1.Basic estimation theory and geometric interpretations
2.Wiener filters; continuous time and discrete time
3.Kalman filters; continuous time and discrete time
4.The innovations Process
5.Stationary Kalman Filter, spectral properties
6.Smoothing (fixed-point, fixed-lag, fixed-time)
7.Numerical and computational issues in Kalman filtering
8.Non-linear filtering
Additional topics selected for the student presentations
After the course, each student is expected to:
- Show a good working knowledge of some fundamental tools (specified by the course content) in optimal filtering.
- Understand to which type of estimation problems linear estimation can be applied.
- Understand the relationship between computational complexity, filter structure, and performance.
- Understand the relationship between optimal filtering, linear estimation, and Wiener/Kalman filtering.
- Approach estimation problems in a systematic way.
- Compute, analyze, and modify state space models.
- Derive and manipulate the time discrete and time continuous Wiener filter equations and compute the Wiener filter for a given estimation problem.
- Derive and manipulate the time discrete and time continuous Kalman filter equations and compute the Kalman filter for a given estimation problem.
- Analyze properties of optimal filters.
- Implement Wiener and Kalman filters (time discrete) and state space models using Matlab.
- Simulate state space models and optimal filters, analyze the results, optimize the filter performance, and provide a written report on the findings.
- Be familiar to the basic theory and know about common methods for optimal filtering in the case of non-Gaussian noise or non-linear models, such as Extended Kalman filter, sigma point filtering and particle filtering.
- Use the acquired knowledge to more easily apprehend research papers in engineering.
- Identify research problems in which linear and non-linear estimation tools may be powerful.
- Apply the knowledge to solve the identified filtering problems.
- Combine several sub problems and solutions to solve more complex problems.
- Show improved skills in problem solving and proof writing as well as in critical assessment of proofs and solutions.
- Show improved skills in oral presentation of technical contents.