Instrumental Error Analysis of a Static Triangulation Positioning System Using Infrared Beacons and a Ring-Topology Infrared Receiver

Cooperative autonomous mobile robots (AMRs) in Industry 4.0 require precise navigation systems, especially indoors, where global navigation satellite system (GNSS) fails. To achieve these goals, variants of local navigation systems are being developed where localization is based on geometric measurements in a beacon–receiver system. Triangulation systems, based on angle measurements, are distinguished by the fact that, in addition to determining position, they allow precise determination of an object’s orientation, which is crucial for autonomous navigation of mobile robots. This article presents the concept of a triangulation positioning system that is completely static, i.e., it does not contain moving, rotating, or measuring elements, making it more durable, fast, and reliable. The proposed system uses an array of photodiodes evenly distributed on the receiver disk for simultaneous measurement of bearing angles to infrared beacons. A detailed mathematical model of the system is developed and enhanced by experimentally obtained photodiode sensitivity characteristics and analog-to-digital converter (ADC) noise data, and a comprehensive numerical–analytical analysis of all major instrumental error sources is performed. The results confirm that the proposed system achieves positioning performance comparable to state-of-the-art local positioning methods and can be an attractive solution for indoor navigation applications where commonly used satellite systems fail.