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Accelerated Identification Algorithms for Exponential Nonlinear Models: Two-Stage Method and Particle Swarm Optimization Method

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Abstract

The traditional least squares (LS) and gradient descent (GD) algorithms can estimate the parameters of the regression models. They can be inefficient when the models have complex structures: (1) the unknown parameters in the information vector make the algorithm be impossible to update the parameters; (2) the zigzagging nature of the gradient descent algorithm and the complex structures lead to slow convergence rates; and (3) the step-size and derivative function calculations may be unsolvable for complex nonlinear models. This paper proposes two kinds of algorithms for exponential nonlinear models. The first is the two-stage algorithm, which decomposes the complex model into a linear part and a nonlinear part, where the linear part is estimated using the LS algorithm and the nonlinear part is identified based on the GD algorithm. The second is the particle swarm optimization algorithm which can simultaneously obtain all the parameters. To increase the convergence rates, the Aitken method is also introduced. The simulation results demonstrate the effectiveness of the proposed algorithms.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 61973137), the Fundamental Research Funds for the Central Universities (No. JUSRP22016), the Funds of the Science and Technology on Near-Surface Detection Laboratory (No. TCGZ2019A001), and the Natural Science Foundation of Jiangsu Province (No. BK20201339).

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  1. School of Science, Jiangnan University, Wuxi, 214122, People’s Republic of China

    Yan Pu, Jing Chen & Yawen Mao

  2. Science and Technology on Near-Surface Detection Laboratory, Wuxi, 214028, People’s Republic of China

    Yingjiao Rong

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  1. Yan Pu
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Correspondence to Yan Pu.

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Pu, Y., Rong, Y., Chen, J. et al. Accelerated Identification Algorithms for Exponential Nonlinear Models: Two-Stage Method and Particle Swarm Optimization Method. Circuits Syst Signal Process 41, 2636–2652 (2022). https://doi.org/10.1007/s00034-021-01907-2

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