Summer of Math Exposition

Fun quick video on a topic that was worth talking about, thanks! The historical context helped make it memorable.

I think some of the background music was distracting.

This was a pretty good introduction to the Kalman filter and the exposition was nicely done. It could use a bit more polish on some of the animations and the conclusion seemed a bit short. The music is also a tad distracting, and I think a brief discussion of how to tune the filter parameters would be useful.

The writer clearly knew what was happening, but the video composition and pace made it hard to understand the quick moving math.

I like the link to Apollo. But I think the explanation could be better, it now follows a bit too much the mathematical formulas.

This submission has great animations, editing, audio, and a great level of detail. I like it, but I think what it lacks is a motivation relevant to a viewer or student: space and apollo missions are always cool, but the understanding is all about one equation, which feels a bit distant. Some “problems” for the viewer, or more relevant and modern examples, could bring it up a bit.

The problem is well-motivated. You do a good job showing the effect each step has, but it would be helpful to see how someone would come up with them. Also, the background music is a bit loud and distracting.

One thing about Kalman filters that I would like to see in the video is a description of how the filter can estimate hidden state parameters given several measurements and a correct model of the system. Bzarg have a good description of this.

The final equation board has too much detail. Maybe you can sparse that out, and focus our attention on some particular things. Or you can explain everything.

I could not follow this exposition, even though I am a PhD student in probability theory and have some (very minimal) exposure to optimal control theory. Unfortunately the explanation doesn’t seem to really say what a Kalman filter is or why the Kalman gain is defined the way it is, and it’s really unclear what I am supposed to take from the examples at the end. Additionally, the production quality is quite low and there seem to be a lot of animations which are not properly synchronized with the voice, which is a bit distracting. But even more distracting is the loud music in the background which suddenly starts and stops. The one place where this video shines is in the history, and I am now convinced that the Kalman filter is incredibly important… I just don’t know what it is.

• 27s introduction too long
• Loved your narration voice
• The 3 mins explanation of the Kalman filter was too fast and hard to follow
• Background jazz is too loud
• Great retro diagrams—maybe could be an interesting source for more visuals?
• Maybe try color coding your equations to correspond to the graph. the notation was a bit hard to pick up quickly. Also I suspect this is a multi-dimensional example, a single dimensional example may have been easier to start with
• Maybe could add more tie-ins to how Kalman filters relate to other mathematical / statistical concepts like Bayesian networks.

The motivation on this piece is great, a very interesting historical story. However the clarity really suffers here. I’d say overall you’ve gone too fast: you’ve introduced terms without really defining them and written variables without explaining what they represent, or which term is which in the equations. As a specific example that’s a bit of a pet peeve of mine, you do examples varying the Q and R terms, but you defined those briefly earlier, and the labels aren’t on the screen anymore, the viewer will have forgotten what those letters stand for and can’t follow the demonstration without pausing the video and going back to figure it out. Until you have worked with a variable for a bit, named it a few times, etc., you really should not refer to it solely by its arbitrary variable name.