Multiple-Source Ellipsoidal Localization Using Acoustic Energy Measurements

TL;DR

This paper introduces a set-membership ellipsoidal localization method for multiple acoustic sources, effectively handling unknown-bounded noise and nonlinear measurements, outperforming traditional algorithms in non-Gaussian noise scenarios.

Contribution

The paper develops an efficient set-membership localization algorithm for multiple sources using ellipsoidal bounds and alternating optimization, addressing unknown-bounded noise and nonlinear measurement challenges.

Findings

The proposed algorithm accurately localizes multiple sources with bounded noise.

It outperforms EM algorithms under non-Gaussian noise conditions.

Numerical examples validate the effectiveness of the ellipsoidal localization approach.

Abstract

In this paper, the multiple-source ellipsoidal localization problem based on acoustic energy measurements is investigated via set-membership estimation theory. When the probability density function of measurement noise is unknown-but-bounded, multiple-source localization is a difficult problem since not only the acoustic energy measurements are complicated nonlinear functions of multiple sources, but also the multiple sources bring about a high-dimensional state estimation problem. First, when the energy parameter and the position of the source are bounded in an interval and a ball respectively, the nonlinear remainder bound of the Taylor series expansion is obtained analytically on-line. Next, based on the separability of the nonlinear measurement function, an efficient estimation procedure is developed. It solves the multiple-source localization problem by using an alternating optimization iterative algorithm, in which the remainder bound needs to be known on-line. For this reason, we first derive the remainder bound analytically. When the energy decay factor is unknown but bounded, an efficient estimation procedure is developed based on interval mathematics. Finally, numerical examples demonstrate the effectiveness of the ellipsoidal localization algorithms for multiple-source localization. In particular, our results show that when the noise is non-Gaussian, the set-membership localization algorithm performs better than the EM localization algorithm.