In Kalman filters we iterate measurement and motion.
This is often called a "measurement update,"
and this is often called "prediction."
In this update we'll use Bayes rule, which is nothing else but a product or a multiplication.
In this update we'll use total probability, which is a convolution,
or simply an addition.
Let's talk first about the measurement cycle and then the prediction cycle,
using our great, great, great Gaussians for implementing those steps.
Suppose you're localizing another vehicle,
and you have a prior distribution that looks as follows.
It's a very wide Gaussian with the mean over here.
Now, say we get a measurement that tells us something about
the localization of the vehicle, and it comes in like this.
It has a mean over here called "mu,"
and this example has a much smaller covariance for the measurement.
This is an example where in our prior we were fairly uncertain about a location,
but the measurement told us quite a bit as to where the vehicle is.
Here's a quiz for you.
Will the new mean of the subsequent Gaussian be over here, over here, or over here?
Check one of these three boxes.