Exact maximum likelihood estimates for sirv covariance matrix: Existence and algorithm analysis

Yacine Chitour (1) , Frédéric Pascal (2)

1 L2S - Laboratoire des signaux et systèmes
2 SONDRA - Sondra, CentraleSupélec, Université Paris-Saclay (COmUE)

In this paper, we investigate the existence and the algorithm analysis of an adaptive scheme that has been introduced for covariance structure matrix estimation in the context of adaptive radar detection under non-Gaussian noise. This latter has been modeled by spherically invariant random vector (SIRV), which is the product c of the square root of a positive unknown random variable tau and an independent Gaussian vector x,c=radic(tau) x. A similar line of work was undertaken in the context of compound Gaussian noise, and this paper extends the previous results in the case of SIRV modeled noise. More precisely, the fixed-point estimate to be studied verifies a nonlinear algebraic equation (E)x=f(x). The aim of this paper is twofold. First, we prove that (E) admits a unique solution x; secondly, we show that the corresponding iterative algorithm xn+1=f(xn) converges to x for every admissible initial condition.

Mots clés: Index Terms-Maximum Likelihood estimate; SIRV model; Fixed Point estimate; iterative algorithm convergence; adaptive detection

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Yacine Chitour, Frédéric Pascal. Exact maximum likelihood estimates for sirv covariance matrix: Existence and algorithm analysis. IEEE Transactions on Signal Processing, 2008, 56 (10), pp.4563-4573. ⟨10.1109/TSP.2008.927464⟩. ⟨hal-00353594⟩