Geometric means and medians with applications to target detection

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.

A Geometric Barycenter-Based Clutter Suppression Method for Ship Detection in HF Mixed-Mode Surface Wave Radar

“…Unlike some target detectors in [22,23,26], which detect the target with the highest geometric distances, we choose the training data with the lowest geometric distances because the lower geometric distance shows more homogeneity with the cell under test. The training data selection strategy is processed as follows,…”

“…The similarity detector (SD) algorithm [16][17][18][19] selects the samples with waveforms that are similar to the CUT. Recently, the information geometry-based SD algorithm has drawn more attentions on covariance estimation and target detection processing [20][21][22][23][24]. A class of covariance matrix estimators, which are associated with suitable distances in the considered space and defined as the geometric barycenter, are proposed to exclude the outliers and clutter for target detection in [25,26].…”

Micro-Distortion Detection of Lidar Scanning Signals Based on Geometric Analysis

“…A charge-coupled device (CCD) [11] is a sensor that uses charge to realize signal transmission, enabling photoelectric conversion and signal charge storage and transfer. According to the working content of the linear array CCD module, chip TCD1209DG [12] with high sensitivity and high resolution is used as a chip of the linear array CCD module.…”

“…where α (k ) in Equation (11) and τ(k ) in Equation (13) that obey Bernoulli distribution represent the distortion that occurs when the sensor transmits to the controller and the controller transmits to the actuator. α (k ) = 1 indicates that the sensor successfully scans the signal set to the controller, and α (k ) = 0 indicates that the sensor is distorted when transmitting the signal set to the controller.…”

Matrix Information Geometry for Signal Detection via Hybrid MPI/OpenMP

“…Information geometry, which is a theory that is based on statistical manifolds, is a differential geometry method for information science problems, which has been applied in numerous areas, e.g., neural networks [3], image processing [4][5][6], information geometric detection [7][8][9][10][11][12], dictionary learning, and sparse coding [13]. Signal detection based on information geometry was first proposed in 1989, when an issue of multisource statistical inference was analyzed and the hypothesis testing problem was explained using a statistical manifold [14], which highlighted the fundamental role that…”