Visible light positioning (VLP) based on light-emitting diodes (LEDs) attracts wide attentions for its high accuracy, low cost and real-time services. Existing single-LED VLP system can provide real-time and accurate services when the user is located in the adjacent area of the LED. However, as the distance from the user to the LED increases, the positioning error increases dramatically. Even though more LEDs are deployed, there lacks an explicit criterion to fuse the LED signals. This paper proposes an indoor positioning system with higher accuracy by selecting the best LED available. We install $N$ LEDs on the ceiling, and each LED provides the user with a positioning result based on the single-LED positioning algorithm. Minimum radiation angle (MRA) criterion is proposed to select the most accurate positioning result among the $N$, which is more accurate than that of the single-LED positioning algorithm. We derive closed-form positioning error expressions of the MRA-based AOA positioning, which serves as a theoretical foundation for LED deployment. Simulation experiments show that the proposed MRA criterion can increase the positioning accuracy, and the analytical error expression of the MRA is reliable.