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3D Radar Imaging from the UAV Nadir

S. Hamed Javadi, Hichem Sahli, André Bourdoux

arXiv:2609.04848v1eess.SP

TL;DR

The paper addresses the inability of conventional UAV SAR to image the nadir region by developing a low-cost MIMO mm-wave InSAR framework for 3D reconstruction. It adds PGA-based phase-error compensation and reports focused, robust point clouds in simulation and successful reconstruction of pond boundaries and surrounding vegetation in flight experiments.

  • Problem

    Conventional UAV SAR methods do not reconstruct regions directly beneath the UAV, limiting radar use in applications requiring nadir sensor fusion.

  • Method

    The paper develops a low-cost MIMO mm-wave InSAR framework for UAV-nadir 3D imaging with PGA-based compensation of phase errors across virtual receive antennas.

  • Results

    Phase compensation improves range-azimuth and across-track focus, while simulations remain sub-meter in RMSE and experiments reconstruct pond boundaries and surrounding trees and vegetation.

  • Takeaways & Limitations

    The framework demonstrates practical 3D radar point-cloud reconstruction from the region directly beneath a UAV using a MIMO FMCW radar.

Abstract

from arXiv · show

Radars improve the sensing robustness of UAVs by operating under poor lighting and weather conditions and seeing through occlusions such as vegetation. However, they suffer from poor angular resolution, which can be addressed using synthetic aperture radar (SAR) algorithms. State-of-the-art UAV SAR methods operate at a depression angle and are not suitable for sensor fusion applications where the data are collected from areas directly below the UAV (i.e., the UAV nadir). In this paper, we present an interferometric SAR (InSAR) framework for reconstructing 3D images from the UAV nadir using a low-cost multi-input-multi-output (MIMO) mm-wave radar. Additionally, an effective method based on the phase gradient autofocus (PGA) is presented for compensating the phase error across the virtual receive antennas. We demonstrate the effectiveness of our 3D imaging algorithm in both simulation and experimental scenarios.

I. INTRODUCTION

UAV radar improves sensing in difficult conditions, but conventional SAR configurations cannot image the region directly beneath the UAV. The paper addresses this nadir gap with a low-cost mm-wave InSAR framework for 3D imaging and evaluates it in simulation and experiments.

  • Radar strengthens UAV sensing in poor light, adverse weather, and through occlusions such as fog and vegetation.
  • Large antenna apertures are impractical or costly, motivating SAR methods that synthesize aperture through radar motion.
  • Conventional UAV SAR methods image down-range and azimuth at depression angles but cannot reconstruct the region directly beneath the UAV.
  • The proposed framework provides 3D nadir imaging with a low-cost mm-wave radar, incorporates UAV attitude angles, and compensates phase errors across virtual MIMO receive antennas.
  • The paper evaluates the proposed framework through both simulation and experiment.

B. SAR imaging with FMCW radar

The FMCW SAR imaging formulation balances image quality and computational complexity using the polar format algorithm, while modeling downward-looking radar geometry and wavenumber-based processing.

  • PFA balances image quality and computational complexity by correcting wavenumber distortion while retaining manageable complexity.
  • The residual video phase error is negligible for current mm-wave FMCW radar technology.
  • The radar is mounted below the UAV, looks downward, and flies along the x-axis in the stated SAR geometry.
  • The slant range is approximated by projecting scatterer position onto the radar line of sight to the SAR reference point.
  • Range-compensated FMCW data are interpolated onto a grid of wavenumbers to enable FFT-based image formation.

A. Configuration

The nadir configuration places the imaging plane beneath the UAV and uses across-track receive baselines for 3D interferometric reconstruction. Phase differences are converted into across-track coordinates under stated geometric assumptions.

  • Nadir SAR imaging uses the down-range direction within the imaging plane, corresponding to zero grazing angle and reduced layover and foreshortening.
  • Two receive antennas separated across-track enable 3D imaging through interferometric processing.
  • The configuration uses a transmitter at the receive-antenna midpoint and assumes planar wavefronts because the scene is in the array far field.
  • A second receive-antenna pair with a different baseline is used for phase unwrapping, with baseline ratios formed from coprime integers.
  • The SAR image provides scatterer y-coordinates, while the interferometric equation calculates their z-coordinates.
  • The paper calls the z-axis across-track because it does not represent scatterer elevation, although the dimensions are equivalent in InSAR terminology.

