1. Satellite geodesy (ge-2112) Introduction E. Schrama

2. Contents What is satellite geodesy Example: GPS navigation solutions Test your knowledge Extended function model –reference systems –items in satellite geodesy –scientific applications

3. What is satellite geodesy? Realize “geodesy” beyond your local horizon with the aid of satellite techniques Observations are range and range rate, or closely related to range and range rate. Parameters are station positions, earth rotation, satellite trajectory parameters, and other related parameters Many applications in science, technology and society

4. Example: GPS pseudo range navigation 1 5 4 3 2 Known: satellite positions satellite clocks 4 ranges Unknown: receiver position receiver clock satellites receiver

5. GPS navigation solution In order to obtain a navigation solution you need to invert the following system of equations In this system the left hand side vectors contains the pseudo range observations corrected for a priori approximations, the matrix contains partial derivatives and the right hand side vector improvements to a priori receiver coordinates and a receiver clock bias. The partial derivatives are obtained from the a priori coordinates. Iterative improvement leads to the eventual navigation solution.

6. Test your knowledge Write out the partial derivatives in the matrix What accuracy is required for the a priori coordinates? Where do the a priori coordinates come from? Rewrite the algorithm for a system of more than 4 pseudo ranges How accurate is the receiver solution in practice?

7. Extended function model In satellite geodesy a general observational model includes more parameters than just coordinates and clock biases Most applications require knowledge of satellite trajectories, GPS provides its trajectories and clocks as a service. Reference systems play a very crucial role

8. Reference systems Relevance of reference systems in geodesy –what again is a reference system? –reference systems in traditional surveying realization of reference systems transformations between reference systems –reference systems in satellite geodesy what is part of such a reference system ITRF vs ICRS, Earth rotation, precession, nutation time reference systems –reference systems in physical geodesy height reference systems –reference systems in physics and astronomy there is a clear synergy

9. Items in satellite geodesy Newton’s laws, inertial - and rotating systems Vision on astronomy before and after Kepler The gravity field is part of the function model Tropospheric and ionospheric delay Other effects: polar motion, tides, various small accelerations acting on the satellite) Processing of data involves instrument parameters, clock delays, etc etc.

10. Scientific applications More accurate station solutions Less redundancy of satellites and receivers GPS receivers on a moving platform Other observation techniques (laser, doppler, etc) Other parameters than stations and clocks Combination with other data