Geometric means and medians with applications to target detection. Issue 6 (1st August 2017)

• Record Type: Journal Article
• Authors: Hua, Xiaoqiang; Cheng, Yongqiang; Wang, Hongqiang; Qin, Yuliang; Li, Yubo
• Is Part Of: IET signal processing. Volume 11:Issue 6(2017)
• Page Start: 711
• Page End: 720
• Publication Date: 2017-08-01
• Subjects: radar detection -- object detection -- radar clutter -- matrix algebra; CFAR detectors -- matrix constant false alarm rate detectors -- finite collection -- radar received clutter data -- radar systems -- target detection problems -- HPD matrix -- Hermitian positive‐definite matrix -- Riemannian manifold -- geometric measures‐based medians -- geometric measures‐based means; Signal processing -- Periodicals; 621.3822
• DOI: 10.1049/iet-spr.2016.0547
• Languages: English
• ISSNs: 1751-9675

Abstract

Abstract : This study explores the application of geometric measures‐based means and medians on the Riemannian manifold of Hermitian positive‐definite (HPD) matrix to target detection problems in radar systems. Firstly, the slow‐time dimension of radar received clutter data in each cell is modelled and mapped to HPD matrix space, which can be described as a complex Riemannian manifold. Each point of this manifold is an HPD matrix. Then, several geometric measures are presented for measuring closeness between two HPD matrices. According to these measures, the means and medians of a finite collection of HPD matrices are deduced, and various matrix constant false alarm rate (CFAR) detectors are designed. The principle of target detection is that if a location has enough dissimilarity from the geometric mean or median estimated by its neighbouring locations, targets are supposed to appear at this location. Moreover, different distance measures adopted in detector can result in different performance of detection. These differences are owing to different measure structure, reflected by the anisotropy of a location on the Riemannian manifold. Numerical experiments are given to demonstrate the relationship between anisotropy of the geometric measures and the detection performance of their corresponding matrix CFAR detectors.