Figure 2. Past light cone of an event in 3 dimensions, the proper time parameterized paths of 3 SVs (in violet) and the lightlike geodesics (in green) followed by the signal from each sate-llite to a event of the trajectory of a receiver. Figure 1. Relativistic emission coordinates: intersection of the four future light cones of the SVs with the past light cone of a receiver. In the Figure only 3 light cones of the SVs are drawn in a Lorentzian spacetime of 3 dimensions. thematical fact that four future light cones generically in- tersect in an unique event, which is just the spacetime position of the receiver or user. dimensional International Terrestrial Reference System (ITRF), which is also an ECEF, plus the International Atomic Time (TAI) and the 3-dimensional International Celestial Reference Frame (ICRF) plus the TCB time be- long to this usual causal Newtonian class. In this relativistic positioning system, any receiver or user at any event in a given spacetime region can know its proper coordinates. The four proper times of four sate- llites ( { τ $^{A}$} ; A = 1 , 2 , 3 , 4 ) read at an event by a receiver or user constitute the null (or light) proper emission coor- dinates or user positioning data of this event, with respect to four SVs, see Figure 2. These four numbers or pa- rameters can be understood as the “distances” between the reception event and the four satellites. As it has been commented above, among the 199 Lorentzian causal classes, in which the four Newtonian ones are included, only one is privileged to construct a generic (valid for a wide class of spacetimes), gravity free (the previous knowledge of the gravitational field is not necessary) and immediate relativistic positioning sys- tem. This is the causal class { s s s s , S S S S S S , l l l l } of the Coll homogeneous coordinate system [4, 2, 5]. In this causal class the null emission coordinates of the Coll positioning system are included. These emission coordi- nates have been also studied in [9, 10, 11] in the special case of a flat Minkowski spacetime without gravity. In a certain domain Ω ⊂ R 4 of the grid of parame- ters { τ $^{A}$} , any user receiving continuously his null emis- sion coordinates from four satellites may know his tra- jectory in the grid of parameters. If the observer has his own clock, with proper time denoted by σ , then he can know his trajectory with proper time parametrization, τ A = τ $^{A}$( σ ) , and his four-velocity, u $^{A}$( σ ) = dτ $^{A}$/dσ . For positioning out a GNSS constellation, i.e. for inter- planetary missions in the Solar system, a “pulsar” Coll relativistic positioning system can be conceived, based on the X-ray signals of four properly selected stable mi- llisecond pulsars and a conventional origin of the emi- ssion coordinates. On the other hand, a navigation project called XNAV (based in pulsars) is being developed during the last years by DARPA and NASA but unfortunately, see [13], is based in the same Newtonian concepts that the GPS or Galileo. However, in this case, it is more compli- cated because post-post-Newtonian corrections must be implemented. The coordinate system of this causal class is always ho- mogeneous and it has associated four families of null 3-surfaces or equivalently a real non-orthogonal null coframe, whose mutual intersections give six families of spacelike 2-surfaces and four congruences of space- like lines. Such a coordinate system does not exist in a Newtonian space-time where the light travels at infinite speed. One satellite clock broadcasting its proper time is des-cribed in the spacetime by a timelike line γ $^{A}$( τ $^{A}$) in which each event of proper time τ A is the vertex of a future light cone. The set of these light cones of a emit- ter constitutes a one-parameter (proper time) family of null hypersurfaces. So, four satellite clocks broadcasting their proper times determine four one-parameter families of lightlike 3-surfaces (future light cones), see Figure 1. Thus, the Coll positioning system makes use of the ma- As the emission coordinates belong to the causal class { s s s s , S S S S S S , l l l l } , there is not a spacetime asym- metry like in the standard Newtonian coframe ( t s s s ) (one timelike “ t ” and three spacelike “ s ”). In emission coordinates obtained from a general real null coframe 4.2. Contravariant metric in emission coordinates 4.1. Coll positioning system 4. RELATIVISTIC POSITIONING