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:
- Introduction, which explains the research problem in informal
terms.
- Theory section, which describes the theory behind the application
and/or methodology and cites books and scientific articles,
where the theory can be found.
- Simulation/results section, where the method is applied to a
simulated or real application.
- Summary section, which summarizes the results.

## Topics

- 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 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.
- Restauration of audio signals with EKF or other non-linear filters.
- Constrained Kalman filtering.
- Continuous-discrete-time non-linear Kalman filters.
- 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.
- Own Topic.

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