广义逆的递推算法及其应用(英文)

Recursive Computation of GeneralizedInverses with Applications

在简化{1}-,{1,2}-和{1,2,3,4}-逆并给出{1,3}-,{1,2,3}-,{1,4}-和{1,2,4}-逆的基础上,得到了递推滤波、固定点平滑、固定滞后平滑和预报算法,并由此得到离散线性随机和定常系统状态的最佳线性最小无偏估计.证明了给出最佳线性无偏估计的充要条件而无需初始状态的先验统计知识.对于定常系统,给出了滤波、固定点平滑、固定滞后平滑和预报形式的无差状态观测器而无需系统是时不变和完全可观测性的.

: Recursive algorithms for computing the {1} -, {1,2} -, and {1,2,3,4} -inverses are simplified) and those for computing the {1,3}-, {1,2,3}-, {1,4}-,and {1,2,4}-inverses are pre-sented. Based on these results,recursive filtering,fixed-point smoothing,fixed-lag smoothing andprediction algorithms are obtained, which give the best linear minimum bias estimates (BLIMBEs)of states of discrete linear stochastic and deterministic systems. Necessary and sufficient conditions for these state estimation algorithms to give the best linear unbiased estimates (BLUEs) are estab-lished- It is proved that the proposed algorithms give BLUEs of states without such requirement of a priori knowledge about the initial state as in the well known Kalman filter theory. In the deter-ministic system case,deadbeat state observers in the form of filtering, fixed-point smoothing, fixed-lag smoothing and prediction give the deadbeat state estimates without such requirements of time-in variance and complete observability as in the well known Luenberger's observer theory.