Coexistence of Near-Field and Far-Field Sources: the Angular Resolution Limit

3rd International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Boyer, Rémy^1 ; El Korso, Mohammed Nabil^2 ; Renaux, Alexandre^1 ; Marcos, Sylvie^1

Laboratoire des Signaux et Systemes (L2S), Université Paris-Sud XI (UPS), SUPELEC, Gif-Sur-Yvette, France^1

Laboratoire SATIE, CNRS, École Normale Suprieure de Cachan, Cachan, France^2

关键词: Angular resolution;    Closed-form expression;    Far-field sources;    Near fields;    Optimal resolution;    Order polynomials;    Passive source localization;    Qualitative information;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/464/1/012002/pdf
DOI  :  10.1088/1742-6596/464/1/012002

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

Passive source localization is a well known inverse problem in which we convert the observed measurements into information about the direction of arrivals. In this paper we focus on the optimal resolution of such problem. More precisely, we propose in this contribution to derive and analyze the Angular Resolution Limit (ARL) for the scenario of mixed Near-Field (NF) and Far-Field (FF) Sources. This scenario is relevant to some realistic situations. We base our analysis on the Smith's equation which involves the Crame´r-Rao Bound (CRB). This equation provides the theoretical ARL which is independent of a specific estimator. Our methodology is the following: first, we derive a closed-form expression of the CRB for the considered problem. Using these expressions, we can rewrite the Smith's equation as a 4-th order polynomial by assuming a small separation of the sources. Finally, we derive in closed-form the analytic ARL under or not the assumption of low noise variance. The obtained expression is compact and can provide useful qualitative informations on the behavior of the ARL.