In a pure visual odometry, a pose transformation matrix between adjacent two frames is estimated by an algorithm based on pixel variation between images. However, pure monocular visual odometers cannot obtain absolute scales; in addition, relying solely on recursive calculations will inevitably lead to cumulative errors. For pure inertial solution calculations, the low-precision IMU will diverge very quickly in a short time. We derive the IMU prediction form based on Lie group and Lie algebra, and apply it to VIO. Based on the idea of graph opt...