Let's take a very simple robot sensing problem, right?
So let's assume that a robot knows the 3D map of its world, okay?
And for now,
we're just going to worry about a robot running around on the floor.
So it's not climbing stairs, instead it's just running around.
And let's assume also that it has noisy depth sensors, so
it can measure depth in a lot of different directions.
And they're noisy, so the, the measurement is uncertain, but
we know about the uncertainty.
That is we have a sensor model.
Okay?
And it moves between frames, and it takes a, a set of readings, and
then it moves again and takes a set of readings, and it moves again.
But the idea is it keeps taking all these readings, and
the question is, how well can it know its state?
So, what is its state?
Montana?. No.
Its state is three values, x, y and theta, its orientation.
Okay? That's why we're just doing a,
a multiple robot on the ground three dimensions.
All right?
So, just to remind you, on a Ba, Bayesian filter framework,
we need four things.
We need some sort of the prior, remember that trip to Delphi, so
you unpack your next prior.
We need a dynamical system model and that's the likelihood of landing in some
new place, given that you're in an old place plus whatever action was taken.
We need a sensor model, remember, a likelihood that's the,
not the probability of being someplace given a measurement.
The likelihood is the probability of getting the measurement given
what your state was, and then we need this stream of observations and
the action data, the Zs and the Us.
For that robot that I described, the state is obvious.
The map will be easy, et cetera.
The thing that's tricky, not tricky, the thing we have to define,
is the sensor model.
So here's a picture of a sensor model, and what this is is,
this is the probability of getting a particular measurement if,
let's say, the actual state was here on this black line, okay?
And, what was nice is when your using a real robot,
you can actually measure the likelihood, so
you, you, you stick the sensor, you know, three meters away, or,
let's see, it's at centimeters, so 200, so 2.3 centimeters away from the wall.
You turn it on, you turn it on, you turn.
You collect a whole bunch of measurements and you see what you get.
That distribution would be this distribution.
Okay?
And in fact, the blue is what was measured.
All right? So that's why the blue's got
the noisy stuff.
And the red is how they approximated it.
And you can see they basically had some sort of a Gaussian function or
something like that.
In fact, you can see that the laser has a less noise than the sonar, okay?
So, this is, this is actually a relatively noisy laser.
A modern laser would be, you know, very precise.
Except that you might have some specular problem, et cetera.
So all of that would be fine, except, you'll notice there's this thing here
and this thing there, and the question is, what's going on when, you know,
the thing is 2.3 meters away and here it says 500.
But, the astute observer will notice you're just using the very last value.
Well what that really is,
is that's the probability that you get no return, okay?
So you're some distance from the wall, you send out your sonar chirp, or
you send out your laser, and it just goes away.
Gets on a train, never comes back.
This happens you guys know what specular reflections are, right?
So when light bounces off to,
turns out that sheet rock is very specular to sonar.
So when you send out a sonar chirp, often it doesn't come back, it skips
like it reflects off, in which case, you don't ever hear the chirp come back.
Or it comes back after having gone through a long echo path.
Likewise, if you're looking at something that's shiny, like a glass wall.
When you point at it, you can see the laser beam.
But when you point it on the side, okay?
It'll be reflective.
It'll be a specular.
So what these values are,
is the probability of getting no return given that you're at some distance.
And in fact, that probability stays the same pretty much no matter what your
distance is.
All right?
So remember, this is not the probability that your distance is actually 500.
It's the probability that you would get this no return
at any given point in time, okay?
So we need to incorporate that noisy model.