The emergence of Automated Guided Vehicle (AGV) has greatly increased the efficiency of the transportation industry, which put forward the urgent requirement for the accuracy and ease of use of 2D planar motion robot positioning. Multi-sensor fusion positioning has gradually become an important technical route to improve overall efficiency when dealing with AGV positioning. As a sensor directly acquiring depth, the RGB-D camera has received extensive attention in indoor positioning in recent years, while wheel odometry is the sensor that comes with most two-dimensional planar motion robots, and its parameters will not change over time. Both the RGB-D camera and the wheel odometry are commonly used sensors for indoor robot positioning, but the existing research on the fusion of RGB-D and wheel odometry is limited based on classic filtering algorithms; few fusion solutions based on optimization algorithm of them are available at present. To ensure the practicability and greatly improve the accuracy of RGB-D and odometry fusion positioning scheme, this paper proposed a tightly-coupled positioning scheme of online calibrated RGB-D camera and wheel odometry based on SE(2) plane constraints. Experiments have proved that the angle accuracy of the extrinsic parameter in the calibration part is less than 0.5 degrees, and the displacement of the extrinsic parameter reaches the millimeter level. The field-test positioning accuracy of the positioning system we proposed having reached centimeter-level on the dataset without pre-calibration, which is better than ORB-SLAM2 relying solely on RGB-D cameras. The experimental results verify the excellent performance of the frame in positioning accuracy and ease of use and prove that it can be a potential promising technical solution in the field of two-dimensional AGV positioning.