Optimality Claims for the FML Covariance Estimator with respect to Two Matrix Norms

被引:45
作者
Aubry, A. [1 ]
De Maio, A. [2 ]
Carotenuto, V. [2 ]
机构
[1] CNR IREA, I-80124 Naples, Italy
[2] Univ Naples Federico II, Dipartimento Ingn Biomed Elettron & Telecomunicaz, I-80125 Naples, Italy
关键词
D O I
10.1109/TAES.2013.6558039
中图分类号
V [航空、航天];
学科分类号
08 ; 0825 ;
摘要
In this correspondence we prove two interesting properties of the fast maximum likelihood (FML) covariance matrix estimator proposed in [1] under the assumption of zero-mean complex circular Gaussian training data sharing the same covariance matrix. The new properties represent optimality claims regardless of the statistical characterization of the data and, in particular, of the multivariate Gaussian assumption for the observables. The optimality is proved with respect to two cost functions involving either the Frobenius or the spectral norm of an Hermitian matrix.
引用
收藏
页码:2055 / 2057
页数:3
相关论文
共 9 条
[1]  
Ben-Tal A, 2012, LECT MODERN CONVEX O
[2]  
Boyd S., 2004, CONVEX OPTIMIZATION, VFirst, DOI DOI 10.1017/CBO9780511804441
[3]   Screening among multivariate normal data [J].
Chen, PY ;
Melvin, WL ;
Wicks, MC .
JOURNAL OF MULTIVARIATE ANALYSIS, 1999, 69 (01) :10-29
[4]  
De Maio A., 2005, IEEE T AERO ELEC SYS, V41, P172
[5]   On the Invariance, Coincidence, and Statistical Equivalence of the GLRT, Rao Test, and Wald Test [J].
De Maio, Antonio ;
Kay, Steven M. ;
Farina, Alfonso .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2010, 58 (04) :1967-1979
[6]  
Farina A., 1992, ANTENNA BASED SIGNAL
[7]  
Horn R.A., 2012, Matrix Analysis
[8]   AN ADAPTIVE DETECTION ALGORITHM [J].
KELLY, EJ .
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, 1986, 22 (02) :115-127
[9]   Fast converging adaptive processor or a structured covariance matrix [J].
Steiner, M ;
Gerlach, K .
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, 2000, 36 (04) :1115-1126