Courses

This course is an introduction to astrodynamics. It covers two-body Keplerian satellite and planetary motion, the geocentric and extraterrestrial trajectories with applications. Students learn how to represent and describe orbits, using Keplerian orbit parameters. Afterwards, they learn how to change orbits and they plan their own mission design in a final project, where they specify impulses, time of flights, and parameters changes to achieve an interplanetary trajectory. This class also covers the Lambert problem, ballistic missiles, gravity assists and fly-by.

This course introduces students to the concept of estimation and gives them the first tools to solve the filtering problem. At first, the course gives elementary notions of probability and covers random processes. The concept of autocorrelation, spectral functions, central moments, and randoma variable transformations are here analyzed. The class covers the response of linear systems to random inputs.

Afterwards, basic estimation techniques are covered, with focus on Maximum Likelihood, Least Square, Maximum A Posteriori, and Minimum Mean Square Error. The students learn how to obtain estimates according to the different approaches.

Laslty, the propagation of uncertainties and estimation are merged to derive the discrete and continuous Kalman filter, with focus on theory and applications. Smoothing is shown and analyzed. Then, thanks to linearization of nonlinear dynamics, the Linearized (LKF) and Extended Kalman Filter (EKF) are studied. Afterwards, the Unscented Transfoamtion and the Unscented Kalman Filter (UKF) is covered. To conclude, Particle Filtering is introduced with an explanation of the Bootstrap Particle Filter (BPF), with examples.

This course builds on the concepts of uncertainty propagation and Kalman Filtering to provide high order nonlinear filters derivations with application sin astrodynamics. Thus, this course refresh teh Kalman Filter and its linearization (EKF), to expand to new accurate filtering techniques, covering the Unscented Kalman Filter (UKF), the polynomial update, importance samplings, particle flow, Gaussian multiple models, and particle filtering. The filters are tested in space applications, through the use of astrodynamical system. Therefore, the students learn navigation, orbit determination, attitude determination, tracking, and so on.