On-the-Fly Extrinsic Calibration of LiDAR–IMU via Nonuniform Motion Model and Excitation Analysis

Extrinsic calibration between LiDAR and IMU is fundamental to autonomous platforms, as the quality of motion estimation and sensor fusion relies heavily on precise intersensor alignment. Traditional methods are typically conducted in controlled laboratory settings, which is impractical for field deployment. On-the-fly calibration, while highly convenient, is often hindered by intense motion and the lack of omnidirectional excitation on ground platforms such as vehicle-mounted systems. To overcome these limitations, in this paper, we propose a real-time LiDAR–IMU extrinsic calibration framework. The method first constructs a non-uniform motion model to precisely estimate LiDAR motion, and then applies a decoupled calibration strategy to independently solve and optimize rotation and translation parameters. Furthermore, to address degraded observability under planar motion, we introduce an excitation analysis module that compensates for insufficient excitation and enhances calibration robustness. We validate effectiveness and stability on public and self-collected datasets, reporting mean ± Standard Deviation (SD) for all six extrinsic parameters (repeatability) and RMSE to a reference (accuracy). On fully excited sequences, our method achieves the smallest SDs on 15/18 IMU–axis pairs, improves calibration accuracy by an average of 6.92%, and reduces processing time by 29.33% compared with state-of-the-art baselines. Under weak excitation, it attains the smallest SDs in 11/12 parameters and improves calibration results by 25.10% with comparable runtime. Overall, the approach enables accurate and robust LiDAR–IMU integration, improving perception quality and system reliability.