A Technique for Compensating the Filter Performance by a Fictitious Noise

Yoshimura, Teizo; Soeda, Takashi

doi:10.1115/1.3426358

Cited by 15 publications

(10 citation statements)

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“…where P(1|0) = 0 and y(k, s) satisfies ). X (16) Proof. Consider the following error difference equation induced by (1) and (13):…”

Section: One-step Prediction Estimationmentioning

confidence: 99%

“…). X Additionally, this can be computed according to (16) by noticing (18) and (19). The proof is completed.…”

Section: One-step Prediction Estimationmentioning

confidence: 99%

“…For deterministic uncertainty, it is very difficult to obtain an optimal estimate. If uncertainties in models can be described in stochastic terms with statistical characteristics, however, it is possible to obtain an optimal estimate [16,17].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Estimation of A Class of Linear Time‐Delay Uncertain Systems

Zhang¹,

Zhang²,

Cui³

2013

Asian Journal of Control

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The state estimation problem is investigated for a class of linear uncertain systems with state and noise delay. The optimal one-step prediction algorithm is presented by introducing a fictitious noise. The predictor is designed based on the projection formula in Hilbert space and has the same dimensions as the original systems. The error covariance consists of two coupled Riccati-type difference equations. The optimal filter and fixed-lag smoother are provided based on the predictor. A numerical example is given to show the effectiveness of the proposed approach.

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“…where P(1|0) = 0 and y(k, s) satisfies ). X (16) Proof. Consider the following error difference equation induced by (1) and (13):…”

Section: One-step Prediction Estimationmentioning

confidence: 99%

“…). X Additionally, this can be computed according to (16) by noticing (18) and (19). The proof is completed.…”

Section: One-step Prediction Estimationmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Estimation of A Class of Linear Time‐Delay Uncertain Systems

Zhang¹,

Zhang²,

Cui³

2013

Asian Journal of Control

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“…The multiplicative noises not only corrupts the observation sequence, but also exists in the state equation. Further, the system is converted into an averaged one only with addition noises by introducing the fictitious noise technique [19], [20], which considerably reduces the design complexity. Then the existence condition is established based on the novel systems, and different kinds of estimation problems treated include one-step prediction, filtering and smoothing.…”

Section: Introductionmentioning

confidence: 99%

A new approach to linear estimation for Markov jump linear systems

Han

Wang

Zhang

2012

2012 24th Chinese Control and Decision Conference (CCDC)

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This paper investigates the linear minimum mean square error estimation for the Markov jump linear system (MJLS). To derive the existence condition of such estimator, we first transform the MJLS into a linear system with multiplicative noises; and then the system is converted into an averaged one just with addition noises by using the fictitious noise technique. The existence condition is established based on the novel transformation, and different kinds of estimators including predictor, filter and smoother are proposed via the projection formula. Compared with the augmented approach, the computational cost is reduced. And the estimators have the same dimensions as the original system.

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“…Wood and SzollosiNagy (1978) estimated the covariance matrix of prediction error and predicted runo by the Kalman ®lter recursive algorithm for an actual river basin. Yoshimura and Soeda (1978) proposed an adaptive ®lter algorithm that was capable of adjusting the system model error.…”

Section: Introductionmentioning

confidence: 99%

Application of the Kalman filter to the Nash model

Lee

Singh

1998

Hydrological Processes

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Abstract:The Nash model was used for application of the Kalman ®lter. The state vector of the rainfall±runo system was constituted by the IUH (instantaneous unit hydrograph) estimated by the Nash model and the runo estimated by the Nash model using the Kalman ®lter. The initial values of the state vector were assumed as the average of 10% of the IUH peak values and the initial runo estimated from the average IUH. The Nash model using the Kalman ®lter with a recursive algorithm accurately predicted runo from a basin in Korea. The ®lter allowed the IUH to vary in time, increased the accuracy of the Nash model and reduced physical uncertainty of the rainfall±runo process in the river basin. #

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A Technique for Compensating the Filter Performance by a Fictitious Noise

Cited by 15 publications

References 0 publications

Optimal Estimation of A Class of Linear Time‐Delay Uncertain Systems

Optimal Estimation of A Class of Linear Time‐Delay Uncertain Systems

A new approach to linear estimation for Markov jump linear systems

Application of the Kalman filter to the Nash model

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