Iterative Broadband Source Localization

TL;DR

This paper extends classical sparse recovery algorithms to localize broadband sources using Slepian subspace models, effectively handling spectral leakage and outperforming standard Fourier-based methods, even with compressed measurements.

Contribution

It introduces a novel approach combining greedy algorithms with Slepian subspace models for broadband source localization, improving robustness and accuracy.

Findings

Successfully localizes broadband sources in adverse scenarios.

Outperforms Fourier-based methods in accuracy.

Effective with compressed measurements, maintaining fidelity.

Abstract

In this paper we consider the problem of localizing a set of broadband sources from a finite window of measurements. In the case of narrowband sources this can be reduced to the problem of spectral line estimation, where our goal is simply to estimate the active frequencies from a weighted mixture of pure sinusoids. There exists a plethora of modern and classical methods that effectively solve this problem. However, for a wide variety of applications the underlying sources are not narrowband and can have an appreciable amount of bandwidth. In this work, we extend classical greedy algorithms for sparse recovery (e.g., orthogonal matching pursuit) to localize broadband sources. We leverage models for samples of broadband signals based on a union of Slepian subspaces, which are more aptly suited for dealing with spectral leakage and dynamic range disparities. We show that by using these models, our adapted algorithms can successfully localize broadband sources under a variety of adverse operating scenarios. Furthermore, we show that our algorithms outperform complementary methods that use more standard Fourier models. We also show that we can perform estimation from compressed measurements with little loss in fidelity as long as the number of measurements are on the order of the signal's implicit degrees of freedom. We conclude with an in-depth application of these ideas to the problem of localization in multi-sensor arrays.