Optimal Filtering for Discrete-Time Linear Systems With Multiplicative White Noise Perturbations and Periodic Coefficients
Optimal Filtering for Discrete-Time Linear Systems With Multiplicative White Noise Perturbations and Periodic Coefficients
复制标题
DOI：
10.1109/tac.2012.2215534
复制
发表时间：
2013-04
影响因子：
6.8
通讯作者：
V. Drăgan
中科院分区：
文献类型：
--
作者：
V. Drăgan
在这个技术简介中，研究了由具有周期系数的离散时间动力系统产生的远程信号的估计问题，该离散时间动力系统受到乘性和加性白色噪声扰动。为了测量由可容许滤波器实现的估计的质量，我们引入了由估计信号zF（t）和远程信号z（t）之间的偏差的均方的塞萨罗极限描述的性能标准。可容许滤波器的状态空间的维数是没有前缀的。最优滤波器的状态空间表示是基于离散时间线性方程的唯一周期解以及适当的具有周期系数的离散时间Riccati方程的稳定解来构造的。
In this technical brief, the problem of the estimation of a remote signal generated by a discrete-time dynamical system with periodic coefficients subject to multiplicative and additive white noise perturbations is investigated. To measure the quality of the estimation achieved by an admissible filter, we introduced a performance criterion described by the Cesaro limit of the mean square of the deviation between the estimated signal zF(t) and the remote signal z(t). The dimension of the state space of the admissible filters is not prefixed. The state-space representation of the optimal filter is constructed based on the unique periodic solution of a discrete-time linear equation together with the stabilizing solution of a suitable discrete-time Riccati equation with periodic coefficients.