About this online course


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Course video

Many satellite applications require extremely accurate positioning of the satellite in order to be able to interpret the data. For example, measuring the height of the oceans and ice sheets and positioning of tectonic plates requires knowing the position of the satellite with centimeter-level accuracy. Reaching this accuracy for a satellite that flies at 500 km altitude with velocities around 7 km/s is a great challenge. This challenge, also known as "Precise Orbit Determination (POD)", will be addressed in this course.

In the course you will learn techniques such as least squares estimation, and Kalman filtering which are widely used statistical techniques for estimating parameters from observations. Concepts such as reference frames, atmospheric refraction and relativity will also be addressed.

During the lectures and assignments, you will be introduced to various ground and space-based tracking systems, including satellite laser ranging, Doppler tracking, and GPS positioning. The course will provide you with several assignments in order to practice the statistical techniques used in satellite orbit determination.

Shooting problems in relation to parameter estimation as applied during this course can be used in a variety of engineering and scientific applications. You will be able to process large data sets acquired by satellite systems or other instruments and estimate parameters in a dynamic model.

On completion of this course you will be able to:

  • Process real-world satellite tracking data.
  • Estimate satellite orbit and dynamic parameters from satellite tracking data.
  • Understand the scientific applications of satellite orbit determination.


Course Syllabus

Week 1: Introduction to statistics
In this week we will introduce basic statistical tools that you will need for the rest of the course. Concepts such as variance, covariance, and correlation will be discussed. In practice exercises these concepts will be applied to observation data. For the homework assignment in this week you will use range-rate data from the TU Delft tracking station.

Week 2: Satellite Observations
You will learn about the different measurements techniques and observations models for determining the orbit of the satellite. The theory will be about observations to/from satellites, light-time, refraction, relativity. In the end you will be able to identify and discuss the different observations techniques.

Week 3: Introduction to satellite navigation
During this week we will dedicate the course to Global Navigation Satellite System techniques. We will discuss the GPS observation system and its uncertainties. Furthermore, this week will be about linearization of the dynamic and observation models. This weeks assignment will be about the GPS navigation solution of the SWARM orbit.

Week 4: Reference Systems
Reference systems are a main element in satellite orbit determination. This week we will discuss the different reference systems used in satellite orbit determination. The lecture discusses the relation between time systems, coordinate systems, potential fields, Earth rotation, precession, nutation and polar motion.

Week 5: Statistics continued
Because of the importance of your knowledge about statistical data handling, we will discuss more theory this week. Elements of statistics are discussed with respect to constraint equations, linear dependency, and implementation of algorithms. For the assignment this week the GPS solution of previous assignment is used and you will determine some parameters of the orbit and observational models used.

Week 6: Batch and sequential filtering
This week the difference between batch and sequential filtering will be shown. Furthermore, subjects like Kalman filtering, state vector, and covariance matrix will be elaborated. The assignment of this week will be about applying a Kalman Filter on the already used GPS navigation solution.

Week 7: Applications
The theory and exercises from the previous weeks can now be applied on real-world cases. In this week several applications of the theory are discussed and results of the modelling will be shown. We will guide you through the procedures applied during POD and the main results obtained for recent Earth Observation missions such as CryoSat-2 and GRACE.

Assignment(s) and Assessment

Four homework assignments:

  • Counts for 50% of the grade
  • Some can be done in pairs, some can be done individually
  • Strict deadlines of 1 or 2 weeks

A written exam:

Literature and Study Materials

Required: Lecture Notes (will be made available during the course), E.J.O. Schrama, Delft University of Technology.



If you successfully complete your online course you will be awarded with a TU Delft certificate.

This certificate will state that you were registered as a non-degree-seeking student at TU Delft and successfully completed the course.

If you decide that you would like to apply to the full Master's program in Aerospace Engineering, you will need to go through the admission process as a regular MSc student. If you are admitted, you can then request an exemption for this course that you completed as a non-degree-seeking student. The Board of Examiners will evaluate your request and will decide whether or not you are exempted.


General admission to this course

Required prior knowledge

  • A relevant BEng or BSc degree in a subject closely related to the content of the course or specialized program in question, such as aerospace engineering, aeronautical engineering, mechanical engineering, civil engineering or (applied) physics.
  • If you do not meet these requirements because you do not have a relevant Bachelor's degree but you have a Bachelor's degree from a reputable institution and you think you have sufficient knowledge and experience to complete the course, you are welcome to apply, stating your motivation and reasons for admission. The faculty of aerospace engineering will decide whether you will be admitted based on the information you have provided. Appeal against this decision is not possible.

Expected prior knowledge
Satisfactory command of the fundamentals of calculus and physics needed at the BSc or BEng level. Basic programming skills in languages MATLAB or Python are important.

Expected Level of English
English is the language of instruction for this online course. If your working language is not English or you have not participated in an educational program in English in the past, please ensure that your level of proficiency is sufficient to follow the course. TU Delft recommends an English level equivalent to one of the following certificates (given as an indication only; the actual certificates are not required for the admission process):

  • TOEFL score 90+ (this is an internet-based test)
  • IELTS (academic version) overall Band score of at least 6.5
  • University of Cambridge: "Certificate of Proficiency in English" or "Certificate in Advanced English"

Admission process

In order to complete your admission process you will be asked to upload the following documents:

  • a CV which describes your educational and professional background (in English)
  • a copy of your passport or ID card (no driver's license)
  • a copy of relevant transcripts and diplomas


If you have any questions about this course or the TU Delft online learning environment, please do not hesitate to contact us by sending an email.

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