Nonlinear Minimum Variance Estimation for Discrete-Time Multi-Channel Systems

Grimble, M.J.; Naz, Shamsher Ali

doi:10.1109/tsp.2009.2016999

Cited by 7 publications

(2 citation statements)

References 19 publications

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“…The theory of NMV estimation (NMVE) was intrıduced by Grimble (2007) using polynomial system models (Grimble, 1995(Grimble, , 2006 and later state-equation-based models (Grimble, 2011(Grimble, , 2012. The NMVE technique involves the estimation of a signal that passes through a communications channel having non-linearities and communication/transport delays (Grimble, 2006).…”

Section: Non-linear Minimum Variance Estimationmentioning

confidence: 99%

Non-linear minimum variance estimation for fault detection systems

Alkaya

Grimble

2014

Transactions of the Institute of Measurement and Control

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A novel model-based algorithm for fault detection in stochastic linear and non-linear systems is proposed. The non-linear minimum variance estimation technique is used to generate a residual signal, which is then used to detect actuator and sensor faults in the system. The main advantage of the approach is the simplicity of the non-linear estimator theory and the straightforward structure of the resulting solution. Simulation examples are presented to illustrate the design procedure and the type of results obtained. The results demonstrate that both actuator and sensor faults can be detected successfully

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Section: Non-linear Minimum Variance Estimationmentioning

confidence: 99%

Non-linear minimum variance estimation for fault detection systems

Alkaya

Grimble

2014

Transactions of the Institute of Measurement and Control

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“…5 is shown a comparison between actual and estimated signals using the Wiener NMV estimator ( [6,7]) and the robust Wiener estimator for the system described above without any uncertainty. The results from the estimators are the same as we could have expected from the theory, in fact with no uncertain models the robust wiener filter correspond to the Wiener NMV filter.…”

Section: The Robust Wiener Optimal Estimator Solution Proofmentioning

confidence: 99%

Robust wiener optimal nonlinear estimation for uncertain systems

Inzerillo

Grimble

2012

2012 20th Mediterranean Conference on Control &Amp; Automation (MED)

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A nonlinear operator based approach to robust estimation is introduced for discrete-time systems. It involves a signal entering a communications channel with nonlinearities, transport delay and uncertainties. The measurements are assumed to be corrupted by coloured noise which is correlated with the signal to be estimated. The signal and noise model parameters are assumed to be subject to perturbations represented by random variables with known means and covariances. The theoretical solution does not involve linearization or approximations. In the limiting case of a linear system the estimator has the form of a Wiener filter in discretetime polynomial matrix system form. I. INTRODUCTIONHE optimal filter for linear systems are well known, like the Wiener ([1]) and the Kalman filter ([2, 3]) that have proved their value in applications. These are based on minimizing a statistical criterion and are optimal in an average sense. Over the last few years a new nonlinear estimation paradigm has emerged which leads to simple filters, smoothers and predictors for classes of nonlinear stochastic systems ([4-7]).There are many techniques for nonlinear estimation and the best known is the Extended Kalman Filter (EKF). The EKF has a similar structure to the Kalman filter but has a nonlinear model within the loop. To accommodate the nonlinearity the model is linearized at each time step to estimate the transition matrix and this is used to update the estimated covariance matrix. The EKF does not include a model for channel dynamics that will be included in the following and the solution involves approximations.In the following a related frequency domain or polynomial system approach to robust nonlinear estimation problems is presented. The system, signal and noise models are assumed to include uncertain elements that can be represented by linear models with probabilistic parameter deviations. The optimal robust filter, smoother, or predictor can be obtained from the results of a frequency weighted estimation problem. The estimation problem involves inferential estimation of a signal which enters a communication channel that contains nonlinearities and S. Inzerillo is with the

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Nonlinear Estimation Methods: Polynomial Systems Approach

Grimble

Majecki

2020

Nonlinear Industrial Control Systems

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Nonlinear Minimum Variance Estimation for Discrete-Time Multi-Channel Systems

Cited by 7 publications

References 19 publications

Non-linear minimum variance estimation for fault detection systems

Non-linear minimum variance estimation for fault detection systems

Robust wiener optimal nonlinear estimation for uncertain systems

Nonlinear Estimation Methods: Polynomial Systems Approach

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