Reduced-order steady-state descriptor Kalman fuser weighted by block-diagonal matrices

For the linear discrete stochastic descriptor systems with multisensor, using the singular value decomposition, it is transformed into two reduced-order non-descriptor subsystems. A new optimal fusion criterion weighted by the block-diagonal matrices is presented, and the corresponding steady-state descriptor Kalman fuser with a three-layer fusion structure is also presented by using the white noise estimation theory. It realizes decoupled fused estimation for two subsystems. In the linear minimum variance sense, the block-diagonal matrices are determined by three different rules such that the diagonal block matrices are matrices, diagonal matrices, or scalars, so that three optimal fused descriptor Kalman estimators weighted by the block-diagonal matrices are obtained. Their accuracy relations are proved. They can handle the fused filtering, smoothing, and prediction problems in a unified framework, and can improve the accuracy of local estimation. They are locally optimal, and are globally suboptimal. In order to compute the optimal weights, the formulas of computing the cross-covariance matrices among local estimation errors are presented. A Monte Carlo simulation example shows their effectiveness.