as the first highest point of the trajectory. Also, these trajectories do not have a rate of climb that is equal to zero for more than 30 seconds, they shall reach a cruise level at least of 300 FL and their durations are at least of 1100 seconds. These filtering conditions permits to keep trajectories that are not affected by a level flight clearance.

Methodology {#subsec:method}
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To assess the model, we evaluate the position error between the TP and the real trajectory. Let $\mathcal{H}(\theta;s_0)$ be the sequence of altitudes generated by the simulation of the hybrid system with the parameters $\theta = \left[ m \quad \Delta T \quad V_1 \quad V_2 \quad V_M \right]^T$ and the initial condition vector $s_0 = \left[ t_0 \quad q_0 \quad h_0 \quad V_0 \right]^T$. Then, the measure is simply the sum of absolute errors. In the case of parameter estimation, we search in the feasible space of parameters $\Theta$, the point $\theta \in \Theta$ that minimizes this measure. So, we have the optimization problem: $$\label{eq:opt}
\theta_{i,j}^* = \underset{\theta \in \Theta}{\operatorname{argmin}} \sum_{n=i}^j \left| \mathcal{H}(\theta;s_0)_n - T_n \right|$$ where $\mathcal{H}(\theta,s_0)$ is the sequence of ordered altitudes obtained for given parameters $\theta$ and initial conditions $s_0$ 