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Related Experiment Video

Updated: Jul 3, 2026

An Automated System for Sound Localization Testing in Hearing-Impaired Listeners

An Automated System for Sound Localization Testing in Hearing-Impaired Listeners

Published on: March 13, 2026

A remark on global positioning from local distances.

¹Department of Mathematics, Program in Applied Mathematics, Yale University, New Haven, CT 06520, USA. amit.singer@yale.edu

Proceedings of the National Academy of Sciences of the United States of America

|July 16, 2008

Summary

Researchers developed a new algorithm to determine the precise 3D locations of points using only partial distance information. This method, applicable to sensor networks and protein analysis, is efficient and handles noisy data effectively.

Related Experiment Videos

Last Updated: Jul 3, 2026

An Automated System for Sound Localization Testing in Hearing-Impaired Listeners

An Automated System for Sound Localization Testing in Hearing-Impaired Listeners

Published on: March 13, 2026

Area of Science:

Computational geometry
Applied mathematics
Biophysics

Background:

Determining global positioning from partial pairwise distances is a challenge in various scientific fields.
Applications include sensor network localization and structural biology (NMR spectroscopy).

Purpose of the Study:

To develop an efficient and robust method for Euclidean space point localization using incomplete distance data.
To leverage matrix properties for coordinate determination.

Main Methods:

The study utilizes the eigenvectors of a specific sparse matrix.
These eigenvectors are shown to directly correspond to the desired spatial coordinates.

Main Results:

A direct correlation was found between matrix eigenvectors and point coordinates.
The proposed method provides an exact solution for coordinate determination.

Conclusions:

The eigenvector approach offers a simple, efficient, and robust algorithm for global positioning from partial distance information.
This method shows promise for applications with noisy or incomplete distance measurements.