Experiment design for impulse response identification with signal matrix models

TL;DR

This paper develops an input design method for impulse response identification using signal matrix models, optimizing data inputs to minimize estimation error in noisy conditions, thereby improving model accuracy.

Contribution

It introduces an optimal input design approach for impulse response estimation within data matrix models, enhancing estimation accuracy under noise.

Findings

Optimized input design reduces mean-square error in estimates.

Numerical results demonstrate improved fit with the proposed method.

Method enhances data-driven system identification accuracy.

Abstract

This paper formulates an input design approach for truncated infinite impulse response identification in the context of implicit model representations recently used as basis for data-driven simulation and control approaches. Precisely, the considered model consists of a linear combination of the columns of a data (or signal) matrix. An optimal combination for the case of noisy data was recently proposed using a maximum likelihood approach, and the objective here is to optimize the input entries of the data matrix such that the mean-square error matrix of the estimate is minimized. A least-norm problem is derived in terms of the optimality criteria typically considered in the experiment design literature. Numerical results showcase the improved estimation fit achieved with the optimized input.