Semiparametric Stochastic CRB for DOA Estimation in Elliptical Data Model

Abstract

This paper aims at presenting a numerical investigation of the statistical efficiency of the MUSIC (with different covariance matrix estimates) and the IAA-APES Direction of Arrivals (DOAs) estimation algorithms under a general Complex Elliptically Symmetric (CES) distributed measurement model. Specifically, the density generator of the CES-distributed data snapshots is considered as an additional, infinite-dimensional, nuisance parameter. To assess the efficiency in the considered semiparametric setting, the Semiparametric Stochastic Cramér-Rao Bound (SSCRB) is adopted as lower bound for the Mean Square Error (MSE) of the DOA estimators.

Slepian-Bangs formulas for parameterized density generator of elliptically symmetric distributions

“…where (a k ) k=1,...,K are the steering vectors parameterized by the DOA θ k with θ def = (θ 1 , ..., θ K ) T , and D θ def = [ da1 dθ1 , ..., daK dθK ] for K sources. This last expression of CRB was given in [11] and [27] as semiparametric CRB without noticing that it was equal to the classic CRB.…”

Refinement and derivation of statistical resolution limits for circular or rectilinear correlated sources in CES data models

“…the number of snapshots T ) efficient, and therefore, its covariance reaches the CRB for the stochastic model. But when g is unknown, some estimates have been proposed in [32] by exploiting the MUSIC algorithm together with the Tyler's or Hubert's M estimate of the covariance with better performance than for the conventional MUSIC algorithm. But none of these estimators is efficient w.r.t.…”

Resolving power of MUSIC-like algorithms for circular or rectilinear correlated sources in CES data models

“…However, these ML estimates cannot be obtained for arbitrary distributed x t and arbitrary C-CES distributed n t in (2). To overcome this difficulty, we consider here an alternative model used in [31], [29] and [33], where the observations y t in (2) are CES distributed. In this case the distributions of x t and n t are not specified, but only their second-order statistics are imposed.…”