Some properties of ordered eigenvalues of a Wishart matrix: application in detection test and model order selection

Abstract

Avenue d'Estree BP 792 -97337 CAYENNE Cedex Guyanne Fraqaise ABS TRACTHigh resolution methods for estimation of parameters in signal processing (bearing angles in array processing or frequencies in spectral analysis for example) can suffer from a bad selection of the model order. This paper proposes an algorithm basedl on the properties of the eigenvalues of the covariance matrix. In the noise only case, this matrix is a Wishart matrix. For white noise the profile of ordered eigenvalues fits an exponential law. The proposed algorithm uses this property and looks for a mismatch between the observed profile and the model in order to detect the presence of a signal. Under estimation may result from the occurence of small signal eigenvalues. Performances is greatly improved by the use of deflation for recursive detection-estimation test. Results of simulations are provided in order to show the capabilities of the algorithm.

Multi-dimensional model order selection

“…For M ≤ N (15) is equal to the q of the EFT [12,13], which means that the PoD of the EFT and the PoD of the M-EFT are the same for M <N. Consequently, the M-EFT automatically inherits from the EFT the property that it outperforms the other matrix-based MOS techniques in the literature for M ≤ N in the presence of white Gaussian noise as shown in [2].…”

“…According to Grouffaud et al [12] and Quinlan et al [13], the noise eigenvalues that exhibit a Wishart profile can have their profile approximated by an exponential curve. Therefore, by applying the exponential approximation for every r-mode, we obtain that…”

Detecting the Number of Clusters in n-Way Probabilistic Clustering

“…Equation (33) [34], exponential fitting test (EFT) [35], [36], modified EFT (M-EFT) [27], etc. In most of such situations, these methods work well.…”

Sensor and Actuator/Surface Failure Detection Based on the Spectral Norm of an Innovation Matrix

“…In (Wu et al, 1995) an algorithm based on the geometrical location of these eigenvalues has been proposed. In (Grouffaud et al, 1996) a new kind of test based on an analytic expression of the ordered eigenvalues profile, obtained under noise only hypothesis. Strategy in this work consists in looking for a break in profile by comparing observed profile and noise only one.…”