Estimating 3D motion from radar data: Exploiting an omnidirectional radar array for motion estimation in the context of SAR imaging on agile platforms

Acquiring an accurate estimate of position is a challenging problem in coherent radar processing techniques such as Synthetic Aperture Radar (SAR). Even more so, for light and agile platforms such as multi-copters. Due to their unpredictable flight path, their motion must be accurately measured during data acquisition, and compensated for during processing. To obtain a focused SAR image, each pulse location must be accurately known to ensure that each pulse is added coherently to the imaging grid. Traditionally, this is achieved with an Inertial Navigation System (INS). While an INS can provide reasonable performance, its weight and size are often a constraint for agile platforms, limiting the available options and attainable accuracy.In this study, we perform an analysis on the applicability of an omnidirectional radar array for explicitly estimating the motion of a multi-copter platform, and improving on the positioning accuracy achieved by the on board INS. Building on existing 1D SAR motion compensation techniques, we develop new methods for estimating the 3D motion of the radar platform by estimating its height and velocity. In addition, we also present a novel 3D autofocus technique termed multi-beam autofocus. This technique allows for the correction of 3D trajectory errors from pulse to pulse by exploiting the beamforming capabilities of the array, and focusing multiple regions as the image is created.Using an Extended Kalman Filter (EKF), we obtain position estimates from the radar velocity measurements based on the last known INS position. We experimentally verify that using our velocity estimation method alone, the positioning performance is already improved compared to that of a state-of-the-art INS, allowing for INS-free imaging using arbitrary flight paths. This enables imaging in GNSS-denied environments, and has the potential to further reduce the weight of the platform. We also show that fusing the estimates obtained from our method with the existing INS output yields an additional performance increase in terms of SAR image focus, improving the resolvability and detectability of weak targets. The presented results open further avenues of research, not only in agile SAR imaging but also in autonomous GNSS-denied navigation