One of the important issues being explored in Industry 4.0 is collaborative mobile robots. This collaboration requires precise navigation systems, especially indoor navigation systems where GNSS (Global Navigation Satellite System) cannot be used. To enable the precise localization of robots, different variations of navigation systems are being developed, mainly based on trilateration and triangulation methods. Triangulation systems are distinguished by the fact that they allow for the precise determination of an object’s orientation, which is important for mobile robots. An important feature of positioning systems is the frequency of position updates based on measurements. For most systems, it is 10–20 Hz. In our work, we propose a high-speed 50 Hz positioning system based on the triangulation method with infrared transmitters and receivers. In addition, our system is completely static, i.e., it has no moving/rotating measurement sensors, which makes it more resistant to disturbances (caused by vibrations, wear and tear of components, etc.). In this paper, we describe the principle of the system as well as its design. Finally, we present tests of the built system, which show a beacon bearing accuracy of Δφ = 0.51°, which corresponds to a positioning accuracy of ΔR = 6.55 cm, with a position update frequency of fupdate = 50 Hz.