We present a tightly-coupled multi-sensor fusion architecture for autonomous vehicle applications, which achieves centimetre-level accuracy and high robustness in various scenarios. In order to realize robust and accurate point-cloud feature matching we propose a novel method for extracting structural, highly discriminative features from LiDAR point clouds. For high frequency motion prediction and noise propagation, we use incremental on-manifold IMU pre-integration. We also adopt a multi-frame sliding window square root inverse filter, so that the system maintains numerically stable results under the premise of limited power consumption. To verify our methodology, we test the fusion algorithm in multiple applications and platforms equipped with a LiDAR-IMU system. Our results demonstrate that our fusion framework attains state-of-the-art localization accuracy, high robustness and a good generalization ability.