1. 1 Parameter-estimation. Sat05_62.ppt, 2005-12-02..

2. 2 Parameters. Sat05_62.ppt, 2005-11-28. State-vector (position and velocity) Transformation Earth-fixed to Inertial Earth-tides (Love-numbers) Plate-movements Conversion local system to geocentric Gravity field (spherical harmonic coefficients) Solar-pressure, Atmosphere, Ionosphere Clock-errors, Instrument-biases Coordinates of observation-stations May result in SINGULAR system of equations Something must be held fixed.

3. 3 Earth-model. Sat05_62.ppt, 2005-11-28. Station-coordinates + Gravity-field= Earth Model

4. 4 Elimination of parameters. Sat05_62.ppt, 2005-11-28. Some parameters may be eliminated by forming differences: Troposphere (two stations sees the same troposphere) Clock-errors

5. 5 Fixing system. Sat05_62.ppt, 2005-11-28. If only ”geometrical observations”= Directions, distances, didtance-differences Then we are only able to determine Coordinate-differences. Orbits must be used ! The laws of Kepler = Dynamic method Earth-center, Equatorial plane. Rotation axis.

6. 6 Processing. Sat05_62.ppt, 2005-11-28. 1.Observations: Raw data to observations 2.Pre-processing: Correction for atmosphere, time, bias, creates normal-points 3.Computes L 0 =Φ(X 0 ): Numerical Integration, coordinate- transformations 4.Least-squares (+collocation ): 5.Error analysis: 6.Computation and analysis of residuals

7. 7 Basic statistical concepts and least-squares. Sat05_62.ppt, 2005-11-28. 1.Statistical concepts 2.Distributions Normal-distribution 2. Linearizing 3. Least-squares The overdetermined problem The underdetermined problem