Bias‐eliminating least‐squares identification of errors‐in‐variables models with mutually correlated noises

“…Note that, the case of mutually correlated noises has been rarely treated in the literature and only with reference to specific approaches, see e.g. Beghelli, Castaldi, and Soverini (1997), Diversi (2013) and Diversi et al (2012).…”

Section: Introductionmentioning

confidence: 99%

A unified framework for EIV identification methods when the measurement noises are mutually correlated

2014

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“…To obtain the unbiased estimates, the bias compensation method was proposed [32]. The basic idea is to compensate the biased least squares estimate by adding a correction term [33][34][35]. Zhang investigated the parameter estimation of the multiple-input single-output linear system with colored noise and introduced a stable prefilter to preprocess the input data for the purpose of obtaining the unbiased estimate [36].…”

Section: Introductionmentioning

confidence: 99%

The Bias Compensation Based Parameter and State Estimation for Observability Canonical State-Space Models with Colored Noise

2018

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This paper develops a bias compensation-based parameter and state estimation algorithm for the observability canonical state-space system corrupted by colored noise. The state-space system is transformed into a linear regressive model by eliminating the state variables. Based on the determination of the noise variance and noise model, a bias correction term is added into the least squares estimate, and the system parameters and states are computed interactively. The proposed algorithm can generate the unbiased parameter estimate. Two illustrative examples are given to show the effectiveness of the proposed algorithm.

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“…However, building the first principle models requires the complete knowledge of physical plants; thus, system identification has attracted much attention. System identification is to recognize the structure and parameters of the systems using available input-output data [19,20]. This paper focuses on the parameter identification problems of multivariate pseudo-linear regressive systems with colored noise.…”

Section: Introductionmentioning

confidence: 99%

Convergence of the recursive identification algorithms for multivariate pseudo‐linear regressive systems

Wang

Ding

2015

Adaptive Control & Signal

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The performance analysis of the recursive algorithms for the multivariate systems with an autoregressive moving average noise process is still open. This paper analyzes the convergence of two recursive identification algorithms, the multivariate recursive generalized extended least squares algorithm and the multivariate generalized extended stochastic gradient algorithm, for pseudo-linear multivariate systems and proves that the parameter estimation errors consistently converge to zero under persistent excitation conditions. The simulation results show that the proposed algorithms work well. 825 distillation column [29]. In the system identification area, Saadatzi et al. used two-input two-output transfer-function matrix models to describe the dynamics of the electric wheelchair on an arbitrary slope, and proposed a pre-compensator to decompose the plant's dynamics and to improve the identification accuracy [30]. Gu et al. combined the recursive least squares algorithm with the state filtering to identify the canonical state space systems [31].In practical industrial processes, the observed output data are always corrupted by various noise. Some methods assume that noise is independent identically distributed or white. However, it may be more reasonable to adopt the colored noise or the correlated noise because noise is unmeasurable [32,33]. The regressive systems involving the colored noise or correlated noise are called the pseudo-linear regressive systems. Cerutti et al. used the autoregressive moving average (ARMA) model to represent the dynamics of brain potentials [34]. Zheng et al. proposed a biased compensation based recursive least squares method for stochastic linear systems with correlated noise [35].On the convergence of the identification algorithms, early researchers always assumed that the observation noise has zero mean, finite second-order moment, and higher-order moment [36]. Some recent studies relaxed these assumptions. Liu and Ding studied the convergence properties of the recursive least squares algorithm for multivariable stochastic systems [37]; Ding and Gu studied the convergence of the auxiliary model based stochastic gradient algorithm for output-error state-delay systems [38]; Ding presented a coupled least squares algorithm for the multivariable stochastic systems and analyzed its convergence [39]. To the best of the authors' knowledge, the performance analysis for the multivariable ARMA systems has not been fully investigated. The main contributions of this paper lie in the following.By utilizing the measurable input-output data, this paper presents a multivariate generalized extended stochastic gradient (M-GESG) algorithm and a multivariate recursive generalized extended least squares (M-RGELS) algorithm for estimating the parameters of multivariate pseudo-linear regressive systems. By using the stochastic martingale theory, this paper analyzes the convergence of the M-GESG algorithm and the M-RGELS algorithm for multivariate systems with ARMA noise process.Briefly, the remainder is...

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Bias‐eliminating least‐squares identification of errors‐in‐variables models with mutually correlated noises

Cited by 14 publications

References 18 publications

A unified framework for EIV identification methods when the measurement noises are mutually correlated

A unified framework for EIV identification methods when the measurement noises are mutually correlated

The Bias Compensation Based Parameter and State Estimation for Observability Canonical State-Space Models with Colored Noise

Convergence of the recursive identification algorithms for multivariate pseudo‐linear regressive systems

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