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A Low-Complexity PFA-Based Autofocus Algorithm for Automotive SAR

S. Hamed Javadi, André Bourdoux, Adnan Albaba, Hichem Sahli

Abstract

Radars provide robust perception of vehicle surroundings by effectively functioning in poor light and adverse weather conditions. Synthetic aperture radar (SAR) algorithms are employed to address the limited angular resolution of radars by enlarging antenna aperture size synthetically as the radar moves. An autofocus algorithm is essential to improve the SAR image quality by compensating for errors mainly caused by inaccurate radar localization. Existing autofocus algorithms are mostly tailored for the frequency domain SAR techniques which are prevalent in aviation and spaceborne applications thanks to their lower complexity in large data processing. However, in the automotive context, the backprojection algorithm (BPA) is often preferred since it provides less distorted images at the cost of more complexity. Addressing the gap in efficient autofocus solutions for time-domain algorithms, this paper introduces a dual-layered autofocus strategy that integrates the Polar Format Algorithm (PFA) with BPA. The first layer employs a novel Localization Error Compensation Autofocus (LECA) processing pipeline to estimate and correct the localization errors within the PFA domain, leveraging its computational efficiency. The second layer seamlessly transfers these corrections to BPA, enabling high-quality SAR imaging while maintaining low complexity. Additionally, the strategy extends Phase Gradient Autofocus (PGA) techniques to enhance the efficiency of localization error compensation for BPA. Validated through real-world automotive experiments, the proposed pipeline delivers state-of-the-art image focus and resolution, setting a new benchmark for computationally efficient SAR imaging.

A Low-Complexity PFA-Based Autofocus Algorithm for Automotive SAR

Abstract

Radars provide robust perception of vehicle surroundings by effectively functioning in poor light and adverse weather conditions. Synthetic aperture radar (SAR) algorithms are employed to address the limited angular resolution of radars by enlarging antenna aperture size synthetically as the radar moves. An autofocus algorithm is essential to improve the SAR image quality by compensating for errors mainly caused by inaccurate radar localization. Existing autofocus algorithms are mostly tailored for the frequency domain SAR techniques which are prevalent in aviation and spaceborne applications thanks to their lower complexity in large data processing. However, in the automotive context, the backprojection algorithm (BPA) is often preferred since it provides less distorted images at the cost of more complexity. Addressing the gap in efficient autofocus solutions for time-domain algorithms, this paper introduces a dual-layered autofocus strategy that integrates the Polar Format Algorithm (PFA) with BPA. The first layer employs a novel Localization Error Compensation Autofocus (LECA) processing pipeline to estimate and correct the localization errors within the PFA domain, leveraging its computational efficiency. The second layer seamlessly transfers these corrections to BPA, enabling high-quality SAR imaging while maintaining low complexity. Additionally, the strategy extends Phase Gradient Autofocus (PGA) techniques to enhance the efficiency of localization error compensation for BPA. Validated through real-world automotive experiments, the proposed pipeline delivers state-of-the-art image focus and resolution, setting a new benchmark for computationally efficient SAR imaging.
Paper Structure (27 sections, 1 theorem, 21 equations, 7 figures, 2 tables)

This paper contains 27 sections, 1 theorem, 21 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related works
  4. Summary of contributions and manuscript organization
  5. Background
  6. FMCW radars
  7. SAR imaging with FMCW radar
  8. PFA
  9. BPA
  10. localization error compensation autofocus (LECA)
  11. Problem statement
  12. PFA autofocus
  13. BPA autofocus
  14. LECA with IC maximization
  15. LECA with PGA
  16. ...and 12 more sections

Key Result

Proposition 1

After the beat signal is compensated w.r.t. the SRP in eq:compensated.signal using measured radar locations, its phase error due to the localization error is approximated by: Hence, the phase error is compensated by: where $\hat{\beta}$ is given by maximizing the image contrast (IC) of the PFA image: IC is defined as the normalized image variance Martorella2005: with $I\triangleq\left|\sigma(x

Figures (7)

  • Figure 1: The SAR 2D geometry. SRP indicates the SAR origin and stands for the SAR reference point.
  • Figure 2: The localization error compensation autofocus (LECA) algorithm. Here, $\rho$ is the learning rate, $\bigtriangledown IC$ indicates the gradient of the image contrast, and $\delta_{IC}$ is a small value used for stopping the gradient ascent algorithm (GAA).
  • Figure 3: LECA-IC for BPA autofocus. The localization error parameter is estimated by maximizing IC by PFA-LECA.
  • Figure 4: LECA with PGA for BPA autofocus.
  • Figure 5: Example #1. (a) The camera image of the SAR target scene. (b) The zoomed-in areas of specified in the PFA SAR images. The other rows depict the results of the different scenarios of SAR imaging.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Proposition