## 2 Related Work
### Related Work of iBeacon Deployment  
The effectiveness and accuracy of a standalone implementation of BLE systems are clearly highly dependent on the environmental conditions [22] and devices [35]. Research on improving the maximum accuracy and efficiency of indoor positioning [36], as well as discussions of placement techniques for positioning such as trilateration and cell-based positioning, has been conducted [35]. The linkages between positioning accuracy, iBeacon arrangement and the number of iBeacons were discussed by [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [37], who found additional iBeacons improved positioning accuracy. The lowest average errors were found by the authors of [37], with a hexagonal iBeacon placement pattern relative to pentagonal, square and triangular layouts. [PERSON], [PERSON], [PERSON] and [PERSON] [38] analysed the signal attenuation of iBeacon and simulated the deployment of iBeacons in random-based and grid-based approaches. The results showed that more iBeacons always led to higher positioning accuracy, and the grid-based approach outperformed random-based approach when the grid interval was small enough. Supporting the idea that additional iBeacons improve accuracy, a three-dimensional positioning experiment conducted by [PERSON], [PERSON] and [PERSON] [39] resulted in maximum errors of 1.2 m in a 7 m \(\times\) 5 m \(\times\) 3 m room with four iBeacons, and a decreased maximum error of 0.77 m with an additional four iBeacons. However, receiving six to eight iBeacons at each fingerprint point was suggested by the authors of [23], which was found to be sufficient, as there was minimal incremental benefit and iBeacon coverage beyond that point to further improve the accuracy of positioning [23]. The iBeacons were typically placed in the room in a high position on the wall or the ceiling for most studies, and the test sites were devoid of obstacles such as furniture and computers [39]. As the installation height affects signal quality, [PERSON], [PERSON] and [PERSON] [22] compared the effects of placing the iBeacons on the ground with a height of 1.2 m. The placement of iBeacons on the ground yielded significant drops in RSSI with a maximum distance of only 12 m, as opposed to the 100 m recorded when the iBeacons were installed at a height of 1.2 m. To reduce the time cost of positioning error calculations, [PERSON], [PERSON], [PERSON] and [PERSON] [40] formulated an approximate function to optimise the BLE iBeacon placement method. They found that in various indoor settings, the approximate function was comparably effective with regards to other node placement methods. A more specific exploration of iBeacon placement was studied by [PERSON] et al. [41], who formulated the Crystal-based iBeacon Placement (CiP) method for placing iBeacons indoors, in order to deploy the smallest number of iBeacons to cover the maximum possible area. To ensure this would happen, user devices must be able to receive sufficient iBeacon messages for positioning. This was achieved by initially deploying three iBeacons in an equilateral triangle, and then extending the coverage by placing iBeacons adjacent to the equilateral triangle, creating a \"crystal shape.\" CiP ensures the shortest possible distance between any three iBeacons, which improves positioning accuracy. CiP was analysed both vertically and horizontally; this method provided a 21.16% improvement in accuracy over random placement and Z-placement, as described by [PERSON], [PERSON], [PERSON] and [PERSON] [42]. The CiP method resulted in a relatively lower location error due to the higher quality of the signals. A novel approach to the Beacon placement problem by [PERSON], [PERSON], [PERSON] and [PERSON] [43] aimed at searching for placement and inference strategies that, when combined, would be optimal for any given environment. They achieved this using a neural network formulation of inference, in conjunction with a differential neural layer that encoded Beacon distribution.