## 6 Conclusions  
In this paper two different approaches had been discussed. The so-called deductive methods, which require a model of propagation, a topological information of the environment, and the exact position of the radio stations, and the so-called inductive methods, which require a previous training phase where the system learns the signal strength in each location. The main shortcoming of this approach is that in some scenarios, the training phase cannot be done or could be very expensive. On the other hand, the Euclidean models are optimum when there are multiple access points and few walls.  
In this work we present a hybrid location system using a new stochastic approach which is based on a combination of deductive and inductive methods. This system has been developed for wireless sensor networks using IEEE 802.11b/g standard in order to use a deployed wireless access network that is also used for internet access and data transfer.  
We have tested the errors based on the number of samples and based on the number of base stations. We have estimated an experimental equation based on the graph trends of the errors of the measures obtained. We have compared our proposal with several methods in order to check our approach.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **[PERSON] _et al._** & **[PERSON] _et_** & **[PERSON] _et al._** & **[PERSON] _et_** & **[PERSON] _et al._** & **[PERSON] _et al._** & **Our** \\  & [24] & _al._[25] & [26] & _al._[27] & [28] & [29] & **system** \\ \hline _Analytical_ & _AA/TOA_ & _RSS/TDOA_ & _TOA/RSS and_ & _TDOA/RSS_ & _RSS_ & _RSS_ & _RSS_ \\ _techniques_ & _Outdoor_ & _Outdoor_ & _Outdoor_ & _Outdoor_ & _Both_ & _Indoor_ & _Both_ \\ _In situ used in_ & _No_ & _No_ & _Yes_ & _Yes_ & _No_ & _No_ & _Yes_ \\ _WSNs?_ & _Mean_ & _122_ & _60_ & _2-3.3_ & _2.1_ & _1.86_ & _1.83_ & _1.8_ \\ _accuracy (m)_ & _Stages_ & \(1\) & \(1\) & \(1\) & \(1\) & \(3\) & \(2\) & \(2\) \\ _Extra_ & _No_ & _No_ & _Yes_ & _Yes_ & _No_ & _No_ & _No_ \\ _messages_ & _Centralized or_ & _Centralized_ & _Both_ & _Distributed_ & _Centralized_ & _Centralized_ & _Centralized_ \\ _distributed_ & _Centralized_ & _Centralized_ & _Both_ & _Distributed_ & _Centralized_ & _Centralized_ & _Centralized_ \\ _Recursively_ & _No_ & _No_ & _No_ & _No_ & _Yes_ & _No_ & _Yes_ \\ _update_ & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Hybrid location systems comparison.  
Our system uses a small set of training samples (inductive information). Given the actual signal strength, we use the closest training samples as a starting point. Then, the deductive propagation model is used to obtain the shift from the training samples. A stochastic approach is used whereby the optimal location can be estimated as the point that maximizes the product of probabilities from each of the closest training samples  
Our proposal combines the advantages of the deductive and inductive methods in order to provide accurate measurements in hard environments (few base stations and/or few trained points). The goal of this work has been to reduce the training phase without losing precision. Now, we are trying to find the proposed model by adding other methods in order to obtain more accurate results.  
The proposed method is useful in cases where a good training phase is not practical (very few samples can be taken in advance), and the precise location of some access points is not known. These environments could be military, such as troop deployments inside buildings or discovery squads for hard environments, environments where the radio coverage is not known in advance (unknown deployments), or even environments where there the APs can be on or off at any time (dynamic environments). We are currently working on enhancing the precision of the proposed model. In future work we will evaluate the performance our proposal in hard environments.