Résolution d'ambiguı̈tés entières sur graphes interférométriques et GPS

The notion of integer ambiguity resolution is associated with the problem of finding the point of  $\text{Z}{}^{\mathrm{n}}$ closest to a point of  $\text{R}{}^{\mathrm{n}}$, the distance being the one induced by a given quadratic form. This problem is solved with the aid of computational techniques currently used in algebra of numbers. The notion of reduced basis then plays a key role. In interferometry (more precisely in phase closure imaging) and in GPS (Global positioning system), the statement of these problems also appeals to the notion of a graph, and thereby, to the related linear algebra. The corresponding approach, which is very attractive from a conceptual point of view, finally leads to very efficient solution methods.