Learning Causal Estimates of Linear Operators From Noisy Data

This article studies the identification problem of linear systems from a set of noisy input-output trajectories. The problem is formulated and solved as a least-square regularized estimate on a suitable function space of finite-bandwidth operators. This abstract setting is well suited to represent a broad class of finite- and infinite-dimensional linear systems. We determine the value of the regularization parameter as a function of the amount of noise on the learning trajectories and we show how to obtain recursive and causal estimates for the case of linear dynamical systems.

Automated summary

This article studies the identification problem of linear systems from a set of noisy input-output trajectories. The problem is formulated and solved as a least-square regularized estimate on a suitable function space of finite-bandwidth operators. This abstract setting is well suited to represent a broad class of finite- and infinite-dimensional linear systems. We determine the value of the regularization parameter as a function of the amount of noise on the learning trajectories and we show how to obtain recursive and causal estimates for the case of linear dynamical systems.