You can reach the course assistant Zheng Zhao (email@example.com) for more information.
Also note the the last topic is "Your Own Topic". Optimally, the project work could be one where you apply the methods to an application within your own research area.
Please use the project work submission folder in the end of this page.
Below some example topics are listed. Some of them are more of literature based and others more of the hands on type. All topics should still include some example(s) related to simulated or real data. Students are strongly encouraged to come up with a topic of their own.
- Find out how the fusion of radar and acceleration sensor measurements works in Apollo Guidance Computer (AGC) and formulate it as a more modern state space model. Simulate and implement the corresponding estimator (EKF).
- Simulate the pseudo-range measurements done by GPS receiver and implement EKF or sigma-point filter, which estimates the position of the GPS receiver.
- Implement teaching of MLP neural network with EKF, UKF, CKF or other non-linear Kalman filter.
- Find out from literature what is a square-root Kalman filter and implement one. Compare the numerical stability of the algorithm to conventional Kalman filter in some almost singular simulated model.
- Discretization and Kalman filter based estimation of a physical system, which is modeled as a partial differential equation. For example, a convection-diffusion equation or wave equation.
- Phase locked loops (PLL) and their relationship with extended Kalman filter.
- Hidden Markov models (HMM), Viterbi decoder and their relationship with optimal filtering and smoothing.
- Restoration of audio signals with EKF or other non-linear filters.
- Parameter Estimation in non-linear State Space Models.
- Constrained Kalman filtering.
- Kalman filtering for linear stochastic differential equations.
- Continuous-discrete-time non-linear Kalman filters. (Useful codes in Github)
- Continuous-time non-linear Kalman filters.
- Theory of continuous-discrete time filtering, Fokker-Planck-Kolmogorov equations.
- Theory of continuous-time filtering, Zakai equation, Kushner-Stratonovich equation. (Useful book: Applied Stochastic Differential Equations. 2019. Simo Särkkä)
- The connection between Gaussian process regression and Kalman filtering and smoothing.
- Kalman filters and non-Gaussian measurement noise.
- Your Own Topic.
The course assignment is returned as a written report in PDF form to the course assistant no later than April 12, 2019. The grading is based on the report. Codes can be included in appendices if they are essential or related to the report. The report should at least contain the following:
- An Introduction. Explains the research problem in informal terms. Based on this, a fellow student on the course should be able to understand how your project relates to the rest of the course.
- A Theory section (Materials and Methods). Describes the theory behind the application and/or methodology and cites books and scientific articles, where the theory can be found.
- Simulation/Results. The method is applied to a simulated or real application. Codes can be included as appendices, if necessary.
- A Summary (Discussion and Conclusion). Summarizes the results and provides insight into the usability of the method. If applicable, also discusses god/bad sides of the approach.
The report must have properly typesetting (e.g., LaTeX). You can use some standard article or report template.
The course work is a compulsory part of the course and must be passed in order to pass the course. The grades in the higher end of the grading scale will be awarded for outstanding performance and potentially interesting viewpoints into the themes. If you fail this part of the course, you will be given an opportunity to refine your report in order to pass the assignment.
(Frequently) Asked Questions:
How much time should be allocated to this part of the course?
Simo has estimated that this part should be a bit more than 1/5 of the whole course. However, as the grade is based on either the exam or the course assignment, those who are aiming for the higher grades should allocate their workload accordingly.
Language to report in?
English. However, you can negotiate with Simo for Finnish/Swedish options.