Based on the state observer theory of dynamic plants operating under uncertainty, we propose a method for reconstructing high-order derivatives of an online signal (for example, a reference action in a tracking system). The method requires neither numerical differentiation nor the presence of an analytical description of the signal. The dynamic differentiator is constructed as a replica of the virtual canonical model with an unknown but bounded input. The use of bounded correction actions and a special structure of the differentiator permit one to reduce the outliers of the resulting estimates at the beginning of a transient compared with a linear differentiator with high-gain coefficients. By way of application, we consider the problem of tracking a spatial trajectory by the center of mass of an unmanned aerial vehicle and present simulation results.