## 1 Reference Systems--Relativistic Positioning vs. Localizing Systems
But RPSs do not have this only advantage. They have the following properties according to [PERSON] [14]: They are (1) 'generic', i.e., they can be constructed whatever is the given spacetime class, (2) (gravity-)'free', i.e., no knowledge of the gravitational field is necessary, and (3) 'immediate', i.e., users can know their coordinates with respect to the given RF without delay. Also, [PERSON] and [PERSON] have extended the characteristics of the RPSs to 'galactic positioning systems' [23]. The first experimental result implementing this protocol was performed by [PERSON] et al. [24; 25] using astronomical data from pulsars used to replace satellites. This galactic positioning protocol has also been very recently and successfully implemented on board the ISS by [PERSON] et al. [26] without any reference to the work of [PERSON], [PERSON], [PERSON] et al., which we quote to do them justice. Finally, it can be noted that these RPSs only work if we own \"GPS/Galileo/Beidou...receivers\" and, obviously, we cannot locate an event that is not itself a \"receiver carrier\". To put it succinctly, we cannot locate a star relatively to the terrestrial RS since this would imply that the star \"holds\" a GPS receiver. What we need for is precisely a RLS that avoids completely the need for any kind of receivers. Roughly speaking, a RLS is a \"radar\" system, relativistically localizing events in spacetime and localizing them in an emission grid provided by an underlying RPS. Basically, a RLS is made of five satellites, four of them providing an underlying RPS. These five satellites exchange time stamps so that each can self-locate in the emission grid of the underlying RPS. In addition, they also have the particularity of being made up of completely \"spherical retinas\". These retinas have their own coordinate systems to locate directions of incident light rays as \"light points\" on their surfaces. Typically, for example, these coordinates are the two angles corresponding to latitude and longitude. Each of these retinas can be considered as celestial spheres on which the directions where the other four satellites are located are visualized by points and, possibly as well the direction of events to be located in the emission grid after localization (see Figure 1); which is naturally the goal. Hence, on each retina, there are four points associated with the other four satellites, and they constitute a projective frame for \(P\mathbb{R}^{2}\). But in addition, these four points are also linked at each instant to pairs of time stamps evolving over time and used in the underlying auto-locating process. As a result, we can translate pairs of angle values into pairs of time stamps that provide additional coordinates for each projective point on the retinas (see Figure 2) associated with an event. More precisely, this angles/time stamps translation makes it possible to assign pairs of time stamps to each event detected on the retinas. Actually, four pairs of time stamps only are necessary. Then, from a reconstruction process, we can assign to each detected event four time stamps from which the event can be located in the emission grid of the underlying RPS. This is a kind of generalization of the now well-known reconstruction process from which 3D views can be obtained from two 2D pictures. From this reconstruction process based on four projective 2D pictures, we get a projective 4D spacetime, i.e., the geometric structure of spacetime is the projective space \(\mathbb{PR}^{4}\). This structure is intrinsic and fully relativistic. No hypothesis is made as to the geometric nature of the Riemannian differentiable manifold of spacetime. In particular, no Lorentzian metric is assumed as well as a possible temporal orientation of spacetime. Only the existence of a minimal causal axiomatics [16] and the complete characterization of the intrinsic projective geometry of the \"retinas\" are necessary.