一种广义离散随机线性系统的状态估计

针对目前关于广义系统状态估计的研究现状，即几乎所有的讨论都集中在奇异矩阵为方阵的情况，讨论了广义矩阵及其性质，利用矩阵的奇异值分解理论，给出了奇异矩阵为条形或带形广义离散线性系统的奇异值标准形式，基于标准形式，利用广义逆矩阵的性质，在两种情况下，将系统分解成两个子系统，通过估计子系统的状态，得到了该系统状态的最优预测和滤波递推方程。结果表明，对于广义系统，该方法有效地减少了计算量。

A state estimation of singular discrete stochastic linear systems

In view of the present situation of study on the state estimation for singular systems that almost all discussions are concentrated on the case of square generalized matrix, authors discuss the generalized inverse matrices and their properties and give the singular value standard form for singular discrete stochastic linear systems with band generalized matrix by the singular value decomposition of the matrix. In the two cases, the singular system is decomposed into two subsystems based on the standard form and using the properties of the generalized inverse matrix. The optimal recursive estimation for predicting and filtering the state for this singular system is obtained by state estimation of subsystems. The result shows that this technique efficiently reduces the amount of computation for the singular system.