Beacon placement strategies in an ultrasonic positioning system

Ultrasonic Positioning Systems (UPSs) are widely used to detect, locate, or track targets. One of the key factors that determines the performance of a UPS is beacon placement. In this article, beacon placement strategies for a two-dimensional array in the xy-plane above the target with an adaptive height are studied and optimized as a function of the beacons characteristics and application requirements in terms of positioning precision and particularly reliability. The effect of positioning requirements on placement is also investigated. It is shown that for triangle or square placements or a hexagon placement with a low precision requirement, the optimal side length of each placement pattern is restricted by the upper bounds of the geometry and reliability, and the placement pattern is valid only when there is a gap between those upper bounds and the lower bound specified by the precision requirement. However, for a hexagon placement with a high precision requirement, the optimal side length is restricted by the upper bound imposed by the precision requirement. The use of a high beacon height with respect to the target allows positioning requirements to significantly reduce the optimal side length. In addition to the beacon height, another important factor is the beacon placement pattern, such as triangle, square, or hexagon. A comparison of the obtained results shows that under a loose precision requirement, triangle placement is the best; when it is moderate, either square or hexagon placement is preferred; and if the precision requirement is stringent, only hexagon placement is feasible. From the comparison of beacon placement strategies, an 18% reduction in the numbers of beacons is readily achievable for commonly available beacons.