Fast rational approximation algorithms of signal and noise subspaces

M. Hasan
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引用次数: 2

Abstract

Fast methods for approximating the dominant and subdominant subspaces have been developed. These methods offer a computational benefit in that subspaces are computed without the costly eigendecomposition or singular value decomposition. More generally we provided a way of splitting an L-dimensional space into several complementary invariant subspaces of the sample covariance matrix, without actually computing any eigenvalues. Frequency estimators such as MUSIC-, minimum-norm-, and ESPRIT-type are then derived using these approximated subspaces. The computation of obtaining these approximate subspaces and estimators are shown to be less than the standard techniques. Through several examples it is demonstrated that these methods have a performance comparable to that of MUSIC yet will require fewer computation to obtain the signal subspace projection.
信号和噪声子空间的快速有理逼近算法
提出了一种快速逼近显性子空间和次显性子空间的方法。这些方法在计算子空间时不需要昂贵的特征分解或奇异值分解。更一般地说,我们提供了一种将l维空间分割成样本协方差矩阵的几个互补不变子空间的方法,而不需要实际计算任何特征值。然后使用这些近似子空间推导出诸如MUSIC-、最小范数-和esprit类型的频率估计器。得到这些近似子空间和估计量的计算比标准方法要少。通过几个实例表明,这些方法具有与MUSIC相当的性能,但需要更少的计算来获得信号子空间投影。
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