Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Multi-Source Localization and Data Association for Time-Difference of Arrival Measurements

Gabrielle Flood, Filip Elvander

TL;DR

This work tackles blind localization of multiple signal sources using time-difference of arrival measurements by jointly solving localization and data association through an optimal transport framework. A candidate source set is constructed from minimal 3D multilateration across chosen receiver-pair sets, avoiding grid-based space discretization. An entropy-regularized, unbalanced OT problem then associates TDOAs to candidate locations, yielding the S best source positions, which are subsequently refined via local optimization to achieve statistically efficient estimates. The method demonstrates robustness to measurement noise and to missing or false TDOA data, and extends OT-based localization to 3D with scalable computation.

Abstract

In this work, we consider the problem of localizing multiple signal sources based on time-difference of arrival (TDOA) measurements. In the blind setting, in which the source signals are not known, the localization task is challenging due to the data association problem. That is, it is not known which of the TDOA measurements correspond to the same source. Herein, we propose to perform joint localization and data association by means of an optimal transport formulation. The method operates by finding optimal groupings of TDOA measurements and associating these with candidate source locations. To allow for computationally feasible localization in three-dimensional space, an efficient set of candidate locations is constructed using a minimal multilateration solver based on minimal sets of receiver pairs. In numerical simulations, we demonstrate that the proposed method is robust both to measurement noise and TDOA detection errors. Furthermore, it is shown that the data association provided by the proposed method allows for statistically efficient estimates of the source locations.

Multi-Source Localization and Data Association for Time-Difference of Arrival Measurements

TL;DR

This work tackles blind localization of multiple signal sources using time-difference of arrival measurements by jointly solving localization and data association through an optimal transport framework. A candidate source set is constructed from minimal 3D multilateration across chosen receiver-pair sets, avoiding grid-based space discretization. An entropy-regularized, unbalanced OT problem then associates TDOAs to candidate locations, yielding the S best source positions, which are subsequently refined via local optimization to achieve statistically efficient estimates. The method demonstrates robustness to measurement noise and to missing or false TDOA data, and extends OT-based localization to 3D with scalable computation.

Abstract

In this work, we consider the problem of localizing multiple signal sources based on time-difference of arrival (TDOA) measurements. In the blind setting, in which the source signals are not known, the localization task is challenging due to the data association problem. That is, it is not known which of the TDOA measurements correspond to the same source. Herein, we propose to perform joint localization and data association by means of an optimal transport formulation. The method operates by finding optimal groupings of TDOA measurements and associating these with candidate source locations. To allow for computationally feasible localization in three-dimensional space, an efficient set of candidate locations is constructed using a minimal multilateration solver based on minimal sets of receiver pairs. In numerical simulations, we demonstrate that the proposed method is robust both to measurement noise and TDOA detection errors. Furthermore, it is shown that the data association provided by the proposed method allows for statistically efficient estimates of the source locations.
Paper Structure (9 sections, 1 theorem, 11 equations, 3 figures)

This paper contains 9 sections, 1 theorem, 11 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Source Localization
  3. Method Outline
  4. Candidate Set Construction
  5. Association Problem
  6. Experimental Validation
  7. Noise sensitivity
  8. Missing and False TDOA Measurements
  9. Conclusions

Key Result

Proposition 1

The unique optimal $(\mathbf{M},\mathbf{m})$ is represented as where $\mathbf{K} =\exp\left(-\frac{1}{\epsilon}\mathbf{C} \right)$, $\mathbf{k} = \exp\left(-\frac{1}{\epsilon}\mathbf{c} \right)$, and where $\boldsymbol{\lambda}$, $\boldsymbol{\mu}$, and $\boldsymbol{\Phi}$ solve the dual problem where $\left\lVert\boldsymbol{\Phi}\right\rVert_{1,\infty} = \max_{j} \sum_{i} \left|[\boldsymbol{\P

Figures (3)

  • Figure 1: Two signal sources observed by four receivers, with hyperbolas corresponding to source locations consistent with TDOA measurements. Left: hyperbolas (TDOAs) labelled according to source. Right: unknown labels, corresponding to the localization and data association problem.
  • Figure 2: Expected localization error (left axis) and the rate of correctly associated TDOA measurements (right axis) for varying noise level $\sigma$.
  • Figure 3: Expected localization error (left axis) and the rate of correctly associated TDOA measurements (right axis) with respect to false and missing measurements, on the top and bottom, respectively. For false measurements the association rate for false-to-void source is included.

Theorems & Definitions (1)

  • Proposition 1