Kalman Filtering Explained

Here I explore the Kalman filter. I am seeking an intuitive, conceptually if not geometric understanding of the Kalman gain matrix.

Literature Search

I start by reading some popular explanations. The first thing I found was this article by a data scientist named Ben Ogorek. He pointed me to a popular stack exchange question and recommend and answer that the author (of the answer) posted on his own website. The article can be found here.

Here is a article with pictures.