Some results on the Weiss–Weinstein bound for conditional and unconditional signal models in array processing

Abstract

In this paper, the Weiss-Weinstein bound is analyzed in the context of sources localization with a planar array of sensors. Both conditional and unconditional source signal models are studied. First, some results are given in the multiple sources context without specifying the structure of the steering matrix and of the noise covariance matrix.Moreover, the case of an uniform or Gaussian prior are analyzed. Second, these results are applied to the particular case of a single source for two kinds of array geometries: a non-uniform linear array (elevation only) and an arbitrary planar (azimuth and elevation) array.

A Ziv-Zakaï type bound for hybrid parameter estimation

“…We remark that the HBZZB is also accurate to predict the SNR threshold for this estimation problem as well as the HBWWB. Such a comparison has already been seen in the literature but in the Bayesian framework only (see [8] and [19]). …”

Hybrid Barankin–Weiss–Weinstein Bounds

“…However, if is independent of , which is encountered in some cases of interest, e.g. [11] and [26] (and references herein), the following closed-form expression of can be obtained when the prior p.d.f.…”

“…is Gaussian and does not depend on the deterministic parameter [26, (25)]: (25) Actually it is possible to formalize further this result by noticing that if , a square matrix and a vector such that: (26) where is a matrix independent of , then:…”

Weiss-Weinstein bound for change-point estimation

“…[13], [14]). Consequently, we will only optimize the bound over h. We first simplify the aforementioned expression in the context of a discrete parameter, then we derive a closed-form expression for change point estimation in the following.…”