Invariance with Respect to the Choice of Generalized Inverse

2011 ◽  
pp. 283-290
Author(s):  
Simo Puntanen ◽  
George P. H. Styan ◽  
Jarkko Isotalo
Keyword(s):  
Generalized Inverse

Erratum: Generalized Inverse of a Matrix Product

SIAM Review ◽  
1967 ◽  
Vol 9 (2) ◽  
pp. 249-249 ◽  
Author(s):  
T. N. E. Greville
Keyword(s):  
Generalized Inverse ◽  
Matrix Product

scholarly journals Acoustic source localization using the open spherical microphone array in the low-frequency range

2019 ◽  
Vol 283 ◽  
pp. 04001
Author(s):  
Boquan Yang ◽  
Shengguo Shi ◽  
Desen Yang
Keyword(s):  
Source Localization ◽  
Generalized Inverse ◽  
Microphone Array ◽  
Low Frequency ◽  
Poor Performance ◽  
Microphone Arrays ◽  
Three Dimension ◽  
Frequency Range ◽  
Array Aperture ◽  
Regularization Matrix

Recently, spherical microphone arrays (SMA) have become increasingly significant for source localization and identification in three dimension due to its spherical symmetry. However, conventional Spherical Harmonic Beamforming (SHB) based on SMA has limitations, such as poor resolution and high side-lobe levels in image maps. To overcome these limitations, this paper employs the iterative generalized inverse beamforming algorithm with a virtual extrapolated open spherical microphone array. The sidelobes can be suppressed and the main-lobe can be narrowed by introducing the two iteration processes into the generalized inverse beamforming (GIB) algorithm. The instability caused by uncertainties in actual measurements, such as measurement noise and configuration problems in the process of GIB, can be minimized by iteratively redefining the form of regularization matrix and the corresponding GIB localization results. In addition, the poor performance of microphone arrays in the low-frequency range due to the array aperture can be improved by using a virtual extrapolated open spherical array (EA), which has a larger array aperture. The virtual array is obtained by a kind of data preprocessing method through the regularization matrix algorithm. Both results from simulations and experiments show the feasibility and accuracy of the method.

Application of the generalized inverse in structural system identification

AIAA Journal ◽  
1984 ◽  
Vol 22 (12) ◽  
pp. 1827-1828 ◽  
Author(s):  
Shyi-Yaung Chen ◽  
Jon-Shen Fuh
Keyword(s):  
System Identification ◽  
Generalized Inverse ◽  
Structural System ◽  
Structural System Identification
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