# Relational Positioning Method for 2D and 3D Ad Hoc Sensor Networks in Industry 4.0
## 1 Introduction  
On a daily basis, position location (PL) becomes a more important issue in wireless systems for security and law enforcement purposes, as well as for resource management, new location-based services (LBSs), and applications (LBAs). Thus far, most of the literature has been focused on planar scenarios. However, sensor networks and the Internet of Things (IoT) have become pervasive concepts that are expected to be used in billions of devices with multiple applications. As an example, the number of IoT-connected devices in 2018 was about 7 billion. Nevertheless, the value of IoT and sensor networks is often related to location information. Therefore, the importance of 3D localization becomes more relevant, as it enables a wide variety of new LBS and new LBA. The concept of Industry 4.0 denotes the emergence of smart factories where automated and decentralized production is enabled by the Internet of Things (IoT). In Industry 4.0, all objects in the factory (i.e., sensors, tools, actuators, etc.) are meant to be connected and communicating with each other, in order to make possible automated and smart adaptive production. In smart factories, it is possible to dynamically adapt the factory operation depending on the operator's location. This implies the knowledge of the position of all the involved operators. Additionally, position location information is crucial for sensor fault detection, which ensures an adaptive factory operation. This creates the necessity for developing alternative position location methods for environments in which GPS systems or traditional indoor localization systems are not able to provide information, [1]. In modern network scenarios, position location is necessary to assist network tasks such as routing, resource management, and the delivery of location-aware services. However, in ad hoc and sensor networks, connectivity constantly changes due to variations in propagation conditions, and node activity or node motion, and these variations create changes in the network topology, [2; 3]. In addition to global navigation satellite systems (GNSSs) that provide 3D geolocation for outdoor applications, most existing positioning techniques deal with planar location environments that are not sufficient for many applications, [4]. Although GNSS has been in place for many years with different technologies, currently, its availability and accuracy are often insufficient for indoor applications. It is recognized that 3D localization is necessary for several applications, such as in emergency call services in tall building environments, museum guides, warehouse stock management, crew monitoring, drone localization, sensor deployment, etc. [5]. Additionally, emerging applications, such as event monitoring for vehicular networks (VANET) [6] or special situations for the safety and security of people in smart cities, can be assessed by sensor networks, when accurate sensor location information is available. In the IoT context, location information enables the implementation of new protocols in several functions of the network layer such as routing, sensor energy harvesting, and security. Similarly, it is responsible for enabling multiple applications such as asset tracking, connected vehicles, smart appliances, tracking of people by wearable devices, assisted living, etc. Therefore, innovative localization methods need to be developed in order to adapt to the new paradigms imposed by the classification of heterogeneous sensor nodes. In this paper, we introduce a new relational searching localization method that is not based on any previous localization technique. Some of its advantages are that distances are estimated based on a hop count criterion, and a very low number of known location nodes or anchors are needed to provide sensor location estimation. These characteristics make it suitable for IoT environments, where low-equipped sensors with very low transmission ranges need to be considered.