# Fast 50 Hz Updated Static Infrared Positioning System Based on Triangulation Method
## 1 Introduction
### Our Previous Work, Motivations and Current Contributions  
Our earlier paper presented a prototype of a Static Triangulation System (STS) [45] with the following parameters: angle measurement accuracy of 0.42\({}^{\circ}\), position determination accuracy of 6.97 cm, and measurement frequency of 12.5 Hz. This system is completely static, i.e., there are no moving/rotating measurement sensors, which makes it more resistant to disturbances (caused by vibrations, wear and tear on components, etc.). Another advantage of such a static system is the possibility of high position update frequencies, which in the case of systems with a rotating measurement sensor is limited by the rotational speed of the sensor. The receiver design (please look at the left part of Figure 1) was based on fabricated Discovery series prototype boards with STM32 microcontrollers. These boards were placed on the prepared PCB construction plate under the housing, which only contains the IR diodes. The overall size of this project was larger compared to the improved version presented in this paper. The operational amplifiers, using through-hole mounting technology, were placed outside the main measurement modules. This positioning could, under certain conditions, cause interference in the analogue measurement paths. The beacon in the previous prototype version consisted of three IR diodes connected in series, surface mounted on a heat sink. Three such beacons were synchronized via a wired path and required an additional microcontroller to manage the cyclic operation. Our earlier prototype of a Static Triangulation System is presented in Figure 1.  
This paper presents a positioning system that improves upon the prototype. It describes a fourfold increase in position reading rate, up to 50 Hz, while maintaining angle measurement accuracy. The frequency of the position update is an important factor when considering highly dynamic and fast velocity objects. For example, a Vecna AMRs robot moves at a speed of 3 m/s, and therefore, for a positioning system operating at 10 Hz, it will move 30 cm between position updates. When the frequency of the positioning system is 50 Hz, the displacement of this robot between position readings is only 6 cm. Current laser scanning systems do not provide better measurements, despite their high cost. Commercial localization systems that use laser scanning for measurement frequency do not perform any better. For example, the ROBOSENSE system from Siman Sensors and Intelligent Machines Ltd. offers a measurement frequency of 10-40 Hz. The LaserNav Position Sensor system from Denning Branch International Robotics has a measurement frequency of 10 Hz, while the AMCO LASERNET beacon tracking system allows measurement at 20 Hz [46; 47]. The updated version of the NAV2 xx sensors offers a measurement frequency of up to 25 Hz [48] compared to 10 Hz in the previous version [47]. To the authors' knowledge, other non-commercial systems using similar hardware do not achieve the same measurement frequency as the authors. The advantages of the solution in terms of compactness (external dimensions of 120 mm) and wireless synchronization of the beacons are presented in addition to the points mentioned above. The beacons have a unique design with a pentagonal shape and integrated infrared emitting diodes, providing an omnidirectional radiation source. The work area can be extended by the addition of one or more beacons. This ensures that two beacons always share each working area. Therefore, a beacon with a beam angle of 360 degrees is required.  
The paper is organized as follows: Section 2 describes the basic principles of the STS positioning system, its design and the test rig used in the experimental studies; Section 3 presents the experimental results obtained under laboratory conditions (outdoor terrace); and Section 4 contains a discussion of the presented results, as well as the conclusions drawn from these results.  
Figure 1: The earlier prototype of the Static Triangulation System.