Mitigating Radar-Inertial Calibration Ambiguities via SO(3) Manifold Steering

Reliable Radar-inertial fusion hinges on accurate extrinsic calibration, yet mmWave Radar poses unique calibration ambiguities: sparse and noisy returns, limited angular resolution, and a fundamental lack of stable geometric correspondences. Prior approaches typically rely on dedicated calibration targets, restrictive motion patterns, or strong scene assumptions, limiting their practicality for real-world deployment. In this paper, we present RadarCalib, a targetless, plug-and-play calibration framework that uses rigorous steering on the SO(3) manifold to establish reliable Radar-inertial constraints. Our key insight is that 3D rotational motion naturally induces a temporal synthetic aperture (TSA), which enables recovery of a fine-grained, high-resolution azimuthal spectrum. This TSA-enhanced representation reveals a highly stable rotationdependent azimuthal shift, which we use as a calibration signal to tightly couple Radar observations with IMU preintegration on the SO(3) manifold. Unlike point-based or motion-prior paradigms, RadarCalib establishes motion-consistent alignment in the spectral domain, regularizing SO(3) optimization and avoiding collapse induced by sparse Radar returns. Extensive real-world experiments show that RadarCalib achieves sub-degree rotational accuracy and outperforms state-of-the-art RadarIMU baselines in accuracy, robustness, and computational efficiency. Our self-collected dataset and code is released at https://github.com/ MetaIoT-WHU/RadarCalib.