The continuity of the positioning service, in all potential environments, and specifically from outdoors to indoors, is a fundamental aspect when one wants to increase the use of location-based services. Many techniques have so far been investigated, ranging from inertial systems to the latest light fidelity approaches. Besides these physical means, an aspect which is almost as important is the associated processing techniques: calculation methods, fusion algorithms, filtering, etc. This leads to our GNSS (Global Navigation Satellite System) based approach. The basic idea is to take advantage of the wide availability of such receivers and the strength of the related community of engineers and researchers. The principle is based on the so-called pseudolites (a cronym for "pseudo satellites") approach which consists in deploying local transmitters.The concept of the pseudolite has been slightly modified over the last years in introducing successively the repeater and the repealite concepts. We now propose a new system based on so-called "Grin-Locs". They are characterized by the ability to carry out absolute positioning with only carrier phase measurements. In addition, there is no longer any need to synchronize the various transmitters, thus leading to the theoretical reduction, by one, of the number of transmitters required in order to obtain 2D or 3D positioning: two are required in 2D and three in 3D. The technical principle is as follows: each transmitter is made up of two antennas located one wave length apart from each other and fed by synchronized signals. The two signals are generated locally at the transmitter and are characterized by the use of two different codes (many other possibilities are available, but the present papers are dealing with this approach). The receiver, which is a completely standard one, measures the difference of the carrier phases of the two above mentioned signals, leading to the determination of an angle of arrival of these signals (once knowing about the location of the transmitter). Another method of calculation, based on the intersection of quadrics, is also suggested although not thoroughly described in the paper. This measurement does not need any synchronization and is, because of the wavelength separation between the two antennas, non-ambiguous. Using two (respectively three) such transmitters leads to the ability to calculate a fix by means of geometrical intersections of straight lines (or quadrics). The present paper briefly describes the principle and the associated mathematics of the Grin-Loc based positioning, and then focuses on the estimation of the potential achievable accuracy. The estimations are based on real measurements carried out on a uBlox 6T put in appropriate receiving conditions using a Spirent 6560 GPS simulator and a LabSat 2 simulator. As expected, positioning accuracy is very good with reduced noise and rapidly increases when noise increases. Nevertheless, absolute accuracies in the range of 30 cm seem to be obtainable in real conditions