A Variational Random Finite-Set Approach to Highly Robust Active-Sonar Multi-Target Tracking Under Strong Reverberation.

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Title: A Variational Random Finite-Set Approach to Highly Robust Active-Sonar Multi-Target Tracking Under Strong Reverberation.
Authors: Yang, Kaiqiang1,2,3,4 (AUTHOR), Hou, Xianghao1,2,3 (AUTHOR) houxianghao1990@nwpu.edu.cn, Yang, Yixin1,2,3 (AUTHOR)
Source: Remote Sensing. May2026, Vol. 18 Issue 9, p1332. 19p.
Subjects: Sound reverberation, Multiple target tracking, Noise, Sonar, Bayesian analysis, Distribution (Probability theory)
Abstract: Highlights: What are the main findings? We propose a robust Student's t-distribution-based delta-Generalized Labeled Multi-Bernoulli (ST-δ-GLMB) filter. This filter addresses the non-stationary, non-Gaussian measurement noise in strong reverberation by using a variational Bayesian inference for online parameter estimation, significantly enhancing the tracking robustness in dynamic underwater environments. We derive closed-form update and propagation rules for the Student's t-distribution parameters within the GLMB framework. This innovation maintains manageable computational complexity and facilitates the practical implementation with minimal modifications to the existing systems. What are the implications of the main findings? Comprehensive validations using Monte Carlo simulations and real sea trial data demonstrate that the ST-δ-GLMB filter outperforms several state-of-the-art algorithms under strong reverberation. It effectively suppresses the increase in OSPA distance, reduces label switching errors, and maintains reliable trajectory continuity. The proposed method achieves a stable estimation of the number of targets (cardinality) and exhibits superior performance in non-stationary noise conditions, which is crucial for dependable underwater multi-target surveillance applications. Active sonar tracking of multiple underwater targets is frequently challenged by intense reverberation, which leads to sonar returns that are both non-stationary and non-Gaussian. In such scenarios, the generalized labeled multi-Bernoulli (GLMB) filter, which relies on a Gaussian assumption, often experiences a rise in an Optimal Subpattern Assignment (OSPA) distance, along with recurrent label switching. To mitigate this problem, a robust delta-generalized labeled multi-Bernoulli technique (ST-δ-GLMB) is introduced; it characterizes noise using a Student's t-distribution and employs variational Bayes to estimate the corresponding parameters. More precisely, the Student's t-distribution is utilized to represent measurement non-stationarity, and an online variational Bayesian estimation of the noise parameters is conducted within a multi-target framework based on the Student's t-model. Moreover, without altering the GLMB data-association and label-management machinery, we derive closed-form updates and propagation for the Student's t-parameters, thereby keeping the recursive computational burden and practical implementability under control. Finally, Monte Carlo simulations and lake-trial data demonstrate that, under non-stationary and heavy-clutter conditions, ST-δ-GLMB maintains stable track continuity and accurate target-number (cardinality) estimates in the presence of non-stationary measurements. [ABSTRACT FROM AUTHOR]
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  Data: A Variational Random Finite-Set Approach to Highly Robust Active-Sonar Multi-Target Tracking Under Strong Reverberation.
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  Data: <searchLink fieldCode="AR" term="%22Yang%2C+Kaiqiang%22">Yang, Kaiqiang</searchLink><relatesTo>1,2,3,4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hou%2C+Xianghao%22">Hou, Xianghao</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<i> houxianghao1990@nwpu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Yixin%22">Yang, Yixin</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Remote+Sensing%22">Remote Sensing</searchLink>. May2026, Vol. 18 Issue 9, p1332. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Sound+reverberation%22">Sound reverberation</searchLink><br /><searchLink fieldCode="DE" term="%22Multiple+target+tracking%22">Multiple target tracking</searchLink><br /><searchLink fieldCode="DE" term="%22Noise%22">Noise</searchLink><br /><searchLink fieldCode="DE" term="%22Sonar%22">Sonar</searchLink><br /><searchLink fieldCode="DE" term="%22Bayesian+analysis%22">Bayesian analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Highlights: What are the main findings? We propose a robust Student's t-distribution-based delta-Generalized Labeled Multi-Bernoulli (ST-δ-GLMB) filter. This filter addresses the non-stationary, non-Gaussian measurement noise in strong reverberation by using a variational Bayesian inference for online parameter estimation, significantly enhancing the tracking robustness in dynamic underwater environments. We derive closed-form update and propagation rules for the Student's t-distribution parameters within the GLMB framework. This innovation maintains manageable computational complexity and facilitates the practical implementation with minimal modifications to the existing systems. What are the implications of the main findings? Comprehensive validations using Monte Carlo simulations and real sea trial data demonstrate that the ST-δ-GLMB filter outperforms several state-of-the-art algorithms under strong reverberation. It effectively suppresses the increase in OSPA distance, reduces label switching errors, and maintains reliable trajectory continuity. The proposed method achieves a stable estimation of the number of targets (cardinality) and exhibits superior performance in non-stationary noise conditions, which is crucial for dependable underwater multi-target surveillance applications. Active sonar tracking of multiple underwater targets is frequently challenged by intense reverberation, which leads to sonar returns that are both non-stationary and non-Gaussian. In such scenarios, the generalized labeled multi-Bernoulli (GLMB) filter, which relies on a Gaussian assumption, often experiences a rise in an Optimal Subpattern Assignment (OSPA) distance, along with recurrent label switching. To mitigate this problem, a robust delta-generalized labeled multi-Bernoulli technique (ST-δ-GLMB) is introduced; it characterizes noise using a Student's t-distribution and employs variational Bayes to estimate the corresponding parameters. More precisely, the Student's t-distribution is utilized to represent measurement non-stationarity, and an online variational Bayesian estimation of the noise parameters is conducted within a multi-target framework based on the Student's t-model. Moreover, without altering the GLMB data-association and label-management machinery, we derive closed-form updates and propagation for the Student's t-parameters, thereby keeping the recursive computational burden and practical implementability under control. Finally, Monte Carlo simulations and lake-trial data demonstrate that, under non-stationary and heavy-clutter conditions, ST-δ-GLMB maintains stable track continuity and accurate target-number (cardinality) estimates in the presence of non-stationary measurements. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Remote Sensing is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3390/rs18091332
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      – Code: eng
        Text: English
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        PageCount: 19
        StartPage: 1332
    Subjects:
      – SubjectFull: Sound reverberation
        Type: general
      – SubjectFull: Multiple target tracking
        Type: general
      – SubjectFull: Noise
        Type: general
      – SubjectFull: Sonar
        Type: general
      – SubjectFull: Bayesian analysis
        Type: general
      – SubjectFull: Distribution (Probability theory)
        Type: general
    Titles:
      – TitleFull: A Variational Random Finite-Set Approach to Highly Robust Active-Sonar Multi-Target Tracking Under Strong Reverberation.
        Type: main
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            NameFull: Yang, Kaiqiang
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            NameFull: Hou, Xianghao
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            NameFull: Yang, Yixin
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 9
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            – TitleFull: Remote Sensing
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