Three‐Stage Filtered Gradient Identification Methods for Multivariable ARX Systems With Colored Noise

Haoming Xing et al.

Optimal Control Applications and Methods2026https://doi.org/10.1002/oca.70063article
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ABSTRACT This article investigates the identification issue of multivariable ARX systems with colored noise. To address the bias caused by colored noise, a data filtering method is applied to whiten the original multivariable system, which filters the input–output data without altering their inherent dynamics and yields a filtered identification model. Considering the computational complexity and burden in multivariable system identification, a three‐stage filtered stochastic gradient algorithm is proposed based on the filtered identification model with a hierarchical strategy. In addition, the historical innovations are utilized to further improve estimation accuracy and convergence performance, resulting in a three‐stage filtered multi‐innovation stochastic gradient algorithm. The numerical examples verify the effectiveness of the proposed algorithms in identifying multivariable ARX systems.

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https://doi.org/https://doi.org/10.1002/oca.70063

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@article{haoming2026,
  title        = {{Three‐Stage Filtered Gradient Identification Methods for Multivariable ARX Systems With Colored Noise}},
  author       = {Haoming Xing et al.},
  journal      = {Optimal Control Applications and Methods},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1002/oca.70063},
}

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0.53

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.70 × 0.15 = 0.10
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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