signal being differentiated. We propose a discretization method for the equations that implements a cumulative smoothing algorithm for time series. This algorithm operates online, without the need for data accumulation, and it solves both interpolation and extrapolation problems without fitting any coefficients to the data.

PaperPDFCode

Code

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Tasks

Time Series

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections