Localization by analysis of the geometrical deformation of a network of communicating entities

We propose an approach for future localization systems which is quite different from the Global Navigation Satellite Systems standard. The idea is to think about the localization process in a relative way, i.e. to consider the entities with regard to each other. We aim at designing a relative system in order to simplify the practical aspects (low power because low range, no complex synchronization processes, etc.), but also in order to considerably improve the precision (by using local phase measurements of carriers typically). The main idea is based on the fact that it is often sufficient to have a 'local understanding' of the localization and that the knowledge of the 'geometry' of the distribution of a set of entities allows us to perform the mission. Furthermore, we know that it is possible to achieve accurate relative measurements between two entities, by using measurements of phases of a carrier for example. We shall thoroughly describe the problem of what could be a precise positioning system not requiring any specific infrastructure, and affordable in terms of technologies as well as low energy consumption. This is made possible by use of mature technologies and by the fact that the proposed radio communication links are carried out at short distances, only between two entities. We suggest using only Doppler-like measurements, similar to a radar approach, but through a single way transmission. It is then possible to know the value of the projection of the difference of the speed vectors of the two entities on the axis which separates them. By using only these measurements, we define a new type of positioning and we also analyze the possibility to go back to an absolute positioning, sometimes made possible by the availability of absolute data, as distances or geographical coordinates of a few terminals. In a second approach, we deal with geometry (the calculation of angles) while introducing measurements relative to a reference terminal. Having studied the feasibility to calculate the various angles, from only Doppler-like measurements of four terminals relatively with the others, we show it is possible to obtain the relative positions of the entities. The problem is however not trivial because numerous symmetries exist. Simulations allow us to provide first validations of these concepts. A third approach, still based on relative measurements between two terminals, consists in using distance measurements. We could envisage for example time of flight measurements between two Ultra Wide Band (UWB) knots. In such a case, the calculations are much easier.