0:00:00.000,0:00:05.000 In Kalman filters we iterate measurement and motion. 0:00:05.000,0:00:08.000 This is often called a "measurement update," 0:00:08.000,0:00:10.000 and this is often called "prediction." 0:00:10.000,0:00:17.000 In this update we'll use Bayes rule, which is nothing else but a product or a multiplication. 0:00:17.000,0:00:24.000 In this update we'll use total probability, which is a convolution, 0:00:24.000,0:00:27.000 or simply an addition. 0:00:27.000,0:00:35.000 Let's talk first about the measurement cycle and then the prediction cycle, 0:00:35.000,0:00:44.000 using our great, great, great Gaussians for implementing those steps. 0:00:44.000,0:00:47.000 Suppose you're localizing another vehicle, 0:00:47.000,0:00:50.000 and you have a prior distribution that looks as follows. 0:00:50.000,0:00:55.000 It's a very wide Gaussian with the mean over here. 0:00:55.000,0:00:58.000 Now, say we get a measurement that tells us something about 0:00:58.000,0:01:03.000 the localization of the vehicle, and it comes in like this. 0:01:03.000,0:01:07.000 It has a mean over here called "mu," 0:01:07.000,0:01:11.000 and this example has a much smaller covariance for the measurement. 0:01:11.000,0:01:16.000 This is an example where in our prior we were fairly uncertain about a location, 0:01:16.000,0:01:21.000 but the measurement told us quite a bit as to where the vehicle is. 0:01:21.000,0:01:23.000 Here's a quiz for you. 0:01:23.000,0:01:36.000 Will the new mean of the subsequent Gaussian be over here, over here, or over here? 0:01:36.000,9:59:59.000 Check one of these three boxes.