Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System

Khalid Abd El Mageed Hag El Amin

doi:doi:10.11648/j.dmath.20250701.11

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Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System

Khalid Abd El Mageed Hag El Amin^*

Published in International Journal of Discrete Mathematics (Volume 7, Issue 1)

Received: 22 May 2025 Accepted: 5 June 2025 Published: 30 August 2025

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Abstract

This article addresses the joint estimation of parameters and states in linear stochastic systems with correlated process and measurement noises. We propose the Kalman Filtering with Correlated Noises based Recursive Generalized Extended Least Squares (KF-CN-RGELS) algorithm, which innovatively integrates a reformulated Kalman filter to handle noise cross-correlation via a gain matrix T, alongside recursive least squares for synchronous parameter-state updates. The algorithm’s key advantage lies in its ability to leverage noise correlation for improved accuracy: experimental results demonstrate that a higher correlation coefficient (ρ_{w, v}=0.8)reduces parameter estimation errors to 0.85% (vs. 1.81% for ρ_{w, v}=0) and enhances state estimation. The method’s robustness is validated under varying noise conditions, offering practical utility in systems like radar guidance and industrial control.

Published in	International Journal of Discrete Mathematics (Volume 7, Issue 1)
DOI	10.11648/j.dmath.20250701.11
Page(s)	1-13
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

Correlated Noises, Least Squares, Linear Stochastic System, Parameter Estimation

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APA Style

Amin, K. A. E. M. H. E. (2025). Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System. International Journal of Discrete Mathematics, 7(1), 1-13. https://doi.org/10.11648/j.dmath.20250701.11

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ACS Style

Amin, K. A. E. M. H. E. Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System. Int. J. Discrete Math. 2025, 7(1), 1-13. doi: 10.11648/j.dmath.20250701.11

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AMA Style

Amin KAEMHE. Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System. Int J Discrete Math. 2025;7(1):1-13. doi: 10.11648/j.dmath.20250701.11

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@article{10.11648/j.dmath.20250701.11,
  author = {Khalid Abd El Mageed Hag El Amin},
  title = {Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System
},
  journal = {International Journal of Discrete Mathematics},
  volume = {7},
  number = {1},
  pages = {1-13},
  doi = {10.11648/j.dmath.20250701.11},
  url = {https://doi.org/10.11648/j.dmath.20250701.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20250701.11},
  abstract = {This article addresses the joint estimation of parameters and states in linear stochastic systems with correlated process and measurement noises. We propose the Kalman Filtering with Correlated Noises based Recursive Generalized Extended Least Squares (KF-CN-RGELS) algorithm, which innovatively integrates a reformulated Kalman filter to handle noise cross-correlation via a gain matrix T, alongside recursive least squares for synchronous parameter-state updates. The algorithm’s key advantage lies in its ability to leverage noise correlation for improved accuracy: experimental results demonstrate that a higher correlation coefficient (ρw, v=0.8)reduces parameter estimation errors to 0.85% (vs. 1.81% for ρw, v=0) and enhances state estimation. The method’s robustness is validated under varying noise conditions, offering practical utility in systems like radar guidance and industrial control.
},
 year = {2025}
}

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TY  - JOUR
T1  - Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System

AU  - Khalid Abd El Mageed Hag El Amin
Y1  - 2025/08/30
PY  - 2025
N1  - https://doi.org/10.11648/j.dmath.20250701.11
DO  - 10.11648/j.dmath.20250701.11
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 1
EP  - 13
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20250701.11
AB  - This article addresses the joint estimation of parameters and states in linear stochastic systems with correlated process and measurement noises. We propose the Kalman Filtering with Correlated Noises based Recursive Generalized Extended Least Squares (KF-CN-RGELS) algorithm, which innovatively integrates a reformulated Kalman filter to handle noise cross-correlation via a gain matrix T, alongside recursive least squares for synchronous parameter-state updates. The algorithm’s key advantage lies in its ability to leverage noise correlation for improved accuracy: experimental results demonstrate that a higher correlation coefficient (ρw, v=0.8)reduces parameter estimation errors to 0.85% (vs. 1.81% for ρw, v=0) and enhances state estimation. The method’s robustness is validated under varying noise conditions, offering practical utility in systems like radar guidance and industrial control.

VL  - 7
IS  - 1
ER  -

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Author Information

Khalid Abd El Mageed Hag El Amin

Department of Electrical Engineering, College of Engineering, Al Neelain University, Khartoum, Sudan

Contact Email

http://orcid.org/0000-0002-7791-3591

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APA Style

Amin, K. A. E. M. H. E. (2025). Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System. International Journal of Discrete Mathematics, 7(1), 1-13. https://doi.org/10.11648/j.dmath.20250701.11

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ACS Style

Amin, K. A. E. M. H. E. Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System. Int. J. Discrete Math. 2025, 7(1), 1-13. doi: 10.11648/j.dmath.20250701.11

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AMA Style

Amin KAEMHE. Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System. Int J Discrete Math. 2025;7(1):1-13. doi: 10.11648/j.dmath.20250701.11

Copy | Download

@article{10.11648/j.dmath.20250701.11,
  author = {Khalid Abd El Mageed Hag El Amin},
  title = {Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System
},
  journal = {International Journal of Discrete Mathematics},
  volume = {7},
  number = {1},
  pages = {1-13},
  doi = {10.11648/j.dmath.20250701.11},
  url = {https://doi.org/10.11648/j.dmath.20250701.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20250701.11},
  abstract = {This article addresses the joint estimation of parameters and states in linear stochastic systems with correlated process and measurement noises. We propose the Kalman Filtering with Correlated Noises based Recursive Generalized Extended Least Squares (KF-CN-RGELS) algorithm, which innovatively integrates a reformulated Kalman filter to handle noise cross-correlation via a gain matrix T, alongside recursive least squares for synchronous parameter-state updates. The algorithm’s key advantage lies in its ability to leverage noise correlation for improved accuracy: experimental results demonstrate that a higher correlation coefficient (ρw, v=0.8)reduces parameter estimation errors to 0.85% (vs. 1.81% for ρw, v=0) and enhances state estimation. The method’s robustness is validated under varying noise conditions, offering practical utility in systems like radar guidance and industrial control.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System

AU  - Khalid Abd El Mageed Hag El Amin
Y1  - 2025/08/30
PY  - 2025
N1  - https://doi.org/10.11648/j.dmath.20250701.11
DO  - 10.11648/j.dmath.20250701.11
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 1
EP  - 13
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20250701.11
AB  - This article addresses the joint estimation of parameters and states in linear stochastic systems with correlated process and measurement noises. We propose the Kalman Filtering with Correlated Noises based Recursive Generalized Extended Least Squares (KF-CN-RGELS) algorithm, which innovatively integrates a reformulated Kalman filter to handle noise cross-correlation via a gain matrix T, alongside recursive least squares for synchronous parameter-state updates. The algorithm’s key advantage lies in its ability to leverage noise correlation for improved accuracy: experimental results demonstrate that a higher correlation coefficient (ρw, v=0.8)reduces parameter estimation errors to 0.85% (vs. 1.81% for ρw, v=0) and enhances state estimation. The method’s robustness is validated under varying noise conditions, offering practical utility in systems like radar guidance and industrial control.

VL  - 7
IS  - 1
ER  -

Copy | Download