Derivation of the Bias of the Normalized Sample Covariance Matrix in a Heterogeneous Noise With Application to Low Rank STAP Filter

• Published in: IEEE transactions on signal processing 2012-01, Vol.60 (1), p.514-518
• Main Authors: Ginolhac, G., Forster, P., Pascal, F., Ovarlez, J.
• Format: Article
• Language: English
• Subjects: Applied sciences; Bias study; Clutter; Computer Science; consistency; Context; Covariance matrix; Detection, estimation, filtering, equalization, prediction; Eigenvalues and eigenfunctions; Engineering Sciences; Exact sciences and technology; Gaussian noise; Information, signal and communications theory; low rank clutter; normalized sample covariance matrix; orthogonal projector; Radar; Signal and communications theory; Signal and Image processing; Signal, noise; SIRV; space time adaptive processing (STAP); Telecommunications and information theory
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2169063

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.