robot or another system in general you just may follow exactly the same steps. You set up the model for the system transition, you set up the model for the measurement and then you derive all the Jacobian matrices which are then required for the prediction and the measurement step of the

Kalman filter. And so in practice after you have set everything up the problem is usually to find good values for the various covariance matrices in the filter. Now when you run your code it will produce this Kalman prediction and correction text file and when you load that you will notice several interesting things. So for example in the beginning our robot sits here

and it doesn't move for the first few steps but it sees those six landmarks. So as it doesn't move the system noise is zero and so in the beginning it will accumulate all the measurements once again which will then result in a smaller error ellipse. As we move on you

can see we have more or less landmarks until we have only two here or even none at this position. So you can see at this position our uncertainty in heading and position is relatively large.

This gets smaller as we have more landmarks in our view and as you see we end up with a pretty smooth and globally correct trajectory. Now let's do the following modification to our code. In the Kalman filter loop I put in this line which means that for a certain position where I may get zero, one or more observations I'll just keep the first observation in the list.

And after we run this we reload the trajectory and now we obtain the following. The trajectory looks more jagged and as we move on we see we always take just one observation if we have at least one and this results in our error ellipse being larger than in the previous case.

But nevertheless our trajectory looks astonishingly good and certainly better than what we've achieved in unit B using our trajectory correction based on an estimation of the similarity transform. Now if we take the last observation instead of the first we will obtain this result which

doesn't look as good anymore. So especially in the beginning we have this movement either due the fact that this landmark is relatively far away and our scanner has maybe some systematic error or due to the fact that this landmark reference position is actually not correct. So

globally we are not doing as good as in the previous case and also notice for example here as we move along how the measurement to this landmark influences how my ellipse is oriented.

So once again this is our final solution and congratulations if you made it successfully through this unit of our SLAM lecture. So see you in the next unit!