Kalman Filter Homework

HOMEWORK MOTIVATION: By the time you face this tutorial, we will have talked about the mathematics of the Kalman filter a lot in class.  The last time that I taught this class, I found that many students had trouble learning the mathematical language of the Kalman filter equations, and an even harder time interpreting this mathematical language.  I want to give you the opportunity to play with various parameters in the Kalman filter equations so that you can see how changing a parameter can alter the behavior of the estimate.

GOAL: Understand how changing various parameters affects the way the Kalman filter works.

  1. Complete the MATLAB tutorial, and summarize what you've learned in one or two paragraphs. 
  2. Repeat the steps done in C7 (concept 7) of the tutorial, but set sig0=10.5 and sest = s + 1.5 * randn(2,1).  Explain the differences from the tutorial results.
  3. Repeat the steps done in the previous problem, but set sig0=1.5 and sest=s+10.5*randn(2,1).  Explain the differences from the tutorial results.
  4. Repeat the steps done in C11 (concept 11) of the tutorial, but set Sx=5*[0.1 0 0 0 0 0; 0 0.1 0 0 0 0; 0 0 4 0 0 0; 0 0 0 0.1 0 0; 0 0 0 0 0.1 0; 0 0 0 0 0 4] and Sz=1*[1 0 ; 0 1].  Explain the differences from the tutorial results.
  5. Repeat the steps done in the previous problem, but set Sx=1*[0.1 0 0 0 0 0; 0 0.1 0 0 0 0; 0 0 4 0 0 0; 0 0 0 0.1 0 0; 0 0 0 0 0.1 0; 0 0 0 0 0 4] and Sz=5*[1 0 ; 0 1].  Explain the differences from the tutorial results.