Non-causal regularized least-squares for continuous-time system identification with band-limited input excitations

TL;DR

This paper investigates non-causal regularized least-squares methods for continuous-time system identification with band-limited inputs, emphasizing the importance of intersample behavior and sinc interpolation in estimation accuracy.

Contribution

It introduces a kernel-based non-causal regularized least-squares approach for estimating continuous-time system responses, highlighting the role of non-causal models in system identification.

Findings

The proposed method outperforms traditional causal estimators in simulations.

Non-causal estimators effectively utilize band-limited input properties.

Numerical results demonstrate improved accuracy in continuous-time system identification.

Abstract

In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is band-limited. The sinc interpolation property of these input signals yields equivalent discrete-time representations that are non-causal. This observation, often overlooked in the literature, is exploited in this work to study non-parametric frequency response estimators of linear continuous-time systems. We study the properties of non-causal least-square estimators for continuous-time system identification, and propose a kernel-based non-causal regularized least-squares approach for estimating the band-limited equivalent impulse response. The proposed methods are tested via extensive numerical simulations.