## 3 Indoor Positioning Systems
### Systems Based on Radio Frequency
#### 3.1.2 Range-Free
The complexity of the indoor environment produces significant differences between the signals received at different locations due to multiple paths, shading, or propagation in NLOS environments [73; 74]. There are two types of fingerprint methods: those that adopt deterministic strategies and those that adopt probabilistic strategies [19; 75; 76]. Deterministic models indicate high levels of accuracy, provided by high data consumption, the strong density of sensory coverage per square meter, or the combination of techniques to reduce spurious data, as perceived in SNR applications for RSSI signals on a Wi-Fi network. In addition to the k-nearest neighbor (KNN) and the weighted k-nearest neighbor (WKNN), other systems are also used to determine positions, such as support factors (SVMs) or linear discriminant analysis. Still, they have a high computational cost when compared to the KNN class algorithms [75; 76]. In the group of probabilistic approaches, the objective is to find the location with the maximum probability of a set of candidate data. An example of the application of this approach is the Horus system, which uses the distribution of signals in the environment and calculates positions with the maximum subsequent probability [77]. Besides, there are also systems based on Bayesian networks and the Kullback-Leibler divergence [78]. The advantage of using fingerprinting with approximation methods is the reduction of computational and operational complexity since it is unnecessary to arrive at the exact value of the mapped record. The disadvantage of the probabilistic model is the complexity of scaling the system to larger areas. The collection of fingerprinting is not limited to measuring the characteristics of radio signals. Recent works have proven that it is possible to use other types of information, such as the magnetic field [79]. The main advantage of fingerprinting methods used with magnetic field information for RSSI signals is that the magnetic field is more stable. While there are some approaches to indoor location using artificially generated magnetic fields, most modern systems use the strength and/or natural orientation of the Earth's magnetic field to identify locations [80]. An IPS based on magnetic fields uses a magnetometer to measure variations in the magnetic field, which will be used to determine a person's position [81]. The position estimation is commonly performed using methods such as digital printing. However, magnetic fields are less able to individualize the identification of a site, as the same value can be found in many different parts of a building unit. Typically, jobs and applications that use magnetic field-based fingerprints compare fingerprint strings instead of making point-to-point comparisons [82]. The sequences of magnetic fields are recorded in databases or adjacency matrices to improve understanding of the location [81]. Another action that helps to improve accuracy is to create an extensive collection of fingerprints for each point of interest. This process is time-consuming and vulnerable to environmental changes or the movement of humans or objects. The accuracy of a fingerprinting method is causally related to the number of points raised from the mapping [55]. The size of the map can be an additional concern, as deterministic and probabilistic approaches affect its construction. Deterministic methods generally involve less calibration effort than probabilistic methods. In fact, finding the probabilistic values includes calculating the signal statistics at each calibration point [83]. Likewise, locating a person who is moving in an indoor environment requires a larger calibration scheme than locating a static object. Recently, several researchers have shown a keen interest in reducing the effort of the calibration process [84]. One way is to collect data about places using a collaborative approach, where several users contribute to the map as they use the system [14; 84].