Plug-In Measure-Transformed Quasi-Likelihood Ratio Test for Random Signal Detection

Recently, we developed a robust generalization of the Gaussian quasi-likelihood ratio test (GQLRT). This generalization, called measure-transformed GQLRT (MT-GQLRT), operates by selecting a Gaussian model that best empirically fits a transformed probability measure of the data. In this letter, a plug-in version of the MT-GQLRT is developed for robust detection of a random signal in nonspherical noise. The proposed detector is derived by plugging an empirical measure-transformed noise covariance, obtained from noise-only secondary data, into the MT-GQLRT. The plug-in MT-GQLRT is illustrated in simulation examples that show its advantages as compared to other detectors.

[1]  A. Farina,et al.  Matched subspace CFAR detection of hovering helicopters , 1999 .

[2]  John Law,et al.  Robust Statistics—The Approach Based on Influence Functions , 1986 .

[3]  Philippe Forster,et al.  Covariance Structure Maximum-Likelihood Estimates in Compound Gaussian Noise: Existence and Algorithm Analysis , 2008, IEEE Transactions on Signal Processing.

[4]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[5]  J. Bai,et al.  Likelihood ratio tests for multiple structural changes , 1999 .

[6]  Alfred O. Hero,et al.  Measure-transformed quasi maximum likelihood estimation with application to source localization , 2015, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[7]  柿沢 佳秀,et al.  Asymptotic theory of statistical inference for time series , 2000 .

[8]  Antonio De Maio,et al.  Modern Radar Detection Theory , 2015 .

[9]  Alfred O. Hero,et al.  Binary Hypothesis Testing via Measure Transformed Quasi-Likelihood Ratio Test , 2016, IEEE Transactions on Signal Processing.

[10]  Inderjit S. Dhillon,et al.  Matrix Nearness Problems with Bregman Divergences , 2007, SIAM J. Matrix Anal. Appl..

[11]  Danilo Orlando,et al.  Adaptive Radar Detection of a Subspace Signal Embedded in Subspace Structured Plus Gaussian Interference Via Invariance , 2016, IEEE Transactions on Signal Processing.

[12]  L. Scharf,et al.  Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals , 2010 .

[13]  Augusto Aubry,et al.  Coincidence of Maximal Invariants for Two Adaptive Radar Detection Problems , 2016, IEEE Signal Processing Letters.

[14]  Jianyu Yang,et al.  Performance analysis of GLRT-based adaptive detector for distributed targets in compound-Gaussian clutter , 2010, Signal Process..

[15]  A. Farina.  Optimised radar processors , 1987 .

[16]  Ben-Gurion.  ROBUST MEASURE TRANSFORMED MUSIC FOR DOA ESTIMATION , 2014 .

[17]  Alfred O. Hero,et al.  Measure-Transformed Quasi-Maximum Likelihood Estimation , 2015, IEEE Transactions on Signal Processing.

[18]  Benjamin Friedlander,et al.  A CFAR Adaptive Subspace Detector for , 2005 .

[19]  Alfred O. Hero,et al.  Measure-transformed quasi likelihood ratio test , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[20]  H. Vincent Poor,et al.  Complex Elliptically Symmetric Distributions: Survey, New Results and Applications , 2012, IEEE Transactions on Signal Processing.

[21]  Ivan A. Canay.  EL inference for partially identified models: Large deviations optimality and bootstrap validity , 2010 .

[22]  Alfred O. Hero,et al.  Robust Multiple Signal Classification via Probability Measure Transformation , 2015, IEEE Transactions on Signal Processing.

[23]  Masanobu Taniguchi,et al.  Discriminant analysis for locally stationary processes , 2004 .

[24]  Alfred O. Hero,et al.  Measure transformed canonical correlation analysis with application to financial data , 2012, 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[25]  Marie-Claude Beaulieu,et al.  Author's Personal Copy Computational Statistics and Data Analysis Finite Sample Multivariate Tests of Asset Pricing Models with Coskewness , 2022 .

[26]  Augusto Aubry,et al.  Radar Detection of Distributed Targets in Homogeneous Interference Whose Inverse Covariance Structure is Defined via Unitary Invariant Functions , 2013, IEEE Transactions on Signal Processing.

[27]  F. Hampel.  The Influence Curve and Its Role in Robust Estimation , 1974 .

[28]  Don H. Johnson,et al.  Statistical Signal Processing , 2009, Encyclopedia of Biometrics.

[29]  Alfred O. Hero,et al.  On Measure Transformed Canonical Correlation Analysis , 2011, IEEE Transactions on Signal Processing.

[30]  Giuseppe Ricci,et al.  Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection , 2002, IEEE Trans. Signal Process..

[31]  Augusto Aubry,et al.  Adaptive Detection of Point-Like Targets in the Presence of Homogeneous Clutter and Subspace Interference , 2014, IEEE Signal Processing Letters.

[32]  K. Gerlach.  Spatially distributed target detection in non-Gaussian clutter , 1999 .

[33]  D. McLaughlin,et al.  Performance of the GLRT for adaptive vector subspace detection , 1996 .

[34]  A. Maio,et al.  Distributed target detection in compound-Gaussian noise with Rao and Wald tests , 2003 .