Next generation GNSS systems will make triple-frequency signals available in a near future. Such systems have the potential to allow or the determination of the second order ionospheric error term. However, the direct estimate of the second order term from triple-frequency measurements may present severe limitations due to tracking noise problems. A measurement campaign has been undertaken in 2007 in Brest to receive signals from the Giove-A experimental satellite. Based on these data, it is shown that a semi-empirical model can be effectively used to derive ionospheric higher order terms from the phase measurements. The model is briefly described and it is shown that a satisfactory noise level is observed on the results. It is thus anticipated that the proposed procedure will offer a practical way to correct future Galileo measurements for ionospheric higher order errors.