Differentiation with high-gain observers in the presence of measurement noise

The error in estimating the derivative(s) of a noisy signal by using a high-gain observer is studied and quantified. The error is bounded in terms of the infinity norms of the noise and a derivative of the signal. The error bound is independent of the frequency or derivatives of the noise. Guidelines are presented for the observer gain design when it is used for on-line differentiation. Analytical and simulation results are presented.