Firstly I think the clarity in general is good. The one piece I think you could do with explaining early on is which pieces of what you are describing are the model of the system and which pieces are the Kalman filter. I was following along as you built the markov model of the state matrix etc and then you called those equations the Kalman filter, but I didn't think we had built a Kalman filter yet.

Your early explanation of the filter (as a method for estimating the state of a system under uncertainty) was great but (unless I missed it) when you introduced the equations I wasn't clear that was the filter. I hope that makes sense.

You’re pointing out a real conceptual issue: where the system model ends and where the Kalman filter begins.

In Kalman filter theory there are two different components:

- The system model

- The Kalman filter (the algorithm)

The state transition and measurement equations belong to the system model. They describe the physics of the system and can vary from one application to another.

The Kalman filter is the algorithm that uses this model to estimate the current state and predict the future state.

I'll consider making that distinction more explicit when introducing the equations. Thanks for pointing this out.