## 3 Indoor Positioning Systems
### Systems Based on Radio Frequency
#### 3.1.1 Range-Based  
There are different ways to extract geometric information from wireless signals. The most common are methods based on the signal propagation time between the transmitter and the receiver, the angle of arrival (AoA), or the intensity of the received signal (received signal strength indicator, RSSI) [44; 45; 46]. Below, we briefly describe the fundamentals of each class of methods, analyzing their advantages and disadvantages. Time-based location: Time-based location uses algorithms that measure the propagation time of a signal between the transmitter and the receiver [44]. This location model is also known as the time of flight (ToF), and applies calculations that indicate the distance, \(d\), between the user and the anchor node, as follows:  
\[d=\frac{c}{4\pi f}\varnothing \tag{1}\]  
where \(c\approx 3\,\times\,10^{8}\) m/s represents the speed, and \(f\) is the signal's modulation frequency. Commonly, 20 MHz are used, resulting in an unambiguous distance rage of 7.50 m. The most straightforward approach is known as the time of arrival (ToA). In ToA, the transmitter includes the time when the signal is transmitted in the radio packet, and the receiver calculates the time spent on the transmission. With this information, the receiver can calculate the distance between two points [9]. The user's position can be obtained using a posteriori method if the distance to several anchor nodes is known. The lateration method estimates the position as the point of intersection of three circles, as shown in Figure 2. The center of these circles is located at the position of the anchor nodes, and the radius is equivalent to the calculated distance estimate. In this model, three circles are needed to obtain a position estimate in a two-dimensional space. The ToA method requires synchronization between all nodes, as the reference time must be the same in all cases [47]. This can be a problem for certain types of wireless networks with simple low-power devices and high restrictions on the complexity of the algorithm, such as WSN  
Figure 2: Lateration method between three nodes (S1, S2, S3) indicating their distances (d1, d2, and d3). that eases the limitation of synchronization between nodes is the time difference of arrival (TDoA). There are two main implementations of TDoA:  
* Calculating the difference in ToA of a signal transmitted to two different receivers: For each TDoA measurement, the transmitter must be in a hyperboloid with a constant range difference between the two positions of the receiver [9]. This method relaxes the synchronization restriction for the receivers. * Calculating the difference in ToA of two signals with different propagation times: Usually, the first signal is the radio packet, propagated in electromagnetic waves (speed of light, 300,000 km/s), and the second is a type of sound signal (340 m/s) [48]. This method eliminates the need for synchronization. However, all nodes must have additional hardware to send both types of signals simultaneously. The use of time-based systems for indoor location has several limitations concerning its accuracy, caused by problems such as building structure, internal layout, and building location, which can cause the signals to be blocked [49; 50]. To overcome this challenge, many studies present the application of combinations of techniques based on synchronized TDoA, based on an efficient hybrid synchronization protocol RBS-PBS. RBS (transmission synchronization in time required) and PBS (transmission synchronization in pairs) are protocols that indicate how the physical resources of the network are combined using codes that modify the number of nodes taking part in the arrangement. The use of these strategies makes the system more robust, reducing its margins of error when compared to the use of traditional TDoA [8]. More recent works are based on UWB technology, which improves the accuracy of the range due to the large bandwidth used [11].