## 5 Experiments
### Analysis of Results
Accordingly, a big error in terms of distance does not correspond to a big error in terms of RSSI if we analyze the relationship where the curve of path loss has a little slope. We also performed some runs that vary the number of anchors in the estimation of the distances. The results are shown in Figures 11-13, where the vertical axis shows the CDF (Cumulative Density Function) of the RSSI estimated error value and the horizontal axis shows the number of anchors used in the estimation process. At first, we have performed the experiments by using the entire set of ten anchors, and then we iteratively removed one anchor in sequence, estimating again each time the RSSI value. These experiments are intended to analyze what is the needed number of anchors to achieve a given error. This is important to either limit the time spent to perform the measurements when only one real anchor is used at different positions or to reduce the number of different anchors used in parallel. In any case, the minimum number of anchor measurements is clearly three. Looking at the curves, we see at first that the behavior is different for the three scenarios. In the first scenario, which is the simplest one, as soon as the minimum number of anchors has been exceeded (three), the probability of the estimation is not affected by error. Indeed, it increases linearly until 7 anchors are used, then the value is stable until 9 anchors are used and then it increases rapidly with 10 anchors. In contrast, in the other two scenarios, the number of anchors is very important, and the estimation would benefit from using more than only ten anchors. In any case, it is possible to note that the probability that the estimation process is not affected by error increases according to logarithm mode and the probability to have some errors decreases after the application of indirect observations for any number of anchors. The improvement of the proposed method is more visible when the number of anchors is low. In all scenarios, the proposed method increases the probability that the RSSI estimation is not affected by error; indeed, in all the considered cases, the CDF of the proposed method is shifted upwards with respect to the CDF of the multilateration method. On average, thanks to the proposed method, the probability to have a correct RSSI estimation is improved by 15%. Figure 11: Cumulative Distribution Function of the RSSI estimation error at varying number of anchors for the office scenario. When performing the proposed iterative method, we have empirically observed that after three iteration, the gap \((\delta x,\delta y)\) is very small and comparable with the variance of the result \(\sigma\). Therefore, in our experiments, we stopped the method after having performed just three iterations (the results shown before refer to this setting). However, we wanted to further investigate this phenomenon, and in Figures 14-16 we present the average error as the number of iterations in the proposed method increases at different number of anchors. These curves confirm that after three iterations, the method does not benefit from performing more steps for all the cases. Indeed, even the number of anchors does not seem to affect the number of iterations that are needed to achieve a stable result. Accordingly, this number appeared to be a good trade-off between computational costs and accuracy. Figure 12: Cumulative Distribution Function of the RSSI estimation error at varying number of anchors for the conference room scenario. Figure 13: Cumulative Distribution Function of the RSSI estimation error at varying number of anchors for the flat scenario. Figure 8:0 Decrease of error by method iteration in the flat. Figure 8:1 Decrease of error by method iteration in the conference room. Figure 8:2 Decrease of error by method iteration in the office.