Identification of Bilinear Systems With White Noise Inputs: An Iterative Deterministic-Stochastic Subspace Approach

Santos, P. Lopes dos; Ramos, José A.; Carvalho, J. L. Martins de

doi:10.1109/tcst.2008.2002041

Cited by 40 publications

(23 citation statements)

References 20 publications

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“…6 Some methods based on the approximation idea have been used in parameter estimation for bilinear systems. Specifically, much attractive attention has been paid to bilinear systems as they are simple nonlinear systems and represent the intermediary structure between linear models and nonlinear models.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, much attractive attention has been paid to bilinear systems as they are simple nonlinear systems and represent the intermediary structure between linear models and nonlinear models. 6 Some methods based on the approximation idea have been used in parameter estimation for bilinear systems. 7 Dai and Sinha utilized the block functions for parameter estimation of the bilinear system.…”

Section: Introductionmentioning

confidence: 99%

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State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

Xiao

Ding

Yang

2019

Adaptive Control & Signal

230

117

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This paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems.It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single-input-single-output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple-input-multiple-output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

Xiao

Ding

Yang

2019

Adaptive Control & Signal

230

117

View full text Add to dashboard Cite

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“…From this idea, a differential Kalman filter based method was derived. This method consists in using two detectors and is identical to the one presented in [18], but the scheduling signals are now first the calculated intake pressure and second the calculated offtake pressure. The two different scheduling signals lead to two different leakage detectors, where each one runs two instances of this Kalman filter; the first instance uses the calculated pressure as the scheduling signal and the second uses the measured pressure.…”

Section: Leakage Detectionmentioning

confidence: 99%

Leakage detection and location in gas pipelines through an LPV identification approach

Santos

Perdicoúlis²,

Jank

et al. 2011

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tA new approach to gas leakage detection in high pressure distribution networks is proposed, where two leakage detectors are modelled as a linear parameter varying (LPV) system whose scheduling signals are, respectively, intake and offtake pressures. Running the two detectors simultaneously allows for leakage location. First, the pipeline is identified from operational data, supplied by REN-Gasodutos and using an LPV systems identification algorithm proposed in [1]. Each leakage detector uses two Kalman filters where the fault is viewed as an augmented state. The first filter estimates the flow using a calculated scheduling signal, assuming that there is no leakage. Therefore it works as a reference. The second one uses a measured scheduling signal and the augmented state is compared with the reference value. Whenever there is a significant difference, a leakage is detected. The effectiveness of this method is illustrated with an example where a mixture of real and simulated data is used.

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“…During the past decades, the minimal order state observer was considered for bilinear systems, and its necessary conditions for the existence of observers were discussed, but the estimation errors depended on the system inputs . Lopes dos Santos et al presented a subspace identification method for bilinear systems by regarding the bilinear term as a second‐order white noise process based on the Picard decomposition . Larkowski et al used the Frisch equations to determine the model parameters and the noise variances based on the bias‐compensated least squares method .…”

Section: Introductionmentioning

confidence: 99%

Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

Liu

Ding

Hayat

2020

Intl J Robust & Nonlinear

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Summary The combined iterative parameter and state estimation problem is considered for bilinear state‐space systems with moving average noise in this paper. There are the product terms of state variables and control variables in bilinear systems, which makes it difficult for the parameter and state estimation. By designing a bilinear state estimator based on the Kalman filtering, the states are estimated using the input‐output data. Furthermore, a moving data window (MDW) is introduced, which can update the dynamical data by removing the oldest data and adding the newest measurement data. A state estimator‐based MDW gradient‐based iterative (MDW‐GI) algorithm is proposed to estimate the unknown states and parameters jointly. Moreover, given the extended gradient‐based iterative (EGI) algorithm as a comparison, the MDW‐GI algorithm can reduce the impact of noise to parameter estimation and improve the parameter estimation accuracy. The numerical simulation examples validate the effectiveness of the proposed algorithm.

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Identification of Bilinear Systems With White Noise Inputs: An Iterative Deterministic-Stochastic Subspace Approach

Cited by 40 publications

References 20 publications

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

Leakage detection and location in gas pipelines through an LPV identification approach

Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

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