# A Review of Pedestrian Indoor Positioning Systems for Mass Market Applications
## 2 Network Based Systems
### Range Based
#### 2.1.1 Time  
Time based localization algorithms measure the propagation time of a signal between the transmitter and the receiver, also known as Time of Flight (ToF) and compute the distance between the user and the anchor node \(d\) as follows,  
\[d=\Delta t\;v, \tag{1}\]  
where \(\Delta t\) is the ToF and \(v\) is the propagation speed. The simplest approach is known as Time of Arrival (ToA). In this case the transmitter includes in the radio packet the time when the signal is transmitted and the receiver computes the reception time. Thus, the receiver has all the information for computing the distance. The position of the user can be obtained employing a lateration method, if the distance to multiple anchors nodes is known. The idea behind lateration methods (see Figure 2) is to estimate the position as the point of intersection of three circles. These circles have the center situated in the position of the anchor nodes and the radius is equivalent to the estimation of distance computed. Note that three different circles are necessary in order to obtain a position estimation in a two dimensional space. It is fundamental in a ToA method to take into account that ToA methods require synchronization between all nodes, as the time of reference must be the same in all cases. This can be a problem for certain kind of wireless networks with simple low power devices and high restrictions in the algorithm complexity, as it is the case of WSNs. An alternative method that relaxes the synchronization constraint is the Time Difference of Arrival (TDoA). There are two main implementations of TDoA:  
* The first TDoA method computes the difference in the 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 receiver positions [4]. This method relaxes the synchronization constraint to the receivers. * The second TDoA method is based on the difference in the ToA of two different signals with different propagation times. Usually, the first signal is the radio packet and the second one is a kind of sound signal due to the difference in the propagation speed between the electromagnetic waves (propagate at the speed of light \(\approx\)300,000 km/s) and the acoustic waves (propagation speed \(\approx\)340 m/s) [68]. This method does not need synchronization but the nodes must include additional hardware in order to send two kind of signals simultaneously. One example of a time based positioning system is the Active Bat system [12]. This system is based on the TDoA of ultrasound signals. The user carries a transmitter and the signals are received by a grid of ceiling mounted receivers, which are synchronized using a wired connection. The system reports accuracies within 9 cm for the 95% of measurements. The main disadvantages of the system are related to the placement of the receivers in the ceiling which increases the cost and reduces the scalability. Another example based also in ultrasound signals is the Cricket system [13]. The working principle of the Cricket system is similar to the Active Bat system but in this case the computation of the position is performed by the user which carries an ultrasound receiver. A set of ultrasound transmitters are deployed around the building, which also transmit radio frequency signals for synchronization. More recent works are based on the UWB technology, which improves the ranging accuracy due to the large bandwidth used [14]. The use of a large bandwidth allows to implement shorter pulses which increase the time resolution and accuracy of the ToF estimations. Therefore the accuracy of the positioning system is also improved. The fundamental limits of wide band localization methods are determined in [69; 70] where the problem is extended to cooperative networks. More information about UWB systems can be found in [9; 14]. The main problem of UWB technology when applied to mass market applications is the level of deployment of these networks around the world.