## 4 Experimental Results
### Comparative Measurement with others Existing Location Systems  
In order to compare our proposal with others, we have evaluated five wireless sensor location systems:  
* Inductive 1. This is an inductive location system which has enough a number of samples for an adequate training.
* Inductive 2. It is also an inductive location system, but in this case, the number of samples is very low.
* Deductive. This system uses the method based on the equation of spread that we have seen in subsection 4.3.
* The Hybrid method. This is our proposed method.
* Ekahau, which is the basis of many currently used location systems [38].  
For the inductive methods we used a system described in our previous work [11]. As has been previously mentioned, inductive methods need a training phase. For the Inductive 1 and Ekahau methods, we collected 312 samples spread equitably throughout the floor of the building. The floor was split in a grid where sampling points are placed every 2 meters. Thirty observations were taken from each training point; 15 of them were taken one day and the other 15 were taken one week later. In contrast, for the Inductive 2 and hybrid methods we used a subset of 56 samples. For the hybrid method we estimated p(\(o_{i}|l\)) using the histogram method shown in references [30,32].  
In the test phase, all these systems were tested for 40 locations (all these locations were different that the training ones, they were randomly placed and they were not inside the training grid). For each location we gathered a mean of 15 RSS consecutive values. This let us take into account the signal variability in the measurements. Each one of the test samples has been applied to the different location methods. Then, we estimate the error measuring the Euclidean distance between the output of the method and the real location of the sample. Figure 5 shows the results obtained for all the location systems as a function of the number of APs. Their graph follows an exponential tends approximately.  
We note that the Inductive 2 method has a higher localization error than the others. This method had 56 training samples. They were few compared with the Inductive 1 method (312 samples). This difference gives considerably more accuracy in the Inductive 1 than the Inductive 2 method.  
With regards to the deductive model, we note that it did not give good results because the floor where the measurements were taken had many walls, so there was very little accuracy when we estimated their loss.  
The hybrid model proposed in this paper has a stable and optimal graph compared to the rest of systems (with few training measures low errors were obtained). As noted in Figure 5, for a certain number of AP (five APs) its average error remains the second best.  
Finally, the Ekahau system together with the Inductive 2 system are the methods with the worst results.  
In Table 2 we can see the average error and the standard deviation of the approached compared in our experiment. We see that the method with less error is the Inductive 1 (1.23 m), this is because the number of samples is adequate. The model with the worst behaviour is the Inductive 2 (3.02 m). The proposed hybrid method has an average error of 1.80 m, with the advantage that training is minimal. A statistical significance test has been calculated using a paired t-test (the hybrid approach is used as reference). A result labelled with a \"'means statistical confidence of 99%. \"' means statistical confidence of 90%.