研究状态空间模型描述的带乘性噪声广义系统,在加性噪声同时刻相关情形下的最优状态滤波算法以及观测噪声最优估计问题.在假设系统正则的情况下,针对乘性噪声为一般随机矩阵即各观测通道乘性噪声同时刻相关的情况,通过受限等价变换的方法,给出了线性最小方差意义下的系统状态滤波算法和观测噪声最优滤波算法.数字仿真结果表明了算法的有效性.%Ihis paper provides faltering algorithms ot state and measurement noise m singular systems with multiplicative noise. Algorithms in paper are derived under state-space model structures, while additive noises in functions are simultaneously correlated. Multiplicative noise in systems is mathematically described in the form of random matrix, which means multiplicative noise in each channel can also be simultaneously correlated. Assuming the singular systems are regular, restricted equivalent transformation into nonsingular systems can be applied in order to proceed. In the sense of linear minimum-variance, the filtering algorithms of measurement noise are optimal, while the state estimation is conditionally optimal. Simulations are illustrated to show the validity of the algorithms.
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