An algebraic denoising scheme

In this paper, the noise filtering problem ("denoising" problem) is approached via a suitable modification of the traditional Luenberger observer approach, also known as the "high gain observer" approach (HGO). The HGO observer is, fundamentally, a Luenberger observer with large stable eigenvalues of the output estimation error dynamics. HGO and some of its modifications have been particularly useful in the linear based control of perturbed linear and nonlinear systems. HGO are, however, inappropriate to deal with noisy injection signals and noisy plants. To overcome this fact, the structure of the Luenberger state estimator reconstructing the time derivatives of the given signal is enhanced against the effects of noise by means of an algebraic filtering scheme. The algebraic filtering consists in a suitable modification of the recently introduced algebraic parameter identification methodology. The proposed approach is capable of attenuating the noise effects significantly. The proposed strategy is illustrated via numerical simulations.