# Relational Positioning Method for 2D and 3D Ad Hoc Sensor Networks in Industry 4.0
## 2 Related Research  
Traditional localization methods using trilateration are commonly used in 2D for the line of sight (LOS) wireless scenarios, resulting in a good performance in the presence of small distance estimation errors [8]. However, those methods do not deal with the 3D multi-hop wireless sensor scenario, in which one generally finds environments with no LOS between nodes and anchors or access points (AP). Thus, range estimations from anchor nodes (with known coordinates) to the node to be located can be based on the aggregation of hop lengths in the connecting paths, which leads to an additive distance error, [9], impairing the node-to-anchor distance estimation process. In ref. [10], the authors propose a beacon-based geometric localization method for 2D sensor networks, where a node initially chooses two reference points, then they create what they call the node's residence area by the range intersection of the two reference points. Subsequently, the node differentiates its estimated position within the residence area using a third reference point, by approximating the radius and half-length of the chord with respect to one of the reference points. Then, the radius and half-length of the chord are used to estimate the sagitta of an arc. Finally, the node estimates its position using the radius, half-length of the chord, and sagitta of an arc. There are several reported works for 3D localization, some of them proposed for indoor environments, where the position of a node is estimated by relating the actual observation with a set of collected observation data previously taken by a set of sensors deployed strategically in the indoor scenario. In ref. [11], the authors provide a survey of indoor position location systems updating the new transmission technologies. In ref. [12], the authors present a survey for indoor localization techniques in the context of IoT. In this paper, the authors discuss different indoor localization systems focusing on user device tracking. They develop an evaluation framework to compare existing indoor localization techniques focusing on the IoT demands. They divide the existing indoor localization techniques into two classifications: monitor-based localization (MBL) and device-based localization, (DBL). In the MBL, a set of anchor nodes passively obtains the position of the user or entity connected to the reference node. In the DBL, the user device uses some reference nodes (RNs) to obtain its relative location. Their evaluation framework focuses on several IoT relevant parameters such as cost, service availability, energy efficiency, accuracy, scalability, etc. Outdoor 3D localization has been commonly conducted through GNSS systems, [4]; however, there is a need to develop alternative 3D PL techniques suitable for places where satellite coverage is not available or limited. In [13], the authors present a localization system for 3D ad hoc networks using aerial sensor nodes equipped with UWB devices to provide 3D positioning capabilities. The proposed technique in [13] firstly uses a local coordinate system that is defined using sensor nodes. Secondly, a calculation of the sensor's coordinates is performed based on a regular trilateration technique. Finally, the sensor nodes progressively become anchor nodes as their locations are estimated. The method is evaluated in a single hop scenario. The method relies on nodes upgrading with UWB devices and antennas to provide 3D positioning capability. The system performance depends on the goodness of distance estimation. In [14], the authors propose a received signal strength indicator (RSSI) range-based 3D localization method for wireless sensor networks, where they formulate a degree of co-planarity and combine it with the traditional DV-Distance algorithm. Then, the set of four anchor nodes with the best degree of co-planarity (the flattest) is selected to calculate the node-of-interest location using simple quadrilateral.