Bayesian estimation of time-varying processes: discrete-time systems

# Project Work (2011)

Each student should select a project work topic from the list below and report it to the teacher latest on March 17th, but preferably already during the February. You can ask for more information about the topics from the lecturer. Also note the the last topic is "Own Topic" and the best project work would be one where you apply the methods to an application within your own research area.

• The project work should be returned to the lecturer (simo.sarkka@tkk.fi) by e-mail in PDF form latest on April 17th.
• The document should contain:
1. Introduction, which explains the research problem in informal terms.
2. Theory section, which describes the theory behind the application and/or methodology and cites books and scientific articles, where the theory can be found.
3. Simulation/results section, where the method is applied to a simulated or real application.
4. Summary section, which summarizes the results.

## Topics

1. 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).
2. Simulate the pseudo-range measurements done by GPS receiver and implement EKF or sigma-point filter, which estimates the position of the GPS receiver.
3. Implement teaching of MLP neural network with EKF, UKF or other non-linear Kalman filter.
4. 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.
5. 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.
6. Phase locked loops (PLL) and their relationship with extended Kalman filter.
7. Hidden Markov models (HMM), Viterbi decoder and their relationship with optimal filtering and smoothing.
8. Restauration of audio signals with EKF or other non-linear filters.
9. Constrained Kalman filtering.
10. Continuous-discrete-time non-linear Kalman filters.
11. Continuous-time non-linear Kalman filters.
12. Theory of continuous-discrete time filtering, Fokker-Planck-Kolmogorov equations.
13. Theory of continuous-time filtering, Zakai equation, Kushner-Stratonovich equation.
14. Own Topic.

Last modified: Thu Feb 17 20:34:01 EET 2011