So, I’d like to take my students onto a little journey to Stanford and show them our self-driving car that uses sensors to sense the environment. So let me dive into the class very much right now. Through our last class, we talked about localization. We had a robot that lived in an environment and that it could use its sensors to determine where in the environment it is. So, here you can see the Google self-driving car using a roadmap localizing itself. But in addition what’s shown here in red are measurements of other vehicles. The car uses lasers and radars to track other vehicles. Today, we’re going to talk about how to find other cars. The reason why we’d like to find other cars is because we wouldn’t want to run into them. So, we have to understand how to interpret sensor data to make assessments not just where these other cars are as in the localization case, but also how fast they’re moving, so that we can drive in a way that avoids collisions within the future. That’s important not just for cars, it matters for pedestrians and bicyclists and understanding where the cars are and making prediction where they’re going to move is absolutely essential for safe driving in the Google car potrait. So in this class, we’ll talk about tracking. The technique I’d like to teach you is called the Kalman Filter. This is an insanely popular technique for estimating the state of a system. It’s actually very similar to the probabilistic localization method we talked in the previous class, Monte Carlo localization. The primary differences are that Kalman Filters estimate a continuous state whereas in Monte Carlo localization, we are forced to chop the word in the discrete places. As a result, the Kalman Filter happens to give us a uni-modal distribution and I’ll tell you in a second what that means, whereas Monte Carlo was fine with multi-modal distributions. Both of these techniques are applicable to robot localization and tracking other vehicles. Consider the car down here. Let’s assume it seizes measurement, an object here, here, here, and here for the time is t equals zero, t equals one, two and three. Where would you assume the object would be a t equals four?