Calibration and Uncertainty Evaluation Using Monte Carlo Method of a Simple 2D Sound Localization System

A simple measurement system (MS) is developed to perform sound localization on a plane and evaluate its performances with specific attention to calibration and uncertainty evaluation. The sensing element is composed of two microphones mounted at the left and right ears on a cap. The localization of sound source is obtained by the estimation of the delay between the time instants of arrival of the sound to the two microphones, through a cross-correlation technique. The principle of this paper is described in mathematical terms and is experimentally validated in the azimuthal angle (θ) range ±90° at three different distances between the microphones. The MS has a nonlinear response over the whole range, on the other hand it can be considered linear within ±15°. In addition, the sensor presents a low discrimination threshold (2 °). The uncertainty evaluation of the MS is performed using the propagation of uncertainty and the Monte Carlo method: simulations show an uncertainty in the range ±90°. The characteristic of wearability, typical feature of sensors used to perform early detection of disorders, the good accuracy and resolution allow the chance to introduce the MS in the field of developmental psychology and, in particular, as a support for early diagnosis of pervasive developmental disorders (e.g., autism spectrum disorders).

I. Introduction

Sound localization is essential in several fields including video conferencing and surveillance, and it represents a fundamental function for robots interacting with humans [1]. The localization of a sound source is mostly based on steerable beam-forming and on time delay estimation obtained from the data processing of two or more signals picked up by different microphones.