Iterative Estimation Algorithm for Bilinear Stochastic Systems by Using the Newton Search

Siyu Liu; Feng Ding

doi:10.62762/TIS.2024.155941

Volume 2, Issue 2, ICCK Transactions on Intelligent Systematics

Volume 2, Issue 2, 2025

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Noroff University College, Norway

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ICCK Transactions on Intelligent Systematics, Volume 2, Issue 2, 2025: 76-84

Free to Read | Research Article | 14 April 2025

Iterative Estimation Algorithm for Bilinear Stochastic Systems by Using the Newton Search

Siyu Liu 1

Feng Ding 2 *

1 College of Engineering, Zhejiang Normal University, Jinhua 321004, China

2 School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China

* Corresponding Author: Feng Ding, [email protected]

DOI: 10.62762/TIS.2024.155941

ARK: ark:/57805/tis.2024.155941

Received: 02 November 2024, Accepted: 26 March 2025, Published: 14 April 2025

Cited by: 2 (Source: Web of Science), 2 (Source: ), 2 (Source: Google Scholar)

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Abstract

This study addresses the challenge of estimating parameters iteratively in bilinear state-space systems affected by stochastic noise. A Newton iterative (NI) algorithm is introduced by utilizing the Newton search and iterative identification theory for identifying the system parameters. Following the estimation of the unknown parameters, we create a bilinear state observer (BSO) using the Kalman filtering principle for state estimation. Subsequently, we propose the BSO-NI algorithm for simultaneous parameter and state estimation. An iterative algorithm based on gradients is given for comparisons to illustrate the effectiveness of the proposed algorithms.

Graphical Abstract

Keywords

newton search

bilinear system

parameter estimation

system identification

iterative method

Data Availability Statement

Data will be made available on request.

Funding

This work was supported by the Young Scientists Fund of the National Natural Science Foundation of Zhejiang Province, China under Grant LQN25F030017.

Conflicts of Interest

The authors declare no conflicts of interest.

Ethical Approval and Consent to Participate

Not applicable.

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APA Style

Liu, S., & Ding, F. (2025). Iterative Estimation Algorithm for Bilinear Stochastic Systems by Using the Newton Search. ICCK Transactions on Intelligent Systematics, 2(2), 76–84. https://doi.org/10.62762/TIS.2024.155941

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TY  - JOUR
AU  - Liu, Siyu
AU  - Ding, Feng
PY  - 2025
DA  - 2025/04/14
TI  - Iterative Estimation Algorithm for Bilinear Stochastic Systems by Using the Newton Search
JO  - ICCK Transactions on Intelligent Systematics
T2  - ICCK Transactions on Intelligent Systematics
JF  - ICCK Transactions on Intelligent Systematics
VL  - 2
IS  - 2
SP  - 76
EP  - 84
DO  - 10.62762/TIS.2024.155941
UR  - https://www.icck.org/article/abs/TIS.2024.155941
KW  - newton search
KW  - bilinear system
KW  - parameter estimation
KW  - system identification
KW  - iterative method
AB  - This study addresses the challenge of estimating parameters iteratively in bilinear state-space systems affected by stochastic noise. A Newton iterative (NI) algorithm is introduced by utilizing the Newton search and iterative identification theory for identifying the system parameters. Following the estimation of the unknown parameters, we create a bilinear state observer (BSO) using the Kalman filtering principle for state estimation. Subsequently, we propose the BSO-NI algorithm for simultaneous parameter and state estimation. An iterative algorithm based on gradients is given for comparisons to illustrate the effectiveness of the proposed algorithms.
SN  - 3068-5079
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  -

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@article{Liu2025Iterative,
  author = {Siyu Liu and Feng Ding},
  title = {Iterative Estimation Algorithm for Bilinear Stochastic Systems by Using the Newton Search},
  journal = {ICCK Transactions on Intelligent Systematics},
  year = {2025},
  volume = {2},
  number = {2},
  pages = {76-84},
  doi = {10.62762/TIS.2024.155941},
  url = {https://www.icck.org/article/abs/TIS.2024.155941},
  abstract = {This study addresses the challenge of estimating parameters iteratively in bilinear state-space systems affected by stochastic noise. A Newton iterative (NI) algorithm is introduced by utilizing the Newton search and iterative identification theory for identifying the system parameters. Following the estimation of the unknown parameters, we create a bilinear state observer (BSO) using the Kalman filtering principle for state estimation. Subsequently, we propose the BSO-NI algorithm for simultaneous parameter and state estimation. An iterative algorithm based on gradients is given for comparisons to illustrate the effectiveness of the proposed algorithms.},
  keywords = {newton search, bilinear system, parameter estimation, system identification, iterative method},
  issn = {3068-5079},
  publisher = {Institute of Central Computation and Knowledge}
}

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