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Real-time tracking of moving objects from scattering matrix in real-world microwave imaging

Seong-Ho Son, Kwang-Jae Lee, Won-Kwang Park

TL;DR

This paper tackles real-time microwave imaging of small moving objects when diagonal S-parameters are unavailable. It proposes a non-iterative Kirchhoff migration approach that uses off-diagonal scattering data and the Born-approximate forward model to form an imaging function $\ rak{F}_{\\mathrm{KIR}}(\\mathbf{r},t)$, whose structure is tied to an infinite series of Bessel functions via a Jacobi–Anger expansion. The authors derive conditions under which moving objects can be uniquely detected, analyze how antenna configuration (e.g., even-number circular arrays) mitigates artifacts, and show that the method is fast and suitable for real-time tracking. Numerical experiments with real data from an ETRI microwave system validate the method's feasibility and reveal its strengths and limitations for small-object detection in practical settings.

Abstract

The problem of the real-time microwave imaging of small, moving objects from a scattering matrix, whose elements are measured scattering parameters, without diagonal elements is considered herein. An imaging algorithm based on a Kirchhoff migration operated at single frequency is designed, and its mathematical structure is investigated by establishing a relationship with an infinite series of Bessel functions of integer order and antenna configuration. This is based on the application of the Born approximation to the scattering parameters of small objects. The structure explains the reason for the detection of moving objects via a designed imaging function and supplies its some properties. To demonstrate the strengths and weaknesses of the proposed algorithm, various simulations with real-data are conducted.

Real-time tracking of moving objects from scattering matrix in real-world microwave imaging

TL;DR

This paper tackles real-time microwave imaging of small moving objects when diagonal S-parameters are unavailable. It proposes a non-iterative Kirchhoff migration approach that uses off-diagonal scattering data and the Born-approximate forward model to form an imaging function , whose structure is tied to an infinite series of Bessel functions via a Jacobi–Anger expansion. The authors derive conditions under which moving objects can be uniquely detected, analyze how antenna configuration (e.g., even-number circular arrays) mitigates artifacts, and show that the method is fast and suitable for real-time tracking. Numerical experiments with real data from an ETRI microwave system validate the method's feasibility and reveal its strengths and limitations for small-object detection in practical settings.

Abstract

The problem of the real-time microwave imaging of small, moving objects from a scattering matrix, whose elements are measured scattering parameters, without diagonal elements is considered herein. An imaging algorithm based on a Kirchhoff migration operated at single frequency is designed, and its mathematical structure is investigated by establishing a relationship with an infinite series of Bessel functions of integer order and antenna configuration. This is based on the application of the Born approximation to the scattering parameters of small objects. The structure explains the reason for the detection of moving objects via a designed imaging function and supplies its some properties. To demonstrate the strengths and weaknesses of the proposed algorithm, various simulations with real-data are conducted.
Paper Structure (7 sections, 2 theorems, 31 equations, 5 figures, 1 table)

This paper contains 7 sections, 2 theorems, 31 equations, 5 figures, 1 table.

Table of Contents

  1. The forward problem and scattering parameters
  2. Kirchhoff migration for a real-time detection: introduction, analysis, and some properties
  3. Introduction to imaging function of the Kirchhoff migration
  4. Structure of the imaging function
  5. Various properties of imaging function
  6. Simulation results with experimental data
  7. Conclusion and perspectives

Key Result

Theorem 2.1

Let $\boldsymbol{\theta}_n=\mathbf{a}_n/R=(\cos\theta_n,\sin\theta_n)^{\mathtt{T}}$ and $\mathbf{r}-\mathbf{r}'=|\mathbf{r}-\mathbf{r}'|(\cos\phi,\sin\phi)^{\mathtt{T}}$. If $|k_\mathrm{b}(\mathbf{a}_n-\mathbf{r})|\geq0.25$ for all $\mathbf{r}\in\Omega$, then $\mathfrak{F}(\mathbf{r},t)$ can be repr where $J_s$ is a Bessel function of the order $s$ of the first kind,

Figures (5)

  • Figure 1: Photos of microwave machine and objects $D_m$, $m=1,2,3,4$.
  • Figure 2: (Example \ref{['Ex1']}) Maps of $\mathfrak{F}(\mathbf{r},t)$ for moving object $D_3(t)$.
  • Figure 3: (Example \ref{['Ex2']}) Maps of $\mathfrak{F}(\mathbf{r},t)$ for moving objects $D_2(t)$ and $D_3(t)$.
  • Figure 4: (Example \ref{['Ex3']}) Maps of $\mathfrak{F}(\mathbf{r},t)$ for moving objects $D_1(t)$ and $D_2(t)$.
  • Figure 5: (Example \ref{['Ex4']}) Maps of $\mathfrak{F}(\mathbf{r},t)$ for moving objects $D_2(t)$ and $D_4(t)$.

Theorems & Definitions (7)

  • Theorem 2.1: Structure of imaging function
  • proof
  • Corollary 2.1: Unique determination of moving objects
  • Example 3.1: Tracking of single moving object
  • Example 3.2: Tracking of moving objects: same radii and material properties
  • Example 3.3: Tracking of moving objects: different radii and material properties
  • Example 3.4: Tracking of moving objects: same radii but different material properties