A Joint Robust Estimation and Random Matrix Framework with Application to Array Processing

Abstract : An original interface between robust estimation theory and random matrix theory for the estimation of population covariance matrices is proposed. Consider a random vector x = ANy ∈ CN with y ∈ CM made of M ≥ N independent entries, E[y] = 0, and E[yy*] = IN. It is shown that a class of robust estimators ĈN of CN = ANA*N, obtained from n independent copies of x, is (N, n)-consistent with the traditional sample covariance matrix r̂N in the sense that ∥ĈN - αr̂N∥ → 0 in spectral norm for some α > 0, almost surely, as N, n → ∞ with N/n and M/N bounded. This result, in general not valid in the fixed N regime, is used to propose improved subspace estimation techniques, among which an enhanced direction-of-arrival estimator called robust G-MUSIC.
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https://hal-supelec.archives-ouvertes.fr/hal-00830302
Contributor : Catherine Magnet <>
Submitted on : Tuesday, June 4, 2013 - 4:34:11 PM
Last modification on : Wednesday, August 21, 2019 - 10:38:02 AM

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Romain Couillet, Frédéric Pascal, Jack W. Silverstein. A Joint Robust Estimation and Random Matrix Framework with Application to Array Processing. 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2013), May 2013, Vancouver, Canada. 5 p., ⟨10.1109/ICASSP.2013.6638930⟩. ⟨hal-00830302⟩

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