Parameter estimation algorithms for dynamical response signals based on the multi‐innovation theory and the hierarchical principle

Xu, Ling; Ding, Feng

doi:10.1049/iet-spr.2016.0220

Cited by 127 publications

(63 citation statements)

References 38 publications

(70 reference statements)

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“…Parameter estimation is significant in system modeling [14,15]. Multi-input multi-output systems widely exist in industrial control areas, which are also called multivariate systems or multivariable systems [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Pan

Jiang

et al. 2018

Complexity

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The identification problem of multivariable controlled autoregressive systems with measurement noise in the form of the moving average process is considered in this paper. The key is to filter the input-output data using the data filtering technique and to decompose the identification model into two subidentification models. By using the negative gradient search, an adaptive data filtering-based gradient iterative (F-GI) algorithm and an F-GI with finite measurement data are proposed for identifying the parameters of multivariable controlled autoregressive moving average systems. In the numerical example, we illustrate the effectiveness of the proposed identification methods.

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Section: Introductionmentioning

confidence: 99%

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Pan

Jiang

et al. 2018

Complexity

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“…From (12) and (14), we have Replacing ( ), ( ) in (26) and (27) with their estimateŝ ( ) and̂( ), replacing c in (26) with its estimateĉ −1 ( ), and replacing in (27) with its estimatê( ), we havê…”

Section: The Hierarchical Gradient Based Iterative Algorithmmentioning

confidence: 99%

“…The parameter estimateŝ( ) andĉ ( ) cannot be computed by (26) and (27), because the information vectors ( ) and ( ) contain unknown variables ( − ) and ( − ), and the parameter vectors and c in (26) and (27) are unknown. We solve this problem by replacing the unknown variables ( − ) and ( − ) with their corresponding estimateŝ, −1 ( − ) and̂− 1 ( − ) at iteration −1 and define the estimateŝ( ) and̂( ) at iteration aŝ…”

Section: The Hierarchical Gradient Based Iterative Algorithmmentioning

confidence: 99%

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The Hierarchical Iterative Identification Algorithm for Multi-Input-Output-Error Systems with Autoregressive Noise

Ding

2017

Complexity

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This paper considers the identification problem of multi-input-output-error autoregressive systems. A hierarchical gradient based iterative (H-GI) algorithm and a hierarchical least squares based iterative (H-LSI) algorithm are presented by using the hierarchical identification principle. A gradient based iterative (GI) algorithm and a least squares based iterative (LSI) algorithm are presented for comparison. The simulation results indicate that the H-LSI algorithm can obtain more accurate parameter estimates than the LSI algorithm, and the H-GI algorithm converges faster than the GI algorithm.

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“…Parameter estimation is a significant part in system identification, and has been widely used in system analysis [1][2][3], system modeling [4][5][6][7], and system control [8,9]. Since many industrial processes are complex and inherently nonlinear, nonlinear system identification has drawn much attention throughout the world [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle

Zhang

Ding

et al. 2018

IET Control Theory & Applications

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128

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Abstract:In the revised paper, we have highlighted the changes made in Blue FONT. This paper presents a combined parameter and state estimation algorithm for a bilinear system described by its observer canonical state space model based on the hierarchical identification principle. The Kalman filter is known as the best state filter for linear systems, but not applicable for bilinear systems. Thus, a bilinear state observer (BSO) is designed to give the state estimates using the extremum principle. Then a BSO based recursive least squares (BSO-RLS) algorithm is developed. For comparison with the BSO-RLS algorithm, by dividing the system into three fictitious subsystems on basis of the decomposition-coordination principle, a BSO based hierarchical least squares algorithm is proposed to reduce the computation burden. Moreover, a BSO based forgetting factor recursive least squares algorithm is presented to improve the parameter tracking capability. Finally, a numerical example illustrates the effectiveness of the proposed algorithms. IntroductionParameter estimation is a significant part in system identification, and has been widely used in system analysis [1][2][3], system modeling [4][5][6][7], and system control [8,9]. Since many industrial processes are complex and inherently nonlinear, nonlinear system identification has drawn much attention throughout the world [10][11][12]. The bilinear approach for modeling these complex processes are proven to be more precise than any other traditional linear models [13]. However, the nonlinear term existing in the bilinear model brings some challenges for bilinear system identification. During the past decades, much work has been carried out on parameter estimation for bilinear systems. For example, dos Santos et al. presented a subspace identification method for bilinear systems by treating the bilinear term as a second-order white noise process [14]. Larkowski et al. addressed the identification problem of the diagonal bilinear errors-in-variables system and extended the bias compensated least squares technique to bilinear systems [15]. Li et al. applied the polynomial transformation technique to obtain the equivalent input-output representation of the bilinear system and proposed the iterative algorithm for parameter estimation [16][17][18]. The recursive least squares (RLS) approach is known as the most commonly used estimation method among numerous different parameter estimation techniques. Although the RLS method offers a fast convergence rate, there exists several problems such as the increase in the computational burden and the decline in the tracking capability [19,20]. The hierarchical identification principle is applied to decompose a bilinear system into several subsystems Nonlinear filtering techniques have attracted much attention in signal processing [26,27] and have wide applications in many areas [28][29][30][31]. The classical Kalman filter (KF) is recognized as the best linear filter for linear systems under Gaussian noises. However, it is not suitable f...

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Parameter estimation algorithms for dynamical response signals based on the multi‐innovation theory and the hierarchical principle

Cited by 127 publications

References 38 publications

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

The Hierarchical Iterative Identification Algorithm for Multi-Input-Output-Error Systems with Autoregressive Noise

State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle

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