Course Contents Course contents
1 Dynamics
Introduction to dynamics
o Planetary Gravity field
o Tides and the three-body problem
o Hill radius and Roche limit
o Relation to planetary sciences and astrodynamics
Solving Equations of motion
o reformulate orbit problem as a system of ordinary differential equations
o efficiency and accuracy of numerical integration methods
o implementation of numerical integration methods
2 Observations techniques and reference systems
Observation techniques
o Laser, Doppler and Camera observations
o Refraction, Electromagnetism, radio- and optical technology
o Tropospheric and ionospheric refraction
o Relativity and the definition of time,
o Classification of time systems (UTC, TAI, etc)
o Light-time effect
o Quality of clocks (Allan Variance behaviour of clocks)
Reference systems
o Local and global coordinate systems
o Definition of geoid and reference ellipsoid, height systems
o Precession and nutation, polar motion, polar wander.
o Newton or Einstein, consequences for reference systems
3 Statistics
Random variables, probability density functions, moments, hypothesis testing
Least squares minimisation
o unconstrained linear parameter estimation,
o data weighting
o nonlinear parameter estimation.
Rank deficient equation systems
o compatibility conditions
o general and homogeneous solutions
o constrained linear parameter estimation
Mechanisation of parameter estimation algorithms
o Choice of algorithms
4 Orbit determination
Perturbation analysis and variational problems
o state transition matrix for initial state vector problems
o partial derivatives for dynamical parameters
Parameter estimation
o Identification of parameters
o batch least squares
o Kalman filter, theory and implementation
5 Applications
Global Navigation Satellite Systems:
o Technology and terminology,
o various data processing strategies and available software
o Modelling deformation of the solid Earth,
o the Earths gravity field and thermospheric density
Satellite laser ranging and Doppler tracking via DORIS
o technology and terminology, results and applications
Observing changes in the cryosphere with satellites
Hydrology and Oceanography observed with satellites
6 Homework assignments
An exercise related to dynamics, observation systems or reference systems
An exercise related to GNSS applied to orbit determination
An exercise related to Kalman filtering
Exercises with the Ghost software, typical examples are to solve:
o initial value problems (state vector estimation)
o problems with parameters in a dynamic model (drag parameter estimation)
o problems with time bias parameters
Study Goals The candidate should be able to:
1) Explain the physical and mathematical aspects of orbit determination (OD), the topics are
1.1) Solar system dynamics
1.2) Equations of motion and variational equations
1.3) Parameter estimation
2) Construct transformations between various coordinate and time systems that play a role in OD
3) Examine error sources in satellite tracking data and implement error mitigation strategies
4) Make use of parameter estimation methods in the context of tracking data for OD
5) Apply relevant statistical techniques within the framework of OD
6) Discuss scientific applications of satellite missions that depend on precise OD
6.1) GNSS techniques to model the deformation of the Earth
6.2) Satellite gravimetry to model the gravity field of the Earth
6.3) Satellite altimetry to model the ocean topography
6.4) Satellite altimeter missions to measure variations of land and sea ice
7) Apply OD with state-of-the-art software
