Indoor positioning with visible light has become increasingly important in recent years. Usually, light sources are modulated at high speeds in order to wirelessly transmit data from the fixtures to a receiver. The accuracy of such systems can range from a few decimeters to a few centimeters. However, additional modulation hardware is required for every light source, thereby increasing cost and system complexity. This paper investigates the use of unmodulated light for indoor positioning. Contrary to previous work, a Kalman filter is used instead of a particle filter to decrease the computational load. As a result, the update rate of position estimation can be higher. Additionally, more resources could be made available for other tasks (e.g., path planning for autonomous robots). We evaluated the performance of our proposed approach through simulations and experiments. The accuracy depends on a number of parameters, but is generally lower than 0.5 m. Moreover, temporary occlusion of the receiver can be compensated in most cases.