was updated by adding a rank-one matrix with eigenvector the direction of progress. An improved version with rank-$\mu$ update was later proposed [@Hansen:ECJ03], and several additional variant made it more and more powerful. The most recent version is the so-called bi-pop-CMA-ES [@bipopCMA2009], that evolves both a large and a small population and outperforms previous versions in case of multi-modal functions. All source code is available on the author’s web page (<http://www.lri.fr/~hansen/index.html>), in different programming languages, including the bi-pop version. Using CMA-ES for parameter estimation is then straightforward, and amounts to interfacing the objective function for BADA TP with the core CMA-ES program, after eventually normalizing its parameters.

Model Validation {#sec:modelValidation}
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This section deals both with the empirical validation of the nominal model and the estimation algorithm used to fit the parameters on the whole trajectory.

Dataset {#subsec:dataset}
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To validate our model, we will use a dataset composed of 262 real departure trajectories of A320. These trajectories have been recorded via a radar systems during one month. For one trajectory, there is a data vector at every 5 seconds composed of the aircraft position, the rate of climb and the true airspeed. Then, the top of climb is calculated 