Non-asymptotic state estimation method using auxiliary time-varying modulating dynamical systems

The classical modulating functions method has undergone significant generalization over the past decade, extending its applicability to state estimation for both linear and nonlinear systems. This advancement involves employing generalized modulating functions, which can be viewed as solutions to a series of auxiliary dynamical systems with zero initial conditions. This paper aims to provide auxiliary time-varying modulating dynamical systems for non-asymptotic and robust state estimation for a class of linear time-varying systems. First, to better introduce the proposed method, a recent modulating functions method applied to the observable canonical form is recalled to deduce algebraic integral formulas for the state variables. Then, the idea of the proposed method is presented to obtain similar state’s formulas. Finally, by comparing these two methods, numerical results are given to demonstrate their accuracy and robustness against corrupting noises.