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Related Experiment Video

Updated: May 5, 2026

An Automated System for Sound Localization Testing in Hearing-Impaired Listeners
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Deep-Sea Target Localization with Entropy Reduction: Sound Ray Bending Correction Based on TOA Time Series Analysis

Yuzhu Kang1,2, Xiaohong Shen1,2, Haiyan Wang1,2

  • 1School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China.

Entropy (Basel, Switzerland)
|May 4, 2026
PubMed
Summary

This study introduces a novel framework for deep-sea target localization using time-of-arrival and angle-of-arrival data, correcting for sound ray bending to improve accuracy in challenging underwater acoustic sensor networks (UASNs). The methods achieve near theoretical limits for precise underwater ranging and localization.

Keywords:
CRLBclosed-form solutiondeep-sea target localizationjoint TOA-AOAsensor position errorsound ray bending

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Area of Science:

  • Oceanography
  • Acoustics
  • Signal Processing

Background:

  • Underwater acoustic sensor networks (UASNs) face significant challenges in target localization due to inhomogeneous sound speed distribution and sound ray bending.
  • Existing methods struggle with accuracy in deep-sea environments, impacting ranging and localization precision.

Purpose of the Study:

  • To propose a joint time-of-arrival (TOA) and angle-of-arrival (AOA) deep-sea target localization framework.
  • To develop methods for sound ray bending correction to enhance slant range measurement accuracy.
  • To improve target localization accuracy and reduce bias in UASNs.

Main Methods:

  • A sound ray bending correction method is applied to TOA time series measurements, considering deep-sea acoustic propagation.
  • A two-step weighted least squares (WLS) closed-form solution using TOA-AOA is proposed for enhanced localization.
  • A Gauss-Newton based maximum likelihood estimation (MLE) method is derived to further reduce localization bias.

Main Results:

  • The sound ray bending correction method significantly improves slant range measurement accuracy.
  • The proposed closed-form solution enhances target localization accuracy, approaching the Cramér-Rao lower bound (CRLB).
  • The Gauss-Newton MLE solution achieves CRLB accuracy in specific geometries and reduces localization bias.

Conclusions:

  • Jointly utilizing TOA and AOA data, coupled with sound ray bending correction, substantially improves deep-sea target localization accuracy in UASNs.
  • The developed WLS and MLE methods provide effective solutions for precise underwater ranging and localization, nearing theoretical performance limits.