White noise deconvolution or input white noise estimation problem has important application background in oil seismic exploration. For the linear discrete time-varying stochastic control systems with multisensor and colored measurement noises, using the Kalman filtering method, under the optimal fusion weighted by matrices, diagonal matrices and scalars, optimal information fusion white noise deconvolution estimators are presented, and for the corresponding timeinvariant systems, the steady-state optimal information fusion white noise deconvolution estimators are also given. The accuracy of the fuser with the matrix weights is higher than that of the fuser with scalar weights, but its computational burden is larger than that of the fuser with scalar weights. The accuracy and computational burden of the fuser with diagonal matrix weights are between both of them. They are locally optimal, and globally suboptimal. The accuracy of the fusers is higher than that of each local white noise estimator. They can handle the white noise fused filtering, smoothing and prediction problems. In order to compute the optimal weights, the new formula of computing the local estimation error cross-covariances is given. A Monte Carlo simulation example for a Bernoulli-Gaussian input white noise shows the effectiveness and performances of the proposed white noise fusers.Keywords-multisensor information fusion; weighted fusion; deconvolution; white noise estimator; reflection seismology; Kalman filtering method
INTRODUCTIONThe input white noise estimation problem for stochastic systems is called deconvolution, which has important application value for finding and discovering the oil field [1-4]. White noise estimators also occur in many fields including communication, signal processing, and state estimation. Mendel [1][2][3] and Mendel and Kormylo [4] present the optimal input white noise estimators with application to oil seismic exploration based on the Kalman filter, but the measurement white noise estimators are not presented. Deng, Zhang, Liu, and Zhou [5] present a unified white noise estimation theory based on the modern time series analysis method, which not only includes the input noise estimators but also includes the measurement white noise estimators. But its limitation is that it can only solve the steady-state white noise estimators, but cannot solve the optimal white noise estimation problem for time-varying system. The general and unified white noise estimation theory based on Kalman filtering for the timeThis work is supported by National Natural Science Foundation of China under varying systems has been presented [6, 7].Recently, Sun [8] gives the optimal information fusion white noise filter weighted by scalars based on Kalman predictor, but it doesn't solve the information fusion white noise smoothing problems. In fact, Sun's white noise fused filter is not suitable for applications. For example, for the multisensor system with uncorrelated noises, Sun's white noise fused filter becomes zero, whose accuracy is low...