Increasing convergence rates of observers and differentiators for a class of nonlinear systems in the output canonical form (under presence of bounded matched disturbances, Lipschitz uncertainties and measurement noises) is investigated. A supervisory algorithm is designed that switches among different values of observer gains to accelerate the estimation. In the noise-free case, the presented switched-gain observer ensures global uniform time of convergence of the estimation error to the origin. In the presence of noise, the goals of overshoot reducing for the initial phase, acceleration of convergence and improvement of asymptotic precision of estimation are achieved. Efficiency of the proposed switching-gain observer is demonstrated by numerical comparison with a sliding mode and linear high-gain observers.