## 4 Experimental Results
### Results Analysis  
Figure 9 shows the error histograms for latitude and longitude using the equation of time correction. They show the absolute error in percentage in the X axis and in the Y axis the number of measures in which the error is given by the X axis. The error percentage for the latitude is:  
\[e_{latitude}\%=\frac{e_{latitude}}{180}100\]  
Similarly, for the longitude:  
\[e_{longitude}\%=\frac{e_{longitude}}{360}100\]  
Figure 9: Histograms showing the absolute percentage error. (**a**) Latitude histogram; (**b**) Longitude histogram.  
The interpretation of these histograms is that most days only have a small error. For instance, more than 10.000 days (almost 35% of the total number of tested days) had less than 1% error in longitude. The red line shows the accumulated percentage. The errors for longitude is less than those for latitude.  
Figure 10 shows the same histograms as in Figure 9 but with kilometers as unit converted using \(1^{\circ}=111.12\) kilometers in latitude and \(1^{\circ}=111.12\cos\varphi\) kilometers in longitude. Moreover, Figure 11 shows a dispersion plot with the error obtained for each day. The results obtained prove that the algorithm works well using only sunlight intensity data. However the error in kilometers is high for most common applications. The dispersion plot (Figure 11) shows that most points are close to the origin. The longitude accuracy is high while the latitude accuracy is somewhat worse, though acceptable. Thus, the dispersion plot is concentrated in a vertical line due to the equinoxes.  
Next, Figure 12 shows results from days where the sunlight signal is noisy and where there were more than two transitions per day. Here, the points are concentrated around zero error and in a vertical line. However, in this case the accuracy is not as high as in the previous examples.  
Figure 11: Dispersion plots of the results. (**a**) Total dispersion plot; (**b**) Dispersion plot focused on the origin.  
Figure 13 also reveals how the error percentage for a given value (manually chosen) varies among different stations as a function of the elevation over the sea level. This image also includes a linear regression plot. Although there too few stations to reliably assess the tendency, it is possible to assert that the higher the station the lower the error. If a station is higher, it will _see_ the sunrise earlier (or the sunset later). This can be translated in terms of decreasing the threshold values (Section 4.1) in function of the height of the sensor over the sea level. This has the same effect as the height: anticipating the sunrise or delaying the sunset. But this parameters depends on the light sensor employed and it also requires a height sensor.  
Figure 12: Dispersion plots of the results for days with noisy measurements.  
Figure 13: Error percentage against elevation of the stations.  
Finally, Figure 14 shows the error of the algorithm for 2010 data for one of the stations. It is interesting to compare this graph with Figure 6. It is possible to see how the equinoxes increases the error enormously in the latitude. On the other hand, the longitude error points out that the error of the system is higher than the error introduced because of the Spencer EqT. Thus, the critical part of the algorithm is to identify accurately the sunrise and sunset times.