A Recursive Parameter Estimation Algorithm for Modeling Signals with Multi-frequencies

Xu, Ling; Song, Guanglei

doi:10.1007/s00034-020-01356-3

Cited by 155 publications

(95 citation statements)

References 69 publications

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“…5. Readâ i,k fromâ k in (42) and readm i,k fromm k in (43), and constructÂ k andM k using (48) and (49). 6.…”

Section: The Combined State and Parameter Estimationmentioning

confidence: 99%

“…Obviously, it is larger than that of the 3S-LSI algorithm. The proposed iterative algorithm for a class of observability canonical bilinear systems in this paper can combine some mathematical tools [39][40][41][42][43] to study the parameter estimation problems of different stochastic systems with colored noises [44][45][46][47][48][49][50][51] and can be applied to other fields [52][53][54][55][56][57] such as signal processing and communication networked systems [58][59][60][61] and transportation communication systems, [62][63][64][65] and engineering systems and so on.…”

Section: The Computational Efficiencymentioning

confidence: 99%

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Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator

Liu

Zhang

Ding

et al. 2020

Adaptive Control & Signal

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Because of the product item of the control input and the state vector, the identification of bilinear systems is difficult. This paper considers the combined parameter and state estimation problems of bilinear state-space systems. On the basis of the observability canonical form and the model transformation, an identification model with a linear combination of the system parameters is obtained. Using the hierarchical principle, the identification model is decomposed into three submodels with fewer variables, and a three-stage least squares-based iterative (3S-LSI) algorithm is presented to estimate the system parameters. Furthermore, we derive a state estimator (SE) for estimating the unknown states, and present an SE-3S-LSI algorithm for estimating the unknown parameters and states simultaneously. After that, the least squares-based iterative algorithm is presented as a comparison. By analyzing the estimation results and the calculation amount, these two algorithms can identify the bilinear system effectively but the 3S-LSI algorithm can improve the computational efficiency. The simulation results indicate the effectiveness of the proposed algorithms.

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“…5. Readâ i,k fromâ k in (42) and readm i,k fromm k in (43), and constructÂ k andM k using (48) and (49). 6.…”

Section: The Combined State and Parameter Estimationmentioning

confidence: 99%

Section: The Computational Efficiencymentioning

confidence: 99%

Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator

Liu

Zhang

Ding

et al. 2020

Adaptive Control & Signal

View full text Add to dashboard Cite

show abstract

“…For example, Wang et al decomposed the bilinear Hammerstein system into two fictitious pseudo‐regressive subsystems based on the hierarchical identification principle, and developed a hierarchical orthogonal matching pursuit optimization algorithm; 27 Xu et al proposed a hierarchical multi‐innovation stochastic gradient estimation method for the frequency response based on the dynamical window data 28 . The related signal modeling methods can be found in the areas such as the recursive parameter estimation algorithm for modeling signals multifrequencies 29,30 …”

Section: Introductionmentioning

confidence: 99%

Maximum likelihood hierarchical least squares‐based iterative identification for dual‐rate stochastic systems

2020

Adaptive Control & Signal

170

104

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For a dual-rate sampled-data stochastic system with additive colored noise, a dual-rate identification model is obtained by using the polynomial transformation technique, which is suitable for the available dual-rate measurement data. Based on the obtained model, a maximum likelihood least squares-based iterative (ML-LSI) algorithm is presented for identifying the parameters of the dual-rate sampled-data stochastic system. In order to improve the computation efficiency of the algorithm, the identification model of a dual-rate sampled-data stochastic system is divided into two subidentification models with smaller dimensions and fewer parameters, and a maximum likelihood hierarchical least squares-based iterative (H-ML-LSI) algorithm is proposed for these subidentification models by using the hierarchical identification principle. The simulation results indicate that the proposed algorithms are effective for identifying dual-rate sampled-data stochastic systems and the H-ML-LSI algorithm has a higher computation efficiency than the ML-LSI algorithm.

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“…For instance, Xu developed several gradient algorithms for sine response signals using the moving window data. [20][21][22] Over the years, some efforts have been advanced to improve the performance of identification algorithms. For example, the decomposition technique has been applied to linear and nonlinear dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Two‐stage recursive identification algorithms for a class of nonlinear time series models with colored noise

Ding

Gan

et al. 2020

Intl J Robust & Nonlinear

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This article concentrates on the recursive identification algorithms for the exponential autoregressive model with moving average noise. Using the decomposition technique, we transform the original identification model into a linear and nonlinear subidentification model and derive a two-stage least squares (LS) extended stochastic gradient (ESG) algorithm. In order to improve the parameter estimation accuracy, we employ the multi-innovation identification theory and develop a two-stage LS multi-innovation ESG algorithm. A simulation example is provided to test the effectiveness of the proposed algorithms.

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A Recursive Parameter Estimation Algorithm for Modeling Signals with Multi-frequencies

Cited by 155 publications

References 69 publications

Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator

Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator

Maximum likelihood hierarchical least squares‐based iterative identification for dual‐rate stochastic systems

Two‐stage recursive identification algorithms for a class of nonlinear time series models with colored noise

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