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Efficient Simulation of Stationary Multivariate Gaussian Random Fields with Given cross-covariance

Applied Mathematics 2016年第17期7卷 2183-2194页

作者： Jakob Teichmann Karl-Gerald van den Boogaart Helmholtz-Zentrum Dresden-Rossendorf Helmholtz Institute Freiberg for Resource Technology Freiberg Germany

The present paper introduces a new approach to simulate any stationary multivariate Gaussian random field whose cross-covariances are predefined continuous and integrable functions. Such a field is given by convolution of a vector of univariate random fields and a functional matrix which is derived by Cholesky decomposition of the Fourier transform of the predefined cross-covariance matrix. In contrast to common methods, no restrictive model for the cross-covariance is needed. It is stationary and can also be reduced to the isotropic case. The computational effort is very low since fast Fourier transform can be used for simulation. As will be shown the algorithm is computationally faster than a recently published spectral turning bands model. The applicability is demonstrated using a common numerical example with varied spatial correlation structure. The model was developed to support simulation algorithms for mineral microstructures in geoscience.

关键词： Image Processing Convolution cross-covariance Cholesky Decomposition Fourier Transformation

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Distributed Fusion Filter for Networked Multi-sensor Systems with Multiple Random Transmission Delays and Packet Dropouts

Distributed Fusion Filter for Networked Multi-sensor Systems...

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第36届中国控制会议

作者： Jing Ma Hao Jin School of Mathematics Science Heilongjiang University School of Computer and Information Engineering Harbin University of Commerce

ISBN: (纸本)9781538629185

This paper is concerned with the distributed fusion filtering problem for networked multi-sensor systems with multiple random transmission delays（RTDs） and packet dropouts（PDs）.Based on the new model and local filters（LFs）proposed in a recent literature,the distributed fusion filter weighted by scalars（DFFWS） is given in the linear minimum variance（LMV） *** cross-covariance matrices（CCMs） between any two local filtering errors are derived to compute the fusion weights（FWs）.The measured data of each sensor are transmitted to the local processor（LP） over different communication channels with different RTD and PD *** each moment,the LP may receive one or multiple data packets or *** at individual LPs are transmitted to the fusion center to obtain a fusion filter.A simulation example shows the effectiveness.

关键词： Distributed fusion filter multi-sensor cross-covariance random delay packet dropout

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Optimal Fusion Reduced-Order Kalman Filters Weighted by Scalars for Stochastic Singular Systems

International Journal of Systems and Control

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International Journal of Systems and Control 2007年第1期 11-20页

作者： Sun Shuli, Ma Jing Department of Automation Heilongjiang University Harbin 150080,China Xiao Wendong Media Processing Department Institute for Infocomm Research Singapore 119613

Based on the optimal fusion algorithm weighted by scalars in the linear minimum variance sense, a distributed optimal fusion reduced-order Kalman filter with scalar weights is presented for discrete-time stochastic singular systems with multiple sensors and correlated noises. It has higher accuracy than any local filter does. Compared with the distributed fusion filter weighted by matrices, it has lower accuracy but has reduced computational burden. Computation formula of cross-covariance matrix of the filtering errors between any two sensors is given. An example with three sensors shows the effectiveness.

关键词： Multisensor Optimal information fusion Reduced-order filter cross-covariance Singular system

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Distributed Fusion Filter for Multi-sensor Descriptor Systems with Multiple Packet Dropouts Based on Prediction Compensation

Distributed Fusion Filter for Multi-sensor Descriptor System...

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第37届中国控制会议

作者： Jing Ma Shuli Sun School of Mathematics Science Heilongjiang University Department of Automation Heilongjiang University

This paper is concerned with the distributed fusion filtering problem for descriptor systems with multiple sensors and multiple packet dropouts. When a packet is lost from a sensor to a local processor over an unreliable network, the predictor of the lost packet is used as a compensator. The original high-order descriptor system is transformed into two reduced-order subsystems（ROSs） by a non-singular linear transformation. By using projection theory, local filters（LFs） are presented for two ROSs in the linear unbiased minimum variance（LUMV） sense. The cross-covariance matrices between any two sensor subsystems and between two ROSs are derived to compute fusion weights, respectively. The distributed fusion filters（DFFs） weighted by matrices are presented for two ROSs in the LUMV sense. Then, DFF for the original descriptor system is obtained. A numerical example is used to show the effectiveness of the presented algorithm.

关键词： Distributed fusion filter multi-sensor descriptor system packet dropout compensator cross-covariance

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Distributed Fusion Steady-State Smoothing for Discrete-time Stochastic Singular Systems

Distributed Fusion Steady-State Smoothing for Discrete-time ...

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第二十四届中国控制会议

作者： Sun Shuli (Department of Automation, Heilongjiang University, Harbin 15008)

＜正＞ Using projection theory, cross-covariance matrices of the steady-state smoothing errors are derived for discrete-time stochastic singular linear systems. The distributed optimal fusion steady-state Kalman smoothers are presented based on three weighted fusion algorithms in the linear minimum variance （LMV） sense. which have better precision than any local smoother does. Further, they have the reduced online computational burden since steady-state values of local prediction and smoothing gains, covariance matrices and fusion weights can be computed offline. A simulation example shows their effectiveness.

关键词： multisensor information fusion distributed fusion steady-state smoother cross-covariance descriptor system

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Optimal Fusion Distributed Filters for Linear Stochastic Systems with Unknown Constant Bias

Optimal Fusion Distributed Filters for Linear Stochastic Sys...

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第二十四届中国控制会议

作者： Shuli Sun (Department of Automation, Heilongjiang University, Harbin 150080)

＜正＞ Based on the multi-sensor optimal information fusion algorithm weighted by matrices in the linear minimum variance sense, two steady-state optimal information fusion distributed filters for the state and constant bias are given for discrete-time linear stochastic control systems with unknown constant bias, respectively They avoid the real-time computation of gains, covariance matrices and weights, so they can reduce the online computational burden. Applying them into a tracking system with three sensors shows the effectiveness.

关键词： multisensor information fusion distributed filters cross-covariance

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