  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-LINS).
