Cramer-Rao bounds on eigenvalue estimates from impulse response data: The multi-observation case
Cramer-Rao bounds on eigenvalue estimates from impulse response data: The multi-observation case
复制标题
脉冲响应数据的特征值估计的 Cramer-Rao 界限：多观察情况
DOI：
10.1109/cdc.2012.6426627
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Sandip Roy
中科院分区：
文献类型：
--
作者：
Jackeline Abad Torres;Sandip Roy
我们研究的效果，有多个观测的非随机模式的线性动力系统的噪声脉冲响应数据的估计。具体来说，对于这个估计问题，我们开发了一个明确的代数表征的Fisher信息矩阵，因此Cramer-Rao界的特征值和残留的传递函数，并制定一些简单的界限上的最小可能的误差方差特征值估计的特征值的位置。我们特别注重发展的Cramer-Rao约束极点估计的多观测的情况下，和那些单独使用时，每个单独的观察估计之间的关系。
We examine the effect of having multiple observations in the estimation of non-random modes of linear dynamical systems from noisy impulse response data. Specifically, for this estimation problem, we develop an explicit algebraic characterization of the Fisher information matrix and hence Cramer-Rao bound in terms of the eigenvalues and residues of the transfer function, and so develop some simple bounds on the minimum possible error variance for eigenvalue estimates in terms of the eigenvalues' locations. We focus especially on developing a relationship between the Cramer-Rao bound on pole estimates for the multi-observation case, and those when each single observation is used separately for estimation.