Let me ask the hard question now.

The algorithm is amazingly simple.

Here are our equations again.

Now let's look at the Kalman filter.

Then that corresponds to a

Lets just go there. Here is the measurement probability function. There is something non trivial here.

You learned something really important.

And similarly, you know,

What we're going to do, is assume that the feature,

And you learned a little bit about how to use them as a belief in a probabilistic filter.

Number 1 Fit a gaussian we now know how this works.

Intuitively speaking, this is the case because we actually gain information.

Then we have a Gaussian distribution that is centered around zero, because that's Mu.

In this video, I'd like to talk about the Gaussian distribution, which is also called the normal distribution.

Since this was so simple, let me quiz you.

In the next video, I'll talk a bit about the Gaussian distribution and review properties of the Gaussian probability distribution, and in videos after that, we will apply it to develop an anomaly detection algorithm.

If I were to measure where the peak of the new Gaussian is, this would be a very narrow and skinny Gaussian.

Thus, I suspect that each of these examples was distributed according to a normal distribution or

Is it possible to represent this function as a Gaussian?

To explain how this works, I have to talk about high dimesional gaussians.

The gaussian will look something like this.

And so therefore, their kinetic energy can be characterized by a velocity dispersion.

Rather than setting x1 to x0 plus 10, we try to express the Gaussian that peaks when these two things are the same.

Starting with the following source code,

You may be given some data points, and you might worry about what is the best Guassian fitting the data?

So this finishes the lecture on Gaussians.

You just made it through the Kalman filter class and the second homework assignment.

I won't prove it to you because it's really trivial.

Here's a quiz for you.

Thrun And the answer is, of course, elongated.

If you forget this go back to the past class and look at this.

Measurement Update So question 1 is measurement update.

That's all happening down here. Here's my Gaussian function with the exponential.

Mu is the mean. Sigma squared is called the variance.

And these are exactly the same calculations as before when we fit a Gaussian but just weighted by the soft correspondence of a data point to each Gaussian.

The way to think about this if there is K different cluster centers shown over here each one of those has a generic Gaussian attached.

Here's a 2 dimensional space.

You learned about what a Gaussian is.

In Kalman filters the distribution is given by what's called a Gaussian.

The histogram is a mere approximation for this continuous distribution.

So this completes my unit on Kalman filters. You learned actually quite a bit.

For this quiz we will assume a degenerative case of 3 data points and just 1 cluster center.

Let's now model a second motion. Say x2 is 5 apart.

And your new sigma square is your old sigma square plus a variance of the motion Gaussian.

A Gaussian is a continuous function over the space of locations, and the area underneath sums up to 1.