Generalized System Reduction Information Fusion State Valuation

For the linear discrete time-invariant stochastic descriptor system with multisensor, based on the singular value decomposition, by the linear transformation, the descriptor system can be transformed into two canonical forms, where each canonical form consists of two reduced-order non-descriptor subsystems. Three different weighted fusion approaches are presented for the original state, transformed state, and subsystems' state, respectively. Each weighted fusion approach is realized via three rules weighted by matrices, diagonal matrices, and scalars, respectively. Using the classical Kalman filtering method and white noise estimation theory, by the three different weighted fusion approaches, the reduced-order information fusion time-varying and steady-state descriptor Kalman estimators are presented for the descriptor system under the two canonical forms, respectively. They can handle the fused filtering, smoothing and prediction problems in a unified framework.The formulas of computing the variance and cross-covariance matrices among local estimation errors are presented, which are applied to compute the optimal weights. It is proved that for each weighted fusion approach, the accuracy of the fuser with matrix weights is higher than that of the fuser with scalar weights, and the accuracy of the fuser with diagonal matrix weights is between both of them, and the accuracy of each fuser is higher than that of local estimators. Many Monte Carlo simulation examples show their effectiveness, and show that the accuracy distinction for fused estimators with different kinds of weights is not obvious, so that the fusers...