This paper proposes a visible light positioning system that utilizes commercial Light-Emitting Diode (LED) lamps as transmitters and Silicon PIN photodiodes as receivers. The light signals are transmitted and received using Intensity Modulation and Direct Detection (IMDD). The lamps are modulated using On–Off Keying (OOK) with the Manchester code, and the medium access control is achieved by Time-Division Multiplexing (TDM). The position is estimated using trilateration based on the Received Signal Strength (RSS). The system’s scalability is accomplished by replicating primary localization cells composed of seven lamps and drawing on the neighborhood synchrony, exploiting the spatial multiplexing property of the light. A basic unit in the cell comprises three lamps forming a localization triangle; then, one primary localization cell shall consist of six triangles sharing lights among basic neighbor units. The cell prototype was implemented to prove the working principle of the system. Three estimation methods were used to compute the position: a deterministic approach based on least-squares regression, an Artificial Neural Network (ANN) per lamp, and an ANN for the complete system. The best per lamp estimator was the ANN, computing positions that reached an experimental accuracy of 2.5 cm under indoor conditions.