The session covered the prediction step of the algorithm as shown in the sessions structure.
To get there we learned about iterated maps, and propagated small perturbations (error propagation) over these maps. The end result was that for a noisy iterated map $$ x_k = A x_{k-1} + B u_{k-1} + \epsilon_{k} $$
the iterated maps for the mean and the covariance are
$$ m_k = A m_{k-1} + B u_{k-1} \qquad P_k = A P_{k-1} A^\top + Q_{k-1} $$
which came out directly of propagating the Gaussian noise through the iterated map.
The participants of this year had a solid background in linear algebra, and well settled notions of iterated maps and ODEs. Hence we went over the material really fast. We covered all what I had prepare for the day and we still had about 2 hours left. We used the remaining time to do individual work on questions and problems selected by the participants.
When I was there, I thought that I should have prepared more material. However, in hindsight, it is really positive to have more time to work individually. There was high motivation to work (I read it as that the material was motivating) and each perform could go deeper in the topic that was of their interest. Super!
For the next section I altered the order I used last time. I will start with examples of application of the KF, to entice and motivate the participants. The examples will include ODE models, even if we have not go over discretization of ODEs. I think this group can handle this, because they are all familiar with the notion of “discretized ODE”.
We will use the first morning session for the examples.
Slides
To download a PDF file with the slides and notes click the image below!
