For the visual-inertial odometry (VIO) in a robotic system, the performance of localisation can be improved by taking into account uncertainties of sensors. In this paper, an initialisation strategy is proposed with respect to monocular visual-inertial localisation, which optimises the temporal offset between a camera and an inertial measurement unit (IMU). Moreover, persistent refinement is involved in front-end processes, and specific states are optimised in back-end processes. Firstly, with assumption that IMU timestamps are valid, influence of the temporal offset between camera and IMU timestamps is analysed, and the temporal offset is derived from reprojection errors so as to align camera and IMU samplings. Then, taking into account camera samplings, both translation and rotation movement is calculated for projected 3D points, and variation of reprojected image features is analysed with respect to the corresponding camera keyframe. At last, the temporal offset and specific states are estimated by optimising reprojection errors, making that influence of the uncertain temporal offset is eliminated for visual-inertial localisation. Comparative experiments are conducted to validate the performance of the proposed approach.
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