Optimal excitation and measurement patterns for networks with tree topology

TL;DR

This paper evaluates optimal excitation and measurement patterns for tree-structured networks, introducing systematic methods to select minimal patterns that maximize estimation accuracy.

Contribution

It introduces the concept of partial information matrix and provides guidelines for selecting minimal EMPs in tree networks, including a new topological condition.

Findings

Optimal EMPs minimize the number of excited and measured nodes.

Accuracy depends on parameter magnitudes and network topology.

Guidelines can serve as a tool for selecting minimal EMPs in practice.

Abstract

In this work we evaluate the excitation and measurement patterns (EMP) for networks with tree topology. We investigate guidelines for the selection of the minimal EMPs, i.e. those with the least number of excited and measured nodes combined, for which the accuracy obtained, in terms of the trace of the asymptotic covariance matrix, is optimal. We introduce the concept of partial information matrix as a means to systematically obtain the information matrix for any dynamic network. For a specific tree class, called cross, we show that the accuracy of a particular module depends on the magnitude of the parameters to be estimated. Furthermore, when all factors are equal, it is best to excite. %we show that for small magnitudes of this parameter, it is best to excite. We extend a topological condition for branches under which the accuracy of a particular module of the network is independent of the other parameters from the tree. We provide a numerical analysis showing that our guidelines could be used as a selection tool for minimal EMPs for tree networks.