To provide basic knowledge on the design of space missions and the navigation and attitude control systems of satellites and space probes. Ability to size and design simple systems for orbit and attitude determination and control of satellites and space probes. Understanding the development and operations of space missions.
1. Space Missions: An Overview
Main Mission Categories
Landers, rovers, atmospheric probes, and aerobots
Planetary exploration missions: flyby and orbiter spacecraft
Fundamentals of space systems engineering: phases of a space mission and key milestones (reviews).
2. Dynamic Systems and Orbit Determination
Introductory Concepts
Linearization of motion equations and observation equations
The least-squares solution
Linearized dynamics equations: state transition matrix, properties, and examples (e.g., free-return trajectories from the Moon)
Statistical significance of the least-squares solution: covariance matrix and its propagation
Weighted least-squares solutions
Least-squares solution with a priori information
A priori information as additional observations: minimum variance estimator and minimum variance estimator with a priori information
Sequential estimation: Kalman filter and extended Kalman filter
Comparison between batch and sequential estimation
The flyby problem and the uncertainty ellipsoid
Square root methods: Householder transformation and SRIF filter.
3. Attitude Determination and Control
The TRIAD algorithm
The Wahba problem: the QUEST algorithm
Stars and star types
Star trackers, Earth sensors, Sun sensors
Fiber optic gyroscopes and hemispherical resonator gyroscopes
Farrenkopf error model
Attitude errors: APE, AME, RPE
Overview of quaternions and their properties
Introduction to Attitude Control
Linearized Euler equations and gravity gradient stabilization (e.g., the case of a space tether)
Analysis of an LTI system using the Laplace transform
Bang-bang control of an axis and PID control of a spacecraft under impulsive and constant disturbances
PD control of an axis
Wheel desaturation maneuvers: state-space analysis of a triaxial satellite in circular orbit
Stability of a triaxial satellite: Laplace domain analysis
Pitch dynamics of a triaxial satellite in Earth orbit under constant external torque
Dynamics of a triaxial satellite under gravity gradient and constant disturbances in roll and yaw axes
Attitude control with magneto-torquers and pitch control of a satellite in circular orbit
Complete RWA control system
Case Study: Attitude control of Cassini during Enceladus flyby.
4. Observables for Orbit Determination and Radiometric Systems
Introduction to Space Communications: Parabolic antennas (prime focus, Cassegrain) and a simple model for antenna gain. Link budget.
Coherent demodulation: a basic Matlab exercise. Bit rate and bit error rate.
Beam-waveguide antennas: architecture and functions of a ground station
Mathematical model of the spacecraft signal: signal tracking via PLL, Doppler measurements, and range and angular measurements.
5. Time, Clocks, and Reference Systems
Time Scales and Relativity of Simultaneity: Concepts from special relativity and the Schwarzschild metric
Dynamic and kinematic definition of reference systems: WGS84 and ITRF.
6. Relativity and Global Navigation Satellite Systems
Basic principles of Global Navigation Satellite Systems (GNSS)
Time, relativity, and GNSS.
"Statistical Orbit Determination", edited by Tapley, Schutz, Born. Elsevier (2004)
"Spacecraft Dynamics and Control", edited by Sidi. Cambridge (1997)
Additional material can be found in the class notes.