In RSSI-based indoor visible light positioning systems, when only RSSI is used for trilateral positioning, the receiver height needs to be known to calculate distance. Meanwhile, the positioning accuracy is greatly affected by multi-path effect interference, with the influence of the multi-path effect varying across different areas of the room. If only one single processing is used for positioning, the positioning error in the edge area will increase sharply. In order to address these problems, this paper proposes a new positioning scheme, which uses artificial intelligence algorithms for point classification. Firstly, height estimation is performed according to the received power data structure from different LEDs, which effectively extends the traditional RSSI trilateral positioning from 2D to 3D. The location points in the room are then divided into three categories: ordinary points, edge points and blind points, and corresponding models are used to process different types of points, respectively, to reduce the influence of the multi-path effect. Next, processed received power data are used in the trilateral positioning method for calculating the location point coordinates, and to reduce the room edge corner positioning error, so as to reduce the indoor average positioning error. Finally, a complete system is built in an experimental simulation to verify the effectiveness of the proposed schemes, which are shown to achieve centimeter-level positioning accuracy.