B. Pipeline

The pipeline compensates positioning-induced phase errors across receive antennas before forming SAR images for the UAV-nadir InSAR framework.

  • 1) Phase error compensation:: The framework models along-track positioning error as a phase error in the compensated beat signal.Only along-track positioning error is considered because other UAV motions are negligible during the SAR CPI.
  • 1) Phase error compensation:: PGA estimates phase-error gradients from redundancy across dominant scatterers and recovers the phase error by integration.The method assumes each range bin is dominated by at most one strong scatterer.
  • 1) Phase error compensation:: PGA is selected because it avoids intensive optimization and suits resource-constrained UAVs, but its slow-time-only assumption can fail for extensive scenes or large apertures.A more appropriate phase-compensation algorithm may be required in those scenarios.
  • 1) Phase error compensation:: Beamforming uses IMU data at the UAV nadir to improve SNR, followed by PFA imaging and PGA estimation of residual phase error.PFA provides a compromise between performance and complexity.
  • 1) Phase error compensation:: Each receive antenna's phase error is compensated by multiplying its range profile by exp[−jϵ(n)] before SAR image formation.The framework diagram identifies ϵ(n) as the phase error.

2) SAR per receive antenna:

After phase-error compensation, the pipeline forms SAR images for each receive antenna and thresholds them to identify common dominant scatterers.

  • 2) SAR per receive antenna:: SAR images are produced by applying a second inverse Fourier transform in slow time after receive-antenna phase compensation.PFA is used as a performance–complexity compromise, although other SAR algorithms may be adopted.
  • 3) Segmentation:: RaySe estimates a Rayleigh-distribution parameter from SAR-image amplitude variance and sets an upper-tail threshold for dominant scatterers.The method uses the Rayleigh-based background-noise amplitude distribution.
  • 3) Segmentation:: Bins detected in all receive-antenna images are intersected to obtain the x and y coordinates of major scatterers.Their z-coordinates are then obtained through interferometric processing.

4) Interferometric processing:

Interferometric processing registers receive-antenna images when needed, unwraps phase differences using multiple baselines, and estimates the across-track coordinate.

  • 4) Interferometric processing:: Accurate registration is required before comparing phase differences from matching pixels across two apertures.Roll variation can make θs time-varying and shift one SAR image relative to the other.
  • 4) Interferometric processing:: The no-misregistration condition becomes stricter as baseline or SAR CPI increases, while short baselines and small CPIs can make registration unnecessary.If the roll-rate limit is exceeded, misregistration must be compensated before interferometric processing.
  • 4) Interferometric processing:: Multi-baseline phase unwrapping uses two receive-antenna pairs with relatively prime baselines to recover the actual phase differences.The wrapped phases are related through integer ambiguity numbers.
  • 4) Interferometric processing:: After unwrapping, the phase difference ψ is used to estimate the scatterers' z-coordinate, with the sign selected according to whether ψ is nonnegative.The across-track estimate uses the average of i because yT varies little during flight.

Accounting for UAV attitude:

The attitude-aware formulation defines the SAR coordinate system from the UAV flight path and accounts for yaw, pitch, and roll behavior during the CPI.

  • Accounting for UAV attitude:: The basic z-coordinate derivation assumes straight x-axis motion without attitude changes, so the framework defines coordinates from the UAV flight path to handle variations.This extends the geometry beyond the no-attitude-change assumption.
  • Accounting for UAV attitude:: Yaw and pitch variations adapt the x- and y-axis directions, while their changes are negligible over the CPI and therefore do not affect the InSAR geometry.The example CPI is about 27 ms in the experiment.

IV. EVALUATION RESULTS

The evaluation uses simulation scenarios to assess the proposed 3D InSAR pipeline, phase-error compensation, and robustness under motion and attitude perturbations. Compensation improves focusing and 3D resolution, while RMSE remains sub-meter across tested scene configurations, although several sensitivity factors are not separately quantified.

