Special Topics - The Kalman Filter (1 of 55) What is a Kalman Filter?

welcome to electron line in this series of videos starting with this one we're going to talk about the Kalman filter now the Kalman