Theoretical Analysis of an Improved Covariance Matrix Estimator in non-Gaussian Noise

Frédéric Pascal (1, 2) , Philippe Forster (3) , Jean-Philippe Ovarlez (2) , Pascal Larzabal (4)

1 SONDRA - Sondra, CentraleSupélec, Université Paris-Saclay (COmUE)
2 DEMR, ONERA, Université Paris Saclay (COmUE) [Palaiseau]
3 GEA - Groupe d'Electromagnétisme Appliqué
4 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

This paper presents a detailed theoretical analysis of a recently introduced covariance matrix estimator, called the Fixed Point Estimate (FPE). It plays a significant role in radar detection applications. This estimate is provided by the Maximum Likelihood Estimation (MLE) theory when the non-Gaussian noise is modelled as a Spherically Invariant Random Process (SIRP). We study in details its properties: existence, uniqueness, unbiasedness, consistency and asymptotic distribution. We propose also an algorithm for its computation and prove the convergence of this numerical procedure. These results will allow to study the performance analysis of the adaptive CFAR radar detectors (GLRT-LQ, BORD,...).

Mots clés: Covariance matrix; Radar detection; Maximum likelihood estimation; Random processes; Detectors; Speckle; Random variables; Additive noise; Equations; Convergence of numerical methods

Domaines: Traitement du signal et de l'image [eess.SP]; Autres [stat.ML]; Applications [stat.AP]

Frédéric Pascal, Philippe Forster, Jean-Philippe Ovarlez, Pascal Larzabal. Theoretical Analysis of an Improved Covariance Matrix Estimator in non-Gaussian Noise. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., Mar 2005, Philadelphia, United States. pp.69-72, ⟨10.1109/ICASSP.2005.1415947⟩. ⟨hal-02495012⟩