Adjusting the generalized likelihood ratio test of circularity robust to non-normality

Ollila, Esa; Koivunen, Visa

doi:10.1109/spawc.2009.5161847

Cited by 25 publications

(18 citation statements)

References 14 publications

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“…With the previous notations, the sphericity test makes use of the GLRT adjusted for CES (Complex Elliptically Symmetric) distributions [7], [8], known as aGLRT.…”

Section: Spherically Invariant Random Processesmentioning

confidence: 99%

Circularity of complex stochastic models in PolSAR and multi-pass InSAR images

Vasile

Totir

2012

2012 IEEE International Geoscience and Remote Sensing Symposium

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Polarimetry and multi-pass interferometry extend the dimensionality of SAR data, so the necessity to have multivariate statistic (and non-Gaussian, because of the high resolution) distributions as models for these types of data: such are the SIRV (Spherically Invariant Random Vectors). However, as the statistic model becomes so complicated, correctly estimating its parameters gets difficult. More, although they are versatile, the SIRV models are not guaranteed to match the PolSAR / InSAR data. To evaluate the pertinence of those models with respect to the PolSAR data, through one of their most important statistic property, namely the circularity, it is the purpose of this paper.

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“…With the previous notations, the sphericity test makes use of the GLRT adjusted for CES (Complex Elliptically Symmetric) distributions [7], [8], known as aGLRT.…”

Section: Spherically Invariant Random Processesmentioning

confidence: 99%

Circularity of complex stochastic models in PolSAR and multi-pass InSAR images

Vasile

Totir

2012

2012 IEEE International Geoscience and Remote Sensing Symposium

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“…The moments (19), which fully determine the null distribution of T , and hence of M , do not depend on the true covariance matrix ⌃ r . Hence we can assume ⌃ r = I 4p when simulating M .…”

Section: G Direct Simulationmentioning

confidence: 99%

“…As with the LRT for complex propriety [19], our LRT for quaternion propriety will be sensitive to departures from Gaussianity which could be an issue when applying the test to physical data.…”

Section: Asymptotic Robustness To Nongaussianitymentioning

confidence: 99%

Testing for Quaternion Propriety

Ginzberg

Walden

2011

IEEE Trans. Signal Process.

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We consider the problem of testing whether a quaternion-valued Gaussian random vector is proper.The quaternion covariance matrix fully describes the second order properties of a quaternion random vector only if the distribution is proper. The exact distribution of the likelihood ratio test under the hypothesis of propriety is derived for general sample size, N, and vector dimensionality, p. As this is in terms of Meijer's G-function, various approximations are considered, including Box-type and saddlepoint approximations. We find in particular that a new approach matching the first three cumulants is easy to implement and extremely accurate.

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“…A general test of circularity, for the class of elliptically symmetric distributions, is presented in [13] assuming a known covariance matrix. A complex GLRT for this distribution is presented in [14] which adjusts the test statistic by an estimate of the fourth moment to handle the non-Gaussian case. This adjustment, however, may be sensitive to outliers and requires many samples to estimate.…”

Section: Introductionmentioning

confidence: 99%

“…The CGGD adapts to a large family of symmetric distributions, from super-Gaussian to sub-Gaussian including specific densities such as bivariate Laplacian and Gaussian distributions. Since the CGGD is also a member of the elliptically symmetric distributions, the normalized kurtosis values of the real and imaginary parts of a complex random variable are a scaled version of the complex kurtosis where the scale factor is nonnegative and is a function of noncircularity as shown in [14]. Since the kurtosis of the complex Gaussian is zero, as in the realvalued case, positive normalized kurtosis values imply a superGaussian distribution, i.e., a sharper peak with heavier tails, and negative normalized kurtosis values imply sub-Gaussian distributions.…”

Section: Introductionmentioning

confidence: 99%

Circularity and Gaussianity Detection Using the Complex Generalized Gaussian Distribution

Novey

Adalı

Roy

2009

IEEE Signal Process. Lett.

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Knowing the statistical properties of a complex-valued signal is important in many signal processing applications by providing the necessary information for choosing the appropriate algorithm. In this paper, we provide generalized likelihood ratio tests (GLRT), based on the complex generalized Gaussian distribution (CGGD), for detecting two important signal properties: 1) the circularity of a complex random variable, not constrained to the Gaussian case and 2) whether a complex random variable is complex Gaussian. These tests can be combined to statistically determine if a complex random variable is, the often assumed, circular Gaussian. Simulations are used to quantify the performance of the detectors followed by application to communication signals and actual radar data.

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Adjusting the generalized likelihood ratio test of circularity robust to non-normality

Cited by 25 publications

References 14 publications

Circularity of complex stochastic models in PolSAR and multi-pass InSAR images

Circularity of complex stochastic models in PolSAR and multi-pass InSAR images

Testing for Quaternion Propriety

Circularity and Gaussianity Detection Using the Complex Generalized Gaussian Distribution

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