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When fusing the measurement data with different sampling frequencies from the light detection and ranging (LiDAR) and inertial measurement unit (IMU), their timestamps should be exactly aligned. However, in reality the timestamps of LiDAR and IMU are typically subject to different influences, which will inevitably generate the time delay error to reduce the accuracy and robustness of the LiDAR-IMU system. To this avail, this article proposes a new method that integrates the double layer recurrent neural network (DLRNN) and multistate constrained Kalman filter (MSCKF) to online correct the LiDAR-IMU time delay errors. In this new method, the MSCKF can improve the DLRNN training accuracy while in return the DLRNN can enhance the error estimating performance of the MSCKF. With this mutual improvement strategy, the time delay error can be precisely corrected in both the static and dynamic operation modes of the LiDAR-IMU system. The main contributions include: 1) Dual-information fusion is

Delay effectsLaser radarIght detection and ranging inertial measurement unit lidar imuMeasurement uncertaintyOnline correctionQ measurementRecurrent neural networksIme delay error