Journal ArticleDOI
Parameter estimation for nonlinear Volterra systems by using the multi-innovation identification theory and tensor decomposition
Xiaobo Gu,Xiaobo Gu +1 more
- Vol. 359, Iss: 2, pp 1782-1802
TLDR
In this article , the identification issue of discrete-time nonlinear Volterra systems and uses a tensorial decomposition called PARAFAC to represent the VOLTERRA kernels.Abstract:
The Volterra model can represent a wide range of nonlinear dynamical systems. However, its practical use in nonlinear system identification is limited due to the exponentially growing number of Volterra kernel coefficients as the degree increases. This paper considers the identification issue of discrete-time nonlinear Volterra systems and uses a tensorial decomposition called PARAFAC to represent the Volterra kernels which can provide a significant parametric reduction compared with the conventional Volterra model. Applying the multi-innovation identification theory, the recursive algorithm by combining the l2-norm is proposed for the PARAFAC-Volterra models with the Gaussian noises. In addition, the multi-innovation algorithm combining with the logarithmic p-norms is investigated for the nonlinear Volterra systems with the non-Gaussian noises. Finally, some simulation results illustrate the effectiveness of the proposed identification methods. read more
Citations
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Journal ArticleDOI
Least squares parameter estimation and multi-innovation least squares methods for linear fitting problems from noisy data
TL;DR: The results of the least squares and multi-innovation least squares algorithms for linear regressive systems with white noises can be extended to other systems with colored noises as mentioned in this paper , and the results of least square and multinomial least square algorithms can be generalized to other problems with different noises.
Journal ArticleDOI
Modeling nonlinear systems using the tensor network B‐spline and the multi‐innovation identification theory
TL;DR: The TNBS can fit nonlinear systems with strong nonlinearity by the meaning of setting a proper degree and knots number and the recursive algorithm by combining the l2$$ {l}_2 $$ ‐norm is proposed to the NARX system with Gaussian noise.
Journal ArticleDOI
Gradient-based Parameter Estimation for a Nonlinear Exponential Autoregressive Time-series Model by Using the Multi-innovation
Jian Pan,Juqing Liu,J. Shu +2 more
Journal ArticleDOI
Filtered auxiliary model recursive generalized extended parameter estimation methods for Box–Jenkins systems by means of the filtering identification idea
TL;DR: In this paper , a filtered auxiliary model generalized extended stochastic gradient identification method was proposed for Box-Jenkins systems. But the proposed method is not applicable to other linear and nonlinear multivariable systems with colored noises.
Journal ArticleDOI
Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems
TL;DR: In this paper , an overall recursive least squares algorithm is developed to handle the difficulty of the bilinear-in-parameter identification model and an overall stochastic gradient algorithm is deduced and the forgetting factor is introduced to improve the convergence rate.
References
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Journal ArticleDOI
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Feng Ding,Tongwen Chen +1 more
TL;DR: The performance analysis and simulation results show that the proposed MISG and MIFG algorithms have faster convergence rates and better tracking performance than their corresponding SG algorithms.
Journal ArticleDOI
Combined parameter and output estimation of dual-rate systems using an auxiliary model
Feng Ding,Tongwen Chen +1 more
TL;DR: It is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance, and that the output estimates uniformly converge to the true outputs.
Journal ArticleDOI
Parameter estimation with scarce measurements
TL;DR: A gradient-based algorithm is derived to estimate the parameters of the input-output representation with scarce measurements, and the convergence properties of the parameter estimation and unavailable output estimation are established using the Kronecker lemma and the deterministic version of the martingale convergence theorem.
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