Algebraic time-derivative estimation in the context of reconstructibility,Algebraische Ableitungsschätzung im Kontext der Rekonstruierbarkeit

The algebraic approach to time-derivative estimation of measurement signals, proposed by Fliess and Sira Ramírez, is developed out of classical results from optimal estimation theory. By means of simple calculations it is shown that the algebraic method may be obtained as a special case of state reconstruction using reconstructibility Gramians. The paper concludes with links to further estimation methods, as least-squares estimation and Kalman-filtering, and briefly points out practical implications.