Non asymptotic estimation methods : a focus on the volterra and modulating functions approaches

Abstract

In this work, we present two non-asymptotic integration transform based estimation methods: the Volterra and modulating functions approaches. We explain the design and reproduce both of the robust Volterra observer of a biased sinusoidal signal and Volterra differentiator. We contribute to the Volterra differentiator by constructing a novel bivariate kernel functions family in order to extend the approach to the noisy scenario and obtain promising results. We also propose a novel type of pseudo-modulating functions that are randomized, relax the differentiability condition and test them on a simple ODE parameter estimation in both noise-free and noisy cases where we obtain a maximum error of 5%. At last, we use the modulating functions based method to estimate the arterial blood flow and Windkessel 2-Element parameter first with analytically generated blood pressure and then using a database and conclude by underlying the data-sensitivity of the method.