# A Review of Pedestrian Indoor Positioning Systems for Mass Market Applications
## 2 Network Based Systems
### Range Based
#### 2.1.3 Rss  
RSS based localization methods estimate the distance between the user and an anchor node using the received signal strength. These methods are based on the concept that the attenuation suffered  
Figure 3: Triangulation method concept.  
by a signal travelling from a transmitter to a receiver depends on the distance travelled. In order to estimate the distance it is necessary to model the wireless environment using a propagation model. Traditionally, the log-distance path loss model is employed, where it is considered that the attenuation (in dB) is proportional to the logarithm of the distance travelled [17], that is,  
\[RSS=P_{1m}-10\alpha\log_{10}d-\gamma, \tag{2}\]  
where \(d\) is the distance between the receiver and the transmitter, \(P_{1m}\) is a reference power measured in dBm at a distance of 1 m from the transmitter, \(\alpha\) is the path loss exponent and \(\gamma\sim\mathcal{N}\left(0,\sigma_{\gamma}^{2}\right)\) models the effects produced by the shadowing. Note that in order to obtain the parameters of the model, i.e., \(P_{1m}\) and \(\alpha\), a small calibration campaign is done at each scenario. The calibration process consists in the collection of the RSS in predefined positions with known distance to anchors and the computation of the model parameters, which is usually done using regression methods. Figure 4 shows the calibration process with the collected samples and the computed log-distance path loss model.  
Once calibrated, distance is estimated according to the path loss model using the Maximum Likelihood Estimator (MLE), which for the case of the distance estimation is [18]:  
\[\hat{d}=10^{\frac{RSS-P_{1m}}{10\alpha}}. \tag{3}\]  
As in the case of time based localization algorithms, the position of the user is estimated combining the distance information of multiple anchor nodes using a lateration method [19]. RSS based methods are attractive due to its inherent simplicity, as far as the RSS measurements are natively supported by most transceivers. Unfortunately, the variability of the wireless channel jointly with the attenuation of the signal due to walls, objects or the human body introduce errors in the distance estimation and makes the RSS based localization algorithms less accurate than time or angle based algorithms. A review of the main sources of error of RSS based algorithms can be found in [20] where the authors also include a list of recommendations for the appropriate implementation of RSS based algorithms.  
An example of a RSS based localization system can be found in [19], where authors use the correlation between the RSS samples in nearby locations to fit different path loss models depending on the position of the user and therefore adapt to changes of the propagation model between areas of the same building. In [18] a cooperative method for the localization of the nodes in a WSN is presented. Other authors employ multiple receivers to enhance the ranging accuracy of RSS measurements and to provide coarse estimations of the heading of the user [22]. In [23] a Bluetooth based system is presented employing a stigmergic approach to mitigate the multipath fading. A comparison of the accuracy of  
Figure 4: Calibration of a propagation model.  
the RSS based methods versus the time based methods is presented in [21] where the authors compute the Cramer-Rao bound under Gaussian and log-normal models.  
RSS based systems can be easily scaled to large areas and multiple number of users due to the simplicity of the RSS measurements (note that the RSS measurements can be obtained even without having to be part of the network). Furthermore, the cost of the system infrastructure is minimum if WiFi networks are employed as they are already worldwide deployed. Unfortunately, the accuracy provided by RSS based systems is low and is negatively affected by the distance between the transmitter and the receiver.