This exercise is about the state-space model and Kalman filter. The project consists of two problems and you are asked to implement parts of the Kalman filter recursions. Your implementations does not need to be general, it is sufficient that it works for the situations discussed in the exercises. You can do the implementations in R or any other programming language that can handle vectors and matrices and for-loops. A better alternative than R is for example Matlab. Note that you should implement the algorithms yourself, it is not acceptable just to use functions from for example R or Matlab, or to use a function you find in the internet.

In your project report you should include any code you use to solve the problems and you should visualise your results in informative plots whenever possible. Please use complete sentences in your report, just keywords or half sentences are not acceptable. The report should be handed in as one (and only one) pdf file if you send it electronically. Please avoid the use of appendices in your report, as this makes it much harder to evaluate the report. In the evaluation of the report the focus will be on your reasoning and your discussion of the results, just as much as on the results.

You are allowed to work (and hand in your report) alone or in groups of two persons. You may work with the same person as you did in Projects 1 and 2, or you may work with another person. Write your name(s) on the report, not student or candidate numbers.

To solve the problems you may use the computers in the student computer lab of the Department of Mathematical Sciences. If you don't already have a user and physical access to these computer labs you must send a mail to the lecturer and ask for this.

Problem 1: Text for problem 1. Problem 2: Text for problem 2.