Towards a median signal detector through the total Bregman divergence and its robustness analysis

Yusuke Ono, Linyu Peng

Research output: Contribution to journalArticlepeer-review

Abstract

A novel family of geometric signal detectors are proposed through medians of the total Bregman divergence (TBD), which are shown advantageous over the conventional methods and their mean counterparts. By interpreting the observation data as Hermitian positive-definite matrices, their mean or median play an essential role in signal detection. As is difficult to be solved analytically, we propose numerical solutions through Riemannian gradient descent algorithms or fixed-point algorithms. Beside detection performance, robustness of a detector to outliers is also of vital importance, which can often be analyzed via the influence functions. Introducing an orthogonal basis for Hermitian matrices, we are able to compute the corresponding influence functions analytically and exactly by solving a linear system, which is transformed from the governing matrix equation. Numerical simulations show that the TBD medians are more robust than their mean counterparts.

Original languageEnglish
Article number108728
JournalSignal Processing
Volume201
DOIs
Publication statusPublished - 2022 Dec

Keywords

  • Geometric median
  • matrix-CFAR
  • nonhomogeneous clutter
  • robustness analysis

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering

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