带状随机线性系统状态的估计问题

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 ,讨论了广义逆矩阵和矩阵的奇异值分解问题。首次提出了带状随机系统的状态估计问题 ,利用矩阵的奇异分解理论给出了带状广义连续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。

State Estimation for Band Stochastic Linear Systems

According to the present situation of study on the state estimation for generalized systems, that is, nearly all discussions are concentrated on the case of square singular matrix, some problems about generalized inverse matrix and singular value decomposition of matrix are discussed. The state estimation for a band stochastic linear system is proposed at the first time, and the standard form of the singular values for band stochastic linear systems is given by the theory of singular value decomposition of matrix. In the two cases, the singular system is decomposed into two subsystems based on the standard form and using the property of the generalized inverse matrix. The optimal recursive equation for predicting and filtering the state of this generalized system is obtained by state estimation of subsystems.