## 3 Indoor Positioning Systems
### Systems Based on Radio Frequency
#### 3.1.2 Range-Free
A more general way of using connectivity information is to use the centroid algorithm, where the position estimate is calculated as the centroid of the position of the received anchor nodes [1], that is:  
\[\hat{m}=\left(\frac{1}{N}\ \sum_{i=1}^{N}x_{i},\ \frac{1}{N}\ \sum_{i=1}^{N}y_{i}\right), \tag{4}\]  
where \(\hat{m}\) is the estimated position of the mobile node and \(x_{i}\) and \(y_{i}\) are the \(x\) and \(y\) coordinates of the \(i_{\text{th}}\) anchor node, respectively. In the centroid method, the accuracy of the position estimate depends on the number of nodes used in the calculation, and a margin of error that remains within predefined limits is tolerable. In general, the level of precision obtained is related to the order of the average distance between anchors implanted in the building. The advantage of the method is its computational simplicity, regardless of the physical or organizational aspect of the scenario. Examples of RFID-based proximity methods can be found in the works of [PERSON] et al., [PERSON] et al., and [PERSON] et al., where the authors review the RFID-based location methods available in the literature [66; 67; 68]. Proximity methods provide accurate position estimations of rooms using low-complexity algorithms [65]. The system's scalability can be achieved by adding more nodes to the network to increase the coverage area. The cost of the system is low if passive RFID tags are used. ZigBee is a wireless communication standard developed by the ZigBee Alliance, which was registered with the IEEE 802.15.4 standard as its physical layer and medium access control [69]. The model was proposed to meet the need for wireless networks with low energy consumption costs and data transmission rates [43]. The architecture of an indoor positioning system based on the ZigBee standard comprises a network of sensors that provide signals to algorithms already known and applied over a wireless sensor network [43]. These algorithms use RSSI values to estimate location, as in other Wi-Fi-Bluetooth techniques, and even in more sophisticated models, such as digital printing and signal propagation [70; 71]. [PERSON] built an indoor positioning system with ZigBee technology [72]. The author combined different approaches, such as signal propagation and fingerprinting, and calculated the best forecast for the location. The results of the experiments show that combinations of techniques provided better positioning compared to individual methods, including approaches using gradients and approximations of linear squares. The model's precision level was around 1.25 m, which corresponds to 98.67% correctness on the mapped locations. Fingerprinting methods: The fingerprinting location system uses the characteristics of information perceived in certain locations, which must be previously identified. Thus, the method requires two phases to be observed: an offline phase and an online phase. In the first phase, the area is divided into small cells to specialize in the identification of each place of interest, allowing the collection of data to form a database. The central idea of the digital printing method is to store a signal pattern in a similar way to a relational database. This pattern is used as a reference in the search for a value by equivalence or approximation. In the second phase, the position is estimated by comparing the captured data with the records stored in the database. When the fingerprinting method is used to map locations through radio signals, the main concern is to perceive the singularity of the signals in different positions due to propagation problems caused by the complexity of indoor environments [2; 27]. Usually, in indoor environments, different types of radio signals can be received, such as signals from Wi-Fi, WSN, or Bluetooth networks implanted in buildings, or coming from the external environment, such as GSM or LTE signals.