On Convergence of Tracking Differentiator with Multiple Stochastic Disturbances

TL;DR

This paper analyzes the convergence and noise robustness of a tracking differentiator under multiple stochastic disturbances, including colored and white noise, demonstrating its effectiveness in mean square and almost sure senses.

Contribution

It provides the first theoretical analysis of a tracking differentiator's convergence in the presence of multiple stochastic disturbances, including colored and white noise.

Findings

Tracks input signal and derivatives in mean square and almost sure senses

Convergence occurs as stochastic noise affecting input vanishes

Numerical simulations validate theoretical results

Abstract

In this paper, the convergence and noise-tolerant performance of a tracking differentiator in the presence of multiple stochastic disturbances are investigated for the first time. We consider a quite general case where the input signal is corrupted by additive colored noise, and the tracking differentiator itself is disturbed by additive colored noise and white noise. It is shown that the tracking differentiator tracks the input signal and its generalized derivatives in mean square and even in almost sure sense when the stochastic noise affecting the input signal is vanishing. Some numerical simulations are performed to validate the theoretical results.