HOUND: High-Order Universal Numerical Differentiator for a Parameter-free Polynomial Online Approximation
HOUND:用于无参数多项式在线近似的高阶通用数值微分器
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…