This question may be hard to explain or understand. I am studying Kalman Filters using this excellent resource. It divides up the process of a Bayesian Filter into two major steps, belief -> prior and prior -> posterior. There is an extended example involving a hallway with doors and a robot (dog) that we are trying to localize.
We start with a 'belief' of where the robot is along the hallway. In the first step we take that 'belief' and incorporate information from a sensor with respect to the environment (e.g. is what is the probability that it is looking at door and from that it comes up with a preliminary probability distribution of where the robot is along the hallway, which is called the 'prior'. Now the robot moves 0 1 or 2 steps. Using that probability distribution, we update the distribution of where the robot might be - this is called the 'posterior'. The cycle is repeated using the posterior of one step as the 'belief' of the next cycle.
Ok so far? Please correct me if I am stating it wrong.
My question is this: the sensing of the door has a probability of being accurate, in other words, the sensor has a certain probability of giving an erroneous reading. And the sensing of the motion also has a chance to be inaccurate, in other words, the robot might think it moved one spot but it really didn't at all.
This may be overthinking it but I want to understand why those two sources of error are treated differently or specially. Why do they have different names (belief, prior, posterior), why do they have to be in that order, why couldn't you have a third measurement which also could have an error factor?