Generalized Millman's formula and its application for estimation problems

Shin, Vladimir; Lee, Young-Hee; Choi, Tae‐Sun

doi:10.1016/j.sigpro.2005.05.015

Cited by 75 publications

(77 citation statements)

References 3 publications

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“…The DF method, however, assimilates each data set resulting from a single experiment separately using a "local" EnKF to obtain a local estimate of parameters. The multiple local estimates are then "fused" using the generalized Millman formula (GMF) algorithm (Bar-Shalom and Campo, 1986;Shin et al, 2006), which constitutes an unbiased linear estimator of multiple correlated or uncorrelated estimates. The two inversion schemes are implemented to assimilate the responses resulting from five pumping tests.…”

Section: A H Alzraiee Et Al: Hydraulic Tomography Data Fusionmentioning

confidence: 99%

“…14) constitutes in essence a weighted average of the "local" estimates of the Y and Z fields, with weights (Eq. 21) that are inversely related to the corresponding "local" covariances (Shin et al, 2006), it produces fused estimates with a coefficient r that cannot be larger than those associated with the best "local" estimate and, consequently, those obtained with the "global" CF estimate. However, the DF scheme has an operational advantage over the CF scheme, in that the "raw" transient data are not required to apply fusion.…”

Section: Decentralized Fusion Of Ht Datamentioning

confidence: 99%

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Estimation of heterogeneous aquifer parameters using centralized and decentralized fusion of hydraulic tomography data

Alzraiee

Baù

Elhaddad

2014

Hydrol. Earth Syst. Sci.

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Abstract. Characterization of spatial variability of hydraulic properties of groundwater systems at high resolution is essential to simulate flow and transport phenomena. This paper investigates two schemes to invert transient hydraulic head data resulting from multiple pumping tests for the purpose of estimating the spatial distributions of the hydraulic conductivity, K, and the specific storage, S s , of an aquifer. The two methods are centralized fusion and decentralized fusion. The centralized fusion of transient data is achieved when data from all pumping tests are processed concurrently using a central inversion processor, whereas the decentralized fusion inverts data from each pumping test separately to obtain optimal local estimates of hydraulic parameters, which are consequently fused using the generalized Millman formula, an algorithm for merging multiple correlated or uncorrelated local estimates. For both data fusion schemes, the basic inversion processor employed is the ensemble Kalman filter, which is employed to assimilate the temporal moments of impulse response functions obtained from the transient hydraulic head measurements resulting from multiple pumping tests. Assimilating the temporal moments instead of the hydraulic head transient data themselves is shown to provide a significant improvement in computational efficiency. Additionally, different assimilation strategies to improve the estimation of S s are investigated. Results show that estimation of the K and S s distributions using temporal moment analysis is fairly good, and the centralized inversion scheme consistently outperforms the decentralized inversion scheme.

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Section: A H Alzraiee Et Al: Hydraulic Tomography Data Fusionmentioning

confidence: 99%

Section: Decentralized Fusion Of Ht Datamentioning

confidence: 99%

Estimation of heterogeneous aquifer parameters using centralized and decentralized fusion of hydraulic tomography data

Alzraiee

Baù

Elhaddad

2014

Hydrol. Earth Syst. Sci.

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“…(b) The covariance in (14) represents the nondiagonal element of the block covariance matrix , which is expressed as follows: (15) at , which is described by the Lyapunov recursive equation.…”

Section: Decentralized Moving Average Filtermentioning

confidence: 99%

Decentralized Moving Average Filtering with Uncertainties

Song¹

2016

Journal of Sensor Science and Technology

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A filtering algorithm based on the decentralized moving average Kalman filter with uncertainties is proposed in this paper. The proposed filtering algorithm presented combines the Kalman filter with the moving average strategy. A decentralized fusion algorithm with the weighted sum structure is applied to the local moving average Kalman filters (LMAKFs) of different window lengths. The proposed algorithm has a parallel structure and allows parallel processing of observations. Hence, it is more reliable than the centralized algorithm when some sensors become faulty. Moreover, the choice of the moving average strategy makes the proposed algorithm robust against linear discrete-time dynamic model uncertainties. The derivation of the error cross-covariances between the LMAKFs is the key idea of studied. The application of the proposed decentralized fusion filter to dynamic systems within a multisensor environment demonstrates its high accuracy and computational efficiency.

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“…An important practical problem in the above systems and architectures is to find a fusion estimate to combine the information from various local estimates to produce a global (fusion) estimate. Optimal mean square linear fusion formulas, for an arbitrary number of local estimates with matrix and scalar weights, have been reported in [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, in spite of its limitations, the decentralized estimation has been widely used and is superior to the centralized estimation in real applications. The aforementioned papers [5][6][7][8][9][10][11][12][13] have not focused on the prediction problem, but most of them have considered only decentralized filtering of state variables in multisensory dynamic models. The decentralized prediction of the state requires special algorithms presented in [14,15].…”

Section: Introductionmentioning

confidence: 99%

Multisensory Prediction Fusion of Nonlinear Functions of the State Vector in Discrete-Time Systems

Song

Shin

2015

International Journal of Distributed Sensor Networks

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We propose two new multisensory fusion predictors for an arbitrary nonlinear function of the state vector in a discrete-time linear dynamic system. Nonlinear function of the state (NFS) represents a nonlinear multivariate functional of state variables, which can indicate useful information of the target system for automatic control. To estimate the NFS using multisensory information, we propose centralized and decentralized predictors. For multivariate polynomial NFS, we propose an effective closed-form computation procedure for the predictor design. For general NFS, the most popular procedure for the predictor design is based on the unscented transformation. We demonstrate the effectiveness and estimation accuracy of the fusion predictors on theoretical and numerical examples in multisensory environment.

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Generalized Millman's formula and its application for estimation problems

Cited by 75 publications

References 3 publications

Estimation of heterogeneous aquifer parameters using centralized and decentralized fusion of hydraulic tomography data

Estimation of heterogeneous aquifer parameters using centralized and decentralized fusion of hydraulic tomography data

Decentralized Moving Average Filtering with Uncertainties

Multisensory Prediction Fusion of Nonlinear Functions of the State Vector in Discrete-Time Systems

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