Scientific Article

Automated Sound Field Estimation combining robotized acoustic measurements and the boundary elements method

¹ LMI, ENSTA, Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, 91120 Palaiseau, France
² U2IS, ENSTA, Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, 91120 Palaiseau, France
³ POEMS, CNRS, Inria, ENSTA, Institut Polytechnique de Paris, 91120 Palaiseau, France

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 9 October 2025
Accepted: 11 February 2026

Abstract

The identification and reconstruction of acoustic fields radiated by unknown structures is usually performed using either Sound Field Estimation or Near-field Acoustic Holography techniques. The latter turns out to be especially useful when data is only available close to the source, but information throughout the whole space is needed. Yet, the lack of amendable and efficient implementations of state-of-the-art solutions, as well as the laborious and often lengthy deployment of acoustic measurements continue to be significant obstacles to the practical application of such methods. The purpose of this work is to address both problems. First, a completely automated metrology setup is proposed, in which a robotic arm is used to gather extensive and accurately positioned acoustic data without any human intervention. The impact of the robot on acoustic pressure measurements is cautiously evaluated, and proved to remain limited below 1 kHz. The Sound Field Estimation is then tackled using the Boundary Element Method, and implemented using the FreeFEM software. Numerically simulated measurements have allowed us to assess the method accuracy, which matches theoretically expected results and proves to remain robust against positioning inaccuracies, provided that the robot is carefully calibrated. The overall solution has been successfully tested using actual robotized measurements of an unknown loudspeaker, with a reconstruction error of less than 30%.