  • Simulation setup: The simulation evaluates 3D imaging from a UAV nadir using a MIMO radar with two transmitters and four receivers forming eight virtual receive antennas.The antenna array points downward, and the radar flies at 7 m/s and 25 m altitude.
  • Phase-error compensation: A 2.5 m/s along-track velocity perturbation produces a dominant quadratic phase error that PGA estimates and significantly compensates.The phase-error mismatch is attributed to range variation caused by the scatterer extent and extended SAR aperture, which violates PGA assumptions.
  • Phase-error compensation: Phase-error compensation produces better-focused SAR images and more focused 3D point clouds, improving both range-azimuth and across-track resolution.The 3D simulation compares point clouds with and without compensation, while the receiver-level comparison shows improved focus at R1.
  • 3D reconstruction: Phase unwrapping is particularly important for correctly estimating larger z values because some simulated phase differences fall outside the wrapping interval.The affected phase differences lie outside (−2π, 2π].
  • Robustness evaluation: Across random scatterer configurations, RMSE remains bounded within a sub-meter range under along-track velocity errors from −2 m/s to 2 m/s and roll perturbations from −5° to 5°.The RMSE is computed over 10 trials and all scatterers using nearest reconstructed-point distance to ground truth.
  • Limitations: The simulations validate the pipeline under representative conditions but do not separately quantify sensitivity to SNR, residual phase error, reduced resolution, or phase-unwrapping errors.A full parametric sensitivity analysis is identified as beyond the scope of the work.

B. Experimental results

The experiment uses a downward-facing MIMO FMCW radar beneath a UAV to reconstruct nadir point clouds, with phase-error compensation improving image focus and contrast. The resulting point clouds capture pond boundaries and surrounding vegetation, while water is barely detected due to specular reflection.

  • Experiment setup: The experiment used a 60 GHz MIMO FMCW radar mounted beneath a DJI Matrice-300 and operated during flight at approximately 25 m altitude.The radar had three transmitters, four receivers, and 12 virtual channels arranged in two cross-track rows.
  • Experiment setup: The UAV flew over a pond while radar–camera calibration enabled overlaying reconstructed radar point clouds on bird’s-eye-view imagery.Calibration used corner reflectors on checkerboards and at least four corresponding radar–camera detections.
  • SAR image results: Phase-error compensation improved the focus of reconstructed 2D SAR images, confirmed by enhanced image contrast across three flight instances.The images captured the pond edge first and progressively revealed tree foliage as the UAV approached the pond end.
  • SAR image results: The misregistration threshold was approximately 624 deg/s, compared with a maximum UAV roll variation rate of 8 deg/s, so image registration was unnecessary.This conclusion follows the stated misregistration criterion for the interferometric setup.
  • 3D point-cloud results: Aggregated nadir point clouds reconstructed pond edges, two trees near the divider, and additional tall trees beside the pond.The water surface was barely detected because it acted as a specular reflector that scattered radar signals away from the radar.

V. CONCLUSION

The paper proposes a downward-facing MIMO FMCW radar framework for 3D point-cloud capture beneath UAVs. It combines nadir SAR imaging, interferometric processing, and phase-error compensation, and demonstrates reconstruction of pond boundaries and surrounding vegetation in flight.

  • Contribution: The framework captures 3D point clouds directly beneath a UAV using a downward-oriented MIMO FMCW radar.The antenna array is mounted on the UAV underside and aligned along the across-track dimension.
  • Contribution: Interferometric processing across two receive-antenna pairs provides the third spatial dimension in the UAV nadir plane.SAR imaging is performed in the nadir plane before interferometric processing.
  • Contribution: The pipeline includes radar phase-error compensation, whose effectiveness was confirmed through simulation.The paper evaluates the framework in both simulated and practical settings.
  • Experimental validation: A flight over a pond successfully reconstructed the pond boundaries, surrounding trees, and vegetation.The resulting point clouds are presented as inputs for rescue models, 3D scene reconstruction, and multimodal object-detection fusion.
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