Indoor positioning seems to be one of the most challenging positioning problems. Many techniques have been proposed for many years now, ranging from inertial sensors to light-based systems. So far, our approaches have been based on a very simple basis : since GNSS (Global Navigation Satellite System) receivers are widely available on mobile terminals, why not use them. Thus, the main principles are based on so-called pseudolites (acronym for "pseudo satellites") which consist in deploying local transmitters. For the last few years, we successively proposed the "repeater" and the "repealite" concepts [9]. We now introduce a new system based on so-called "Grin-Locs". A Grin-Loc is characterized by its ability to carry out absolute positioning with carrier phase measurements. The main advantage of Grin-Locs is that there are no longer any synchronization constraints. Measurements from any two different Grin-Locs are completely independent: the induced simplification of the deployment aspects is huge. Each Grin-Loc is composed of two antennas loc ated one wavelength apart from each other. The locally generated signals are using two different codes and the standard receiver carries out measurements of the difference of the carrier phases of the two above mentioned signals. In our implementation of the system, the calculations of the position are based on the in tersection of quadrics. Note that with this approach, measurements are non-ambiguous. The present paper briefly describes the principle and the associated mathematics of the Grin-Loc based positioning in the specific case of a single transmitter composed of six double antennas. The mounting can be seen as a multi-radar system located at a single position. Of course, this setting is not optimal n terms of Dilution Of Precision (DOP), but gives an idea of the potential and limits of the proposed approach. In addition, the end of the paper shows achievable performances in the case of a deployment of several such mountings. As expected, positioning accuracy is very good with no noise and rapidly increases with it. Coverage maps are provided as output of the various simulations