7.1416 (4.8556)    2.5496 (2.5282)
         10min.         9.6714 (6.6146)    1.4057 (1.7441)
         15min.         10.9441 (9.0016)   2.1957 (2.2600)
         20min.         11.8008 (8.8068)   2.0546 (2.1367)

  : \[tab:badaVad\] Modelization Errors - Mean and Standard Deviation

Results {#subsec:result}
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Table \[tab:badaVad\] shows the evolution of the mean errors and the standard deviation with time for both models: with nominal values and with tuned values. The first important evidence is the inaccuracy of the Total-Energy Model to model the positions at the beginning of the trajectory. As a matter of fact, for the tuned values, the errors at 2 minutes are the highest. An explanation consists in the fact that the aircraft states (position, speed, heading) change rapidly at the beginning of the trajectory and the selected five parameters are not sufficient to capture this complexity. Furthermore, the optimization of the equation eq.\[eq:opt\] has a global scope and so, the errors generated by local behaviors of the aircraft are ignored in favor of the common behavior. This depends directly on the selected values of $i$,$j$ in $\theta_{i,j}^*$, which in this case are $i=0$ and $j= t_{toc}$ where $t_{toc}$ is the time at top of climb. From our dataset, this common behavior happens around 10 minutes where the errors are 