Derivation of the bias of the normalized sample covariance matrix in a heterogeneous noise with application to low rank STAP filter

Guillaume Ginolhac 1 Philippe Forster 1 Frédéric Pascal 2 Jean-Philippe Ovarlez 3, 2
1 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie
2 SONDRA - Sondra, CentraleSupélec, Université Paris-Saclay
3 ONERA - The French Aerospace Lab [Palaiseau]
Abstract : In a previous work, we have developed a low-rank (LR) spatio-temporal adaptive processing (STAP) filter when the disturbance is modeled as the sum of a low-rank spherically invariant random vector (SIRV) clutter and a zero-mean white Gaussian noise. This LR-STAP filter is built from the normalized sample covariance matrix (NSCM) and exhibits good robustness properties to secondary data contamination by target components. In this correspondence, we derive the bias of the NSCM with this noise model. We show that the eigenvectors estimated from the NSCM are unbiased. The new expressions of the expectation of NSCM eigenvalues are also given. From these results, we also show that the estimate of the clutter subspace projector based on the NSCM used in our LR-STAP is a consistent estimate of the true one. Results on numerical data validates the theoretical approach.
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Journal articles
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https://hal-supelec.archives-ouvertes.fr/hal-00780733
Contributor : Anne-Hélène Picot <>
Submitted on : Thursday, January 24, 2013 - 4:46:36 PM
Last modification on : Friday, June 21, 2019 - 11:18:21 AM

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Guillaume Ginolhac, Philippe Forster, Frédéric Pascal, Jean-Philippe Ovarlez. Derivation of the bias of the normalized sample covariance matrix in a heterogeneous noise with application to low rank STAP filter. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2012, 60 (1), pp.514-518. ⟨10.1109/TSP.2011.2169063⟩. ⟨hal-00780733⟩

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