How the Kalman filter uses its knowledge of a system's dynamics to predict its next move, and why that derives from Bayesian probability rules

I'm wondering if in some situations, a Kalman filter simplifies to equations that are easy to implement? What do degenerate forms of it look like?

## The Kalman filter on a moving target

I'm wondering if in some situations, a Kalman filter simplifies to equations that are easy to implement? What do degenerate forms of it look like?