On the error matrix in optimal linear filtering of stationary processes
On the error matrix in optimal linear filtering of stationary processes
复制标题
平稳过程最优线性滤波的误差矩阵
DOI：
10.1109/tit.1973.1055075
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发表时间：
1973
期刊：
影响因子：
--
通讯作者：
J. Snyders
中科院分区：
文献类型：
--
作者：
J. Snyders
研究了加性噪声下二阶平稳过程最优线性因果滤波的误差协方差矩阵。建立了用最优传递函数表示误差矩阵的公式，在非奇异情况下，最优传递函数用谱密度表示。这些是先前发表的标量结果的直接推广，推导同样基于Hardy空间理论。得到了最小误差（即最优误差协方差矩阵的轨迹）的显式界限，以便在白噪声中滤波。此外，导出了在多个白噪声信道上传输相同信号时误差协方差矩阵的显式表达式。
The error covariance matrix corresponding to optimal linear causal filtering of second-order stationary processes in additive noise is considered. Formulas expressing this error matrix in terms of the optimal transfer function are established, and in the nonsingular case the optimal transfer function is expressed in terms of the spectral densities. These are straightforward generalizations of previously published scalar results, and the derivation is similarly based on Hardy space theory. Explicit bounds on the minimal error (i.e., the trace of the optimal error covariance matrix) are obtained for filtering in white noise. Furthermore, an explicit expression for the error covariance matrix is derived for the case of transmitting the same signal over several white-noise channels.