Optimal excitation and measurement pattern for cascade networks

TL;DR

This paper investigates how to optimally select excitation and measurement patterns in cascade networks to maximize parameter estimation accuracy, providing theoretical guidelines and numerical validation.

Contribution

It introduces a method to identify the most accurate experimental pattern in cascade networks based on asymptotic covariance analysis, under specific assumptions.

Findings

Optimal patterns can be determined based on network topology.

Equal precision can be achieved across different experimental settings.

Guidelines are valid beyond initial assumptions, confirmed by numerical results.

Abstract

This work deals with accuracy analysis of dynamical systems interconnected in a cascade structure. For a cascade network there are a number of experimental settings for which the dynamic systems within the network can be identified. We study the problem of choosing which excitation and measurement pattern delivers the most accurate parameter estimates for the whole network. The optimal experiment is based on the accuracy assessed through the asymptotic covariance matrix of the prediction error method, while the cost criterion is the number of excitations and measurements. We develop theoretical results under the assumptions that all dynamic systems are equal and with equal signal-to-noise ratio throughout the network. We show that there are experimental settings which result in equal overall precision and that there is an excitation and measurement pattern that yields more accurate results than others. From these results a guideline based on the topology of the network emerges for the choice of the experimental setting. We provide numerical results which attest that the principles behind this guideline are also valid for more general situations.