Most of the existing LiDAR-inertial navigation systems are based on frame-to-map registrations, leading to inconsistency in state estimation. The newest solid-state LiDAR with a non-repetitive scanning pattern makes it possible to achieve a consistent LiDAR-inertial estimator by employing a frame-to-frame data association. In this letter, we propose a robust and consistent frame-to-frame LiDAR-inertial navigation system (FF-LINS) for solid-state LiDARs. With the INS-centric LiDAR frame processing, the keyframe point-cloud map is built using the accumulated point clouds to construct the frame-to-frame data association. The LiDAR frame-to-frame and the inertial measurement unit (IMU) preintegration measurements are tightly integrated using the factor graph optimization, with online calibration of the LiDAR-IMU extrinsic and time-delay parameters. The experiments on the public and private datasets demonstrate that the proposed FF-LINS achieves superior accuracy and robustness than the state-of-the-art systems. Besides, the LiDAR-IMU extrinsic and time-delay parameters are estimated effectively, and the online calibration notably improves the pose accuracy. The proposed FF-LINS and the employed datasets are open-sourced on GitHub (https://github.com/i2Nav-WHU/FF-LINSTest).
