On the global optimality of unbiased minimum-variance state estimation for systems with unknown inputs

Hsieh, Chien-Shu

doi:10.1016/j.automatica.2010.01.029

Cited by 58 publications

(55 citation statements)

References 20 publications

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“…Various filters were developed under different assumptions for the systems with unknown inputs; see, e.g., Cheng, Ye, Wang, and Zhou (2009), Darouach and Zasadzinski (1997), Darouach, Zasadzinski, and Xu (1994), Fang and Callafon (2012), Gillijns and De Moor (2007), Hsieh (2000Hsieh ( , 2010 and Kitanidis (1987), among many others. Most of these researches used the technique of minimum variance unbiased estimation, hence leading to an unbiased minimum-variance ✩ This work was jointly funded by UK Engineering and Physical Sciences Research Council (EPSRC) and BAE Systems (EP/H501401/1).…”

Section: Introductionmentioning

confidence: 99%

On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs

2015

Automatica

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a b s t r a c tFor linear stochastic time-varying systems, we investigate the properties of the Kalman filter with partially observed inputs. We first establish the existence condition of a general linear filter when the unknown inputs are partially observed. Then we examine the optimality of the Kalman filter with partially observed inputs. Finally, on the basis of the established existence condition and optimality result, we investigate asymptotic stability of the filter for the corresponding time-invariant systems. It is shown that the results on existence and asymptotic stability obtained in this paper provide a unified approach to accommodating a variety of filtering scenarios as its special cases, including the classical Kalman filter and state estimation with unknown inputs.

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Section: Introductionmentioning

confidence: 99%

On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs

2015

Automatica

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“…The algorithms are often referred to as joint input-state estimation algorithms and combine both input and state estimation, e.g. [18,19,20,21,22,23]. Recursive combined deterministic-stochastic approaches allow online joint input-state estimation, thereby accounting for measurement errors, modelling errors, and additional unknown vibration sources.…”

Section: Introductionmentioning

confidence: 99%

Verification of joint input-state estimation for force identification by means of in situ measurements on a footbridge

Maes

Nimmen

Lourens

et al. 2016

Mechanical Systems and Signal Processing

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This paper presents a verification of a joint input-state estimation algorithm using data obtained from in situ experiments on a footbridge. The estimation of the input and the system states is performed in a minimum-variance unbiased way, based on a limited number of response measurements and a system model. A dynamic model of the footbridge is obtained using a detailed finite element model that is updated using a set of experimental modal characteristics. The joint inputstate estimation algorithm is used for the identification of two impact, harmonic, and swept sine forces applied to the bridge deck. In addition to these forces, unknown stochastic forces, such as wind loads, are acting on the structure. These forces, as well as measurement errors, give rise to uncertainty in the estimated forces and system states. Quantification of the uncertainty requires determination of the power spectral density of the unknown stochastic excitation, which is identified from the structural response under ambient loading. The verification involves comparing the estimated forces with the actual, measured forces. Although a good overall agreement is obtained between the estimated and measured forces, modeling errors prohibit a proper distinction between multiple forces applied to the structure for the case of harmonic and swept sine excitation.

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“…The algorithms are often referred to as joint input-state estimation algorithms and combine both input and state estimation, e.g. (Klinkov and Fritzen 2006, Hsieh 2010, Eftekhar Azam et al 2015). Gillijns and De Moor (2007) have proposed an algorithm where the input estimation is performed prior to the state estimation step.…”

Section: Introductionmentioning

confidence: 99%

Verification of joint input-state estimation by means of a full scale experiment on a footbridge

Maes

Nimmen²,

Lourens³

et al. 2016

Life-Cycle of Engineering Systems: Emphasis on Sustainable Civil Infrastructure

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This paper presents a verification of a state-of-the-art joint input-state estimation algorithm using data obtained from in situ experiments on a footbridge. A dynamic model of the footbridge is based on a detailed finite element model that is calibrated using a set of experimental modal characteristics. The joint input-state estimation algorithm is used for the identification of two impact, harmonic, and swept sine forces applied to the bridge deck. In addition to these forces, unknown stochastic forces, such as wind loads, are acting on the structure. These forces, as well as measurement errors, give rise to uncertainty in the estimated forces and system states. Quantification of the uncertainty requires determination of the power spectral density of the unknown stochastic excitation, which is identified from the structural response under ambient loading. The verification involves comparing the estimated forces with the actual, measured forces. Although a good overall agreement is obtained between the estimated and measured forces, modeling errors prohibit a proper distinction between multiple forces applied to the structure for the case of harmonic and swept sine excitation.

show abstract

On the global optimality of unbiased minimum-variance state estimation for systems with unknown inputs

Cited by 58 publications

References 20 publications

On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs

On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs

Verification of joint input-state estimation for force identification by means of in situ measurements on a footbridge

Verification of joint input-state estimation by means of a full scale experiment on a footbridge

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