Kernel-based non-asymptotic parameter estimation of continuous-time systems

This work introduces a framework devoted to the design of parametric estimators with very fast convergence properties for continuous-time dynamic systems characterized by bounded relative degree and possibly affected by structured perturbations. More specifically, the design of suitable kernels of non-anticipative linear integral operators gives rise to estimators that are ideally not influenced by the transient effects due to the unknown initial conditions of the hidden states of the system under concern. The analysis of the properties of the kernels guaranteeing such a fast convergence is addressed and two classes of admissible kernel functions are introduced. The operators induced by the proposed kernels admit implementable (i.e., finite-dimensional and internally stable) state-space realizations. Numerical examples are reported to show the effectiveness of the proposed methodology; comparisons with some existing algebraic estimators are addressed as well.