Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer

Kang Song Ju; Myong Hyok Sin

doi:doi:10.11648/j.engmath.20250902.13

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Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer

Kang Song Ju, Myong Hyok Sin^*

Published in Engineering Mathematics (Volume 9, Issue 2)

Received: 4 November 2025 Accepted: 22 November 2025 Published: 29 December 2025

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Abstract

We have designed an interacting multi-model strong robust adaptive unscented Kalman filter for bearing only tracking of an underwater vehicle approaching the observer. To solve the problem of tracking an approaching underwater vehicle to the observer based on only its bearing, an interactive multi-model robust adaptive unscented Kalman filter is proposed in this paper. First, a new model of the bearing sense motion towards the observer is proposed to construct a set of realistic target motion modes consisting of linear and curved motion modes. In addition, to account for the influence of outliers in the target bearing measurements, the distribution of measurement noise is assumed to have a Student’s t-distribution, and the probability distribution of the degree of function and the scaling matrix of this distribution is assumed to have a gamma distribution and an inverse Wishart distribution. Thus, the model interaction step is to factorize the mixed probability density function using variational Bayesian method and, based on this, a predictive update method is proposed. In the measurement update phase, the posterior probability density function is obtained in factorization form using variational Bayesian method, and based on this, a posteriori mode probability calculation method is proposed. Simulation results show that our proposed method greatly improves the convergence rate of target tracking error.

Published in	Engineering Mathematics (Volume 9, Issue 2)
DOI	10.11648/j.engmath.20250902.13
Page(s)	46-67
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Bearing only Tracking, Unscented Kalman Filter, Inverse Wishart Distribution, Interactive Multi-Model

References

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APA Style

Ju, K. S., Sin, M. H. (2025). Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer. Engineering Mathematics, 9(2), 46-67. https://doi.org/10.11648/j.engmath.20250902.13

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ACS Style

Ju, K. S.; Sin, M. H. Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer. Eng. Math. 2025, 9(2), 46-67. doi: 10.11648/j.engmath.20250902.13

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AMA Style

Ju KS, Sin MH. Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer. Eng Math. 2025;9(2):46-67. doi: 10.11648/j.engmath.20250902.13

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@article{10.11648/j.engmath.20250902.13,
  author = {Kang Song Ju and Myong Hyok Sin},
  title = {Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer},
  journal = {Engineering Mathematics},
  volume = {9},
  number = {2},
  pages = {46-67},
  doi = {10.11648/j.engmath.20250902.13},
  url = {https://doi.org/10.11648/j.engmath.20250902.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20250902.13},
  abstract = {We have designed an interacting multi-model strong robust adaptive unscented Kalman filter for bearing only tracking of an underwater vehicle approaching the observer. To solve the problem of tracking an approaching underwater vehicle to the observer based on only its bearing, an interactive multi-model robust adaptive unscented Kalman filter is proposed in this paper. First, a new model of the bearing sense motion towards the observer is proposed to construct a set of realistic target motion modes consisting of linear and curved motion modes. In addition, to account for the influence of outliers in the target bearing measurements, the distribution of measurement noise is assumed to have a Student’s t-distribution, and the probability distribution of the degree of function and the scaling matrix of this distribution is assumed to have a gamma distribution and an inverse Wishart distribution. Thus, the model interaction step is to factorize the mixed probability density function using variational Bayesian method and, based on this, a predictive update method is proposed. In the measurement update phase, the posterior probability density function is obtained in factorization form using variational Bayesian method, and based on this, a posteriori mode probability calculation method is proposed. Simulation results show that our proposed method greatly improves the convergence rate of target tracking error.},
 year = {2025}
}

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TY  - JOUR
T1  - Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer
AU  - Kang Song Ju
AU  - Myong Hyok Sin
Y1  - 2025/12/29
PY  - 2025
N1  - https://doi.org/10.11648/j.engmath.20250902.13
DO  - 10.11648/j.engmath.20250902.13
T2  - Engineering Mathematics
JF  - Engineering Mathematics
JO  - Engineering Mathematics
SP  - 46
EP  - 67
PB  - Science Publishing Group
SN  - 2640-088X
UR  - https://doi.org/10.11648/j.engmath.20250902.13
AB  - We have designed an interacting multi-model strong robust adaptive unscented Kalman filter for bearing only tracking of an underwater vehicle approaching the observer. To solve the problem of tracking an approaching underwater vehicle to the observer based on only its bearing, an interactive multi-model robust adaptive unscented Kalman filter is proposed in this paper. First, a new model of the bearing sense motion towards the observer is proposed to construct a set of realistic target motion modes consisting of linear and curved motion modes. In addition, to account for the influence of outliers in the target bearing measurements, the distribution of measurement noise is assumed to have a Student’s t-distribution, and the probability distribution of the degree of function and the scaling matrix of this distribution is assumed to have a gamma distribution and an inverse Wishart distribution. Thus, the model interaction step is to factorize the mixed probability density function using variational Bayesian method and, based on this, a predictive update method is proposed. In the measurement update phase, the posterior probability density function is obtained in factorization form using variational Bayesian method, and based on this, a posteriori mode probability calculation method is proposed. Simulation results show that our proposed method greatly improves the convergence rate of target tracking error.
VL  - 9
IS  - 2
ER  -

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Author Information

Kang Song Ju

Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea

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Myong Hyok Sin

Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea

Contact Email

http://orcid.org/0009-0009-0994-5469

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APA Style

Ju, K. S., Sin, M. H. (2025). Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer. Engineering Mathematics, 9(2), 46-67. https://doi.org/10.11648/j.engmath.20250902.13

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ACS Style

Ju, K. S.; Sin, M. H. Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer. Eng. Math. 2025, 9(2), 46-67. doi: 10.11648/j.engmath.20250902.13

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AMA Style

Ju KS, Sin MH. Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer. Eng Math. 2025;9(2):46-67. doi: 10.11648/j.engmath.20250902.13

Copy | Download

@article{10.11648/j.engmath.20250902.13,
  author = {Kang Song Ju and Myong Hyok Sin},
  title = {Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer},
  journal = {Engineering Mathematics},
  volume = {9},
  number = {2},
  pages = {46-67},
  doi = {10.11648/j.engmath.20250902.13},
  url = {https://doi.org/10.11648/j.engmath.20250902.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20250902.13},
  abstract = {We have designed an interacting multi-model strong robust adaptive unscented Kalman filter for bearing only tracking of an underwater vehicle approaching the observer. To solve the problem of tracking an approaching underwater vehicle to the observer based on only its bearing, an interactive multi-model robust adaptive unscented Kalman filter is proposed in this paper. First, a new model of the bearing sense motion towards the observer is proposed to construct a set of realistic target motion modes consisting of linear and curved motion modes. In addition, to account for the influence of outliers in the target bearing measurements, the distribution of measurement noise is assumed to have a Student’s t-distribution, and the probability distribution of the degree of function and the scaling matrix of this distribution is assumed to have a gamma distribution and an inverse Wishart distribution. Thus, the model interaction step is to factorize the mixed probability density function using variational Bayesian method and, based on this, a predictive update method is proposed. In the measurement update phase, the posterior probability density function is obtained in factorization form using variational Bayesian method, and based on this, a posteriori mode probability calculation method is proposed. Simulation results show that our proposed method greatly improves the convergence rate of target tracking error.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer
AU  - Kang Song Ju
AU  - Myong Hyok Sin
Y1  - 2025/12/29
PY  - 2025
N1  - https://doi.org/10.11648/j.engmath.20250902.13
DO  - 10.11648/j.engmath.20250902.13
T2  - Engineering Mathematics
JF  - Engineering Mathematics
JO  - Engineering Mathematics
SP  - 46
EP  - 67
PB  - Science Publishing Group
SN  - 2640-088X
UR  - https://doi.org/10.11648/j.engmath.20250902.13
AB  - We have designed an interacting multi-model strong robust adaptive unscented Kalman filter for bearing only tracking of an underwater vehicle approaching the observer. To solve the problem of tracking an approaching underwater vehicle to the observer based on only its bearing, an interactive multi-model robust adaptive unscented Kalman filter is proposed in this paper. First, a new model of the bearing sense motion towards the observer is proposed to construct a set of realistic target motion modes consisting of linear and curved motion modes. In addition, to account for the influence of outliers in the target bearing measurements, the distribution of measurement noise is assumed to have a Student’s t-distribution, and the probability distribution of the degree of function and the scaling matrix of this distribution is assumed to have a gamma distribution and an inverse Wishart distribution. Thus, the model interaction step is to factorize the mixed probability density function using variational Bayesian method and, based on this, a predictive update method is proposed. In the measurement update phase, the posterior probability density function is obtained in factorization form using variational Bayesian method, and based on this, a posteriori mode probability calculation method is proposed. Simulation results show that our proposed method greatly improves the convergence rate of target tracking error.
VL  - 9
IS  - 2
ER  -

Copy | Download