1. An Autonomous Relativistic Positioning System Uroš Kostić Martin Horvat Andreja Gomboc University of Ljubljana, Faculty of Mathematics and Physics

2. User Satellite tracking from Earth Constants of motion Coordinate transformation

3. User Satellite tracking from Earth Constants of motion Coordinate transformation emission coordinates (Coll 2002, Rovelli 2002) (from Coll & Pozzo, CQG 23, 2006)

4. User Satellite tracking from Earth Constants of motion Coordinate transformation ISL

5. User Constants of motion Coordinate transformation ISL Data reduction + Clock correction ABC – Autonomous Basis of Coordinates University of Ljubljana, ESA Advanced Concepts Team (Ariadna study 09/1301, 09/1301 CCN, PECS project Relativistic GNSS)

6. ISL perturbed space-time Earth multipoles ocean tides, solid tides Moon, Sun, Jupiter, Venus relativity, Kerr SchwarzschildRegge-Wheeler-Zerilli multipole expansion

8. User Constants of motion Coordinate transformation Data reduction + Clock correction Positioning algorithm in GR

9. User Constants of motion Coordinate transformation Data reduction + Clock correction ABC – Autonomous Basis of Coordinates

12. 12D minimization ABC – Autonomous Basis of Coordinates

13. 12D minimization ABC – Autonomous Basis of Coordinates 12D minimization

14. ABC – Degeneracies no perturbations

15. ABC – Degeneracies Earth multipoles Solid tides Ocean tides

16. t x y ABC – Autonomous Basis of Coordinates

17. ABC – Refinement of gravitational parameters

20. Robustness of recovering constants of motion with respect to noise in the data Consistency of description with redundant number of satellites Possibility to use the constellation as a clock with long term stability Its realization does not rely on observations from Earth No entanglement with Earth internal dynamics No Earth stations for maintaining of the frame Stability and accuracy Based on well-known satellite dynamics Satellite orbits are very stable in time, and can be accurately described Applications in science geophysics, relativistic gravitation and reference frames determine/refine values of gravitational parameters ABC – Autonomous Basis of Coordinates