Localization

Now, you've learned the foundation of all localization techniques!
You know that:, first, a robot starts out with some certainty/uncertainty about its position in a world, which is represented by an initial probability distribution, often called the initial belief or the prior. Then it cycles through sensor measurements and movements.

Sense/Move Cycle

1. When a robot senses, a measurement update happens; this is a simple multiplication that is based off of Bayes' rule, which says that we can update our belief based on measurements! This step was also followed by a normalization that made sure the resultant distribution was still vald (and added up to 1).
2. When it moves, a motion update or prediction step occurs; this step is a convolution that shifts the distribution in the direction of motion.

After this cycle, we are left with an altered posterior distribution!