The novel reconstruction strategy for signals with uncertain dynamic properties

For the reconstruction of signals based on a sequence of observations governed by uncertain dynamic properties, we propose a new method by using Taylor´s formula and tracking differentiators. The method can be summarized as follows: Firstly, for a sequence of observations with uncertain dynamic properties, and/or the measurement contains noise, we use tracking-differentiators to smooth the observation results or filter the noise, and obtain the estimation of their differential values. Secondly, for the reconstruction of the signal nearby the given points, we use Taylor´s formula to construct the values. Theoretical estimation is provided to guarantee the precision of the relevant reconstruction results. Comparative analysis is also provided to show the advantages of the method. And simulation results for reconstructing certain kinds of observations indicate the effectiveness of the method.