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