I am honestly not entirely sure why or what state of mind I was in circa 2017 to write, edit, and act! in this video, but I did.

This is an adaption of a Greek-Style story which someone else wrote, I don’t know who.

Video produced mostly by myself in front of a green screen, with help from my lovely mother as well as a very nice teacher named Joseph O’Brian.

suppose we have some aircraft, let’s consider a sensor on this aircraft which is measuring the altitude:

there’s a true altitude \(h_{t}\) that our system is at, and a measured altitude \(\hat{h}_{t}\), which has some relation.

We can make a observation model through a linear conditional Gaussian:

\begin{align} O \qty(o | s) &= O\qty(\hat{h} | h) \\ &= \mathcal{N}\qty(\hat{h} \mid f_{\theta}\qty(h), \sigma^{2}) \\ &= \mathcal{N}\qty(\hat{h} \mid \theta_{1} h + \theta_{2} \mid\sigma^{2}) \end{align}

algebra is the study of…

• symbols/variables
• transformations/operations: “add”, “multiply”
• simple functions
• abstraction
• substitution