LEARNING OUTCOMES OF THE COURSE UNIT
After completing the course, students should be able to independently solve problems associated with mathematical modeling, verification and testing of designs for space applications.
COURSE CURRICULUM
Lectures:
1. Vector algebra and analysis
2. Differential geometry
3. Differential calculus of a function of two or more variables (including extrema)
4. Integral calculus of functions of two and more variables (double, triple integrals; use in geometry and physics)
5. Transformation: Z-transformation, KLT, SVD, FFT.
6. Relationship of impulse char, and LTI transfer functions. FIR filters
7. Basics of probability and statistics. Random variable. Moment characteristics.
8. Theory of estimation in general: BLUE, ML, LS. Estimation quality criteria.
9. Theory of estimates and testing (point and interval estimation, testing of moment characteristics).
10. Reliability of systems.
11. Random processes. Stationary, ergodic.
12. Spectral analysis of stochastic signals. Autocorrelation.
13. Detection of signals hidden in noise.
Exercises
1. Vector algebra and analysis
2. Examples from the field of differential geometry
3. Differential calculus of a function of two or more variables (including extrema)
4. Integral number of functions of two or more variables
5. Modeling and use of KLT, SVD, FFT transformations in Matlab.
6. Design of filters and modeling of the relationship between impulse response and transfer function of the system.
7. Test or individual work
8. Modeling of a random variable and calculation of their characteristics.
9. Work with estimates and measurement of their quality.
10. Hypothesis testing: simulation, numerical analysis and testing in Matlab.
11. Simulation of random processes.
12. Spectral analysis of stochastic signals. Autocorrelation.
13. Detection and testing of signals hidden in noise. ROC curve.
AIMS
The aim of the course is to present to students a specialized mathematical-statistical apparatus, which is important for understanding and interconnecting the principles of electrical and mechanical systems and practical verification of acquired skills.
