## 2 Related Works
### Deductive Methods  
As shown in reference [4], the effectiveness of the measurement techniques based on location algorithms in indoor environments is limited by multiple reflections. That paper describes the RADAR system which is based on RF. The system uses the received signal strength information for a trilateration system and signal propagation models to locate the device. While the empirical model has higher precision, the signal propagation method is easier to use.  
In [14], measurement based statistical models of TOA, AOA and RSS are presented and used to generate localization performance boundaries. Such boundries are useful as design tools to help choose among measurement methods, select neighborhood size, set minimum reference node densities, and compare localization algorithms.  
[PERSON] proposed, in reference [15], a system that processes the signals received from the emitter on an array of sensors. The system considers sensors with arbitrary locations and arbitrary directional characteristics (gain/phase/polarization) in a noise interference environment of arbitrary covariance matrix. The author proposes the multiple signal classification (MUSIC) algorithm to determine the parameters of multiple wave fronts arriving and then the method calculates the position.  
A paper where the authors explain another trilateration based location system is [19]. [PERSON] and [PERSON] present an indoor positioning architecture that does not require a signal strength map, simply requiring the placement of special VOR (VHF Omnidirectional Ranging) Base Stations (VORBA). The accuracy of the positions obtained by their system, of 2.1 meter median error, is comparable to the original RADAR. Its basic idea is to find the strongest maximums in the signal strength, and use them as the most likely directions in which the device can be placed.  
Reference [20] describes two approaches developed by the same authors of this paper, where wireless sensors could find their position using WLAN technology. The scenario is an indoor environment that contains walls, several sources of interferences, multipath effects, humidity and temperature variations, etc. Both approaches are based on the RSS. The first approach uses a training session and the position is calculated based on a heuristic model using the data obtained from the training session. The second approach uses a triangulation model with some fixed access points and a signal propagation model based on wall looses to calculate the position.  
The techniques based on RSS are easier to implement. This is due to the fact that standard wireless devices possess features for measuring this value. As indicated in [21], we must take into account that the location error in triangulation systems is very low when the number of base stations is higher than seven and the triangulation analysis is in three dimensions. As we have said previously, when the number of base stations is high, the location system provides more precision, but it makes the sensor estimate more distances (for every base station), so the sensor could need more processing time, diminishing the overall system performance [20].