A Generalization of the Fixed Point Estimate for Packet-Scaled Complex Covariance Matrix Estimation

Abigael Taylor (1, 2) , Philippe Forster (3) , Franck Daout (3) , Helene M. Oriot (1) , Laurent Savy (1)

1 ONERA - The French Aerospace Lab [Palaiseau]
2 Télécom ParisTech
3 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

In this paper, the problem of estimating complex-valued proportional covariance matrices is addressed. The obtained estimate generalizes the fixed point estimate to scaled packets of data, and is hence called the generalized fixed point estimate (GFPE). The statistical properties (bias, consistency, and asymptotical distributions) of the estimate are presented, and verified through simulations. As an example of application, a radar detection problem is considered. The GFPE is used in the well-known adaptive normalized matched filter (ANMF), and the obtained empirical probability of false alarms threshold curve is compared to the theoretical one. The ANMF is also used to compare the GFPE to the fixed point estimate.

Mots clés: COVARIANCE MATRICES; ESTIMATION; PROPORTIONALITY; FIXED POINT ESTIMATE

Domaines: Electromagnétisme

Abigael Taylor, Philippe Forster, Franck Daout, Helene M. Oriot, Laurent Savy. A Generalization of the Fixed Point Estimate for Packet-Scaled Complex Covariance Matrix Estimation. IEEE Transactions on Signal Processing, 2017, 65 (20), p. 5393 - 5405. ⟨10.1109/TSP.2017.2731324⟩. ⟨hal-01632717⟩