Robust Filtering for Linear Time-Invariant Continuous Systems

Neveux, Philippe; Blanco, Eric; Thomas, Gérard

doi:10.1109/tsp.2007.896104

Cited by 26 publications

(10 citation statements)

References 12 publications

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“…Different form the deterministic form of observer (7), the gain matrix of M is a time-variant matrix. It satisfies the following equality (15) And the matrix of ) (t P can be determined by the following Riccati equation…”

Section: Results On Stochastic Systemsmentioning

confidence: 99%

“…All these methods have experienced a lot of interests from researchers, but it has found few practical industrial applications due to difficulties in obtaining convergent state estimates [5]. In recent years, other methods, such as wavelet [3], neural network [6], Fourier transformation [2], robust filtering [7], etc, have been proposed to meet the needs of different requirements. Unfortunately, most of those methods cannot solve the problem completely.…”

Section: Introductionmentioning

confidence: 99%

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The Algorithm on Adaptive Filtering and Generalized Derivative Estimating for Signals with Uncertain Dynamics

Wang

2009

2009 WRI World Congress on Computer Science and Information Engineering

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We consider the problem of adaptive filtering and related derivative estimating for signals with uncertain dynamics this paper. Based on the control method of uncertain systems, a new algorithm is proposed. The theoretical analysis and a special form of filter are given. It is shown that the filter doesn't depend on the unmodeled part of systems' dynamics and makes no assumptions regarding the classification of systems. The filter is also robust about the initial errors of the observations. And the most important of all is that we can also get the derivatives by the filter as well. It will be helpful for system prediction. Simulation results are provided to demonstrate the efficiency of the method.

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Section: Results On Stochastic Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Algorithm on Adaptive Filtering and Generalized Derivative Estimating for Signals with Uncertain Dynamics

Wang

2009

2009 WRI World Congress on Computer Science and Information Engineering

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“…Another recent technique is that of Neveux, Blanco and Thomas [32] and Zhou [41], which penalises the sensitivity of estimation errors to parameter variations, by minimizing both the estimation error as well as its gradient with respect to the uncertain parameters.…”

Section: Introductionmentioning

confidence: 99%

Parameter Uncertainty in the Kalman--Bucy Filter

Allan¹,

Cohen²

2019

SIAM J. Control Optim.

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In standard treatments of stochastic filtering one first has to estimate the parameters of the model. Simply running the filter without considering the reliability of this estimate does not take into account this additional source of statistical uncertainty. We propose an approach to address this problem when working with the continuous time Kalman-Bucy filter, by making evaluations via a nonlinear expectation. We show how our approach may be reformulated as an optimal control problem, and proceed to analyse the corresponding value function. In particular we present a novel uniqueness result for the associated Hamilton-Jacobi-Bellman equation.

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“…This paradigm has been adopted to filter design for single-input single-output systems in the frequency domain [5]. In this technical note, we investigate robust state estimation for multi-input multi-output systems under this framework.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Penalization Based Robust State Estimation for Uncertain Linear Systems

Zhou

2010

IEEE Trans. Automat. Contr.

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This technical note deals with robust state estimation when parametric uncertainties nonlinearly affect a plant state-space model, based on a simultaneous minimization of nominal estimation errors and their sensitivities. An analytic solution is derived for the optimal estimator which can be recursively realized. This estimator has a form similar to the robust estimator of [6], and its computational complexity is comparable to the Kalman filter. Under certain conditions, this robust estimator is proved to converge to a stable system, its estimation errors have a bounded covariance matrix, and the estimate is asymptotically unbiased. Numerical simulations show that the obtained estimator has nice estimation performances.Index Terms-Recursive state estimation, regularized least-squares, robustness, structured parametric uncertainty.

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Robust Filtering for Linear Time-Invariant Continuous Systems

Cited by 26 publications

References 12 publications

The Algorithm on Adaptive Filtering and Generalized Derivative Estimating for Signals with Uncertain Dynamics

The Algorithm on Adaptive Filtering and Generalized Derivative Estimating for Signals with Uncertain Dynamics

Parameter Uncertainty in the Kalman--Bucy Filter

Sensitivity Penalization Based Robust State Estimation for Uncertain Linear Systems

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