Linear Dynamic Filtering with Noisy Input and Output

Markovsky, Ivan; Moor, Bart De

doi:10.1016/s1474-6670(17)35007-3

Cited by 11 publications

(8 citation statements)

References 10 publications

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“…A recursive solution of the smoothing problem is obtained by dynamic programming in [24]. An alternative derivation by isometric state representation is given in [14].…”

Section: B Numerical Implementationmentioning

confidence: 99%

Application of structured total least squares for system identification and model reduction

Markovsky

Willems

Huffel

et al. 2005

IEEE Trans. Automat. Contr.

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Abstract-The following identification problem is considered:Minimize the 2 norm of the difference between a given time series and an approximating one under the constraint that the approximating time series is a trajectory of a linear time invariant system of a fixed complexity. The complexity is measured by the input dimension and the maximum lag. The question leads to a problem that is known as the global total least squares problem and alternatively can be viewed as maximum likelihood identification in the errors-in-variables setup. Multiple time series and latent variables can be considered in the same setting. Special cases of the problem are autonomous system identification, approximate realization, and finite time optimal 2 model reduction. The identification problem is related to the structured total least squares problem. This paper presents an efficient software package that implements the theory. The proposed method and software are tested on data sets from the database for the identification of systems DAISY.

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“…A recursive solution of the smoothing problem is obtained by dynamic programming in [24]. An alternative derivation by isometric state representation is given in [14].…”

Section: B Numerical Implementationmentioning

confidence: 99%

Application of structured total least squares for system identification and model reduction

Markovsky

Willems

Huffel

et al. 2005

IEEE Trans. Automat. Contr.

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“…Two types of AVRs have been considered in the case study. The discrete DAEs for the IEEE-DC1A type of AVR are given by (20), while for the IEEE-ST1A type of AVR they are given by (21). In the case of manual excitation, the field excitation voltage, E f d , is equal to a constant reference, V ref .…”

Section: Power System Modeling and The Discrete Daesmentioning

confidence: 99%

“…One way of including these noises in the DAEs is to model them as input noises [21]. But this would require linearization and would therefore defeat the purpose of unscented transformation and non-linear filtering.…”

Section: Pseudo Inputs and Decentralized Filtersmentioning

confidence: 99%

Decentralized Dynamic State Estimation in Power Systems Using Unscented Transformation

Singh

Pal

2014

IEEE Trans. Power Syst.

245

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Abstract-This paper proposes a decentralized algorithm for real-time estimation of the dynamic states of a power system. The scheme employs phasor measurement units (PMUs) for the measurement of local signals at each generation unit; and subsequent state estimation using unscented Kalman filtering (UKF). The novelty of the scheme is that the state estimation at one generation unit is independent from the estimation at other units, and therefore the transmission of remote signals to a central estimator is not required. This in turn reduces the complexity of each distributed estimator; and makes the estimation process highly efficient, accurate and easily implementable. The applicability of the proposed algorithm has been thoroughly demonstrated on a representative model. Index Terms-dynamic state estimation, decentralized, phasor measurement units, unscented transformation, Kalman filter.

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“…the inputs are also affected by measurement noise, Kalman filtering cannot directly be applied (Guidorzi et al, 2003). The EIV filtering problem, which deals with the optimal estimation of noise free input and output signals, has been solved in (Guidorzi et al, 2003) and (Markovsky and De Moor, 2005). A unified framework for both, Kalman filtering and EIV filtering has been presented in (Diversi et al, 2005), where the EIV filtering problem is solved by the means of a standard Kalman filter (Kf) applied to a reformulated model.…”

Section: Introductionmentioning

confidence: 99%

AN INVESTIGATION OF EXTENDED KALMAN FILTERING IN THE ERRORS-IN-VARIABLES FRAMEWORK - A Joint State and Parameter Estimation Approach

Linden¹,

Vinsonneau²,

Burnham³

2007

Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics

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The paper addresses the problem of errors-in-variables filtering, i.e. the optimal estimation of inputs and outputs from noisy observations. While the optimal solution is known for linear time-varying systems of known parameterisation, this paper considers a suboptimal approach where only an approximated set of parameters is available. The proposed filter is derived by the means of joint state and parameter estimation using the extended Kalman filter approach which, in turn, leads to a coupled state-parameter estimation procedure. However, the resulting parameter estimates appear to be biased in the presence of input noise. The novel filter is compared with a previously proposed suboptimal filter.

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Linear Dynamic Filtering with Noisy Input and Output

Cited by 11 publications

References 10 publications

Application of structured total least squares for system identification and model reduction

Application of structured total least squares for system identification and model reduction

Decentralized Dynamic State Estimation in Power Systems Using Unscented Transformation

AN INVESTIGATION OF EXTENDED KALMAN FILTERING IN THE ERRORS-IN-VARIABLES FRAMEWORK - A Joint State and Parameter Estimation Approach

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