# Optimal Experiment Design in Nonlinear Parameter Estimation with Exact Confidence Regions

## TL;DR

This paper develops a new optimal experiment design method for nonlinear systems that explicitly considers exact confidence regions, using novel approximation techniques to improve computational efficiency and accuracy.

## Contribution

It introduces a framework for OED based on exact CRs with ellipsoidal approximations, advancing beyond linearized approaches.

## Key findings

- Exact CR-based OED improves measurement informativeness.
- Ellipsoidal approximation reduces computational complexity.
- Comparison shows advantages over linearized methods.

## Abstract

A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the least-squares parameter estimates. The optimal design is achieved by using the available (experimental) degrees of freedom such that more informative measurements are obtained. Unlike the commonly used approaches, which base the OED procedure upon the linearized CRs, we explore a path where we explicitly consider the exact CRs in the OED framework. We use a methodology for a finite parametrization of the exact CRs within the OED problem and we introduce a novel approximation technique of the exact CRs using inner- and outer-approximating ellipsoids as a computationally less demanding alternative. The employed techniques give the OED problem as a finite-dimensional mathematical program of bilevel nature. We use two small-scale illustrative case studies to study various OED criteria and compare the resulting optimal designs with the commonly used linearization-based approach. We also assess the performance of two simple heuristic numerical schemes for bilevel optimization within the studied problems.