Unimodality-Constrained Matrix Factorization for Non-Parametric Source Localization

TL;DR

This paper introduces a non-parametric source localization method that uses unimodality-constrained matrix factorization to accurately identify multiple sources without prior knowledge of signal propagation models, outperforming baseline methods in efficiency.

Contribution

It proposes a novel unimodality-constrained matrix factorization framework for source localization that does not rely on signal models or spatial signatures, with efficient algorithms for peak detection.

Findings

Achieves faster MSE reduction than O(1/M^1.5) without noise.

Detects a single source with only 1/5 of the energy samples of baseline.

Improves multi-source detection performance significantly.

Abstract

Herein, the problem of simultaneous localization of multiple sources given a number of energy samples at different locations is examined. The strategies do not require knowledge of the signal propagation models, nor do they exploit the spatial signatures of the source. A non-parametric source localization framework based on a matrix observation model is developed. It is shown that the source location can be estimated by localizing the peaks of a pair of location signature vectors extracted from the incomplete energy observation matrix. A robust peak localization algorithm is developed and shown to decrease the source localization mean squared error (MSE) faster than O(1/M^1.5) with M samples, when there is no measurement noise. To extract the source signature vectors from a matrix with mixed energy from multiple sources, a unimodality-constrained matrix factorization (UMF) problem is formulated, and two rotation techniques are developed to solve the UMF efficiently. Our numerical experiments demonstrate that the proposed scheme achieves similar performance as the kernel regression baseline using only 1/5 energy measurement samples in detecting a single source, and the performance gain is more significant in the cases of detecting multiple sources.