Photodiode-based visible light positioning (VLP) systems can achieve centimeter-level accuracy, high positioning frequency, and low signal processing complexity. Thus they can serve as infrastructures for smart cities and smart villages, providing coordinates information for navigation, mobile communication, monitoring, and sensing systems. However, the implementation of such systems requires expensive devices and positioning accuracy is hampered by the imperfection of electronics and beacon light-emitting diode (LED) databases. In this work, a simple and efficient framework for implementing VLP systems is developed. New techniques are proposed for calibrating the non-ideal electronics, and for constructing the beacon LED databases. The framework is compatible with various VLP algorithms and can be realized with economical devices. As an illustrative example, an angle-of-arrival VLP system with four beacon LEDs is built, which has an average 3D positioning error of 1.45 cm, an average rotation estimation error of 1.90°, and a positioning frequency over 100 Hz. All these experimental results show advantages over current state-of-the-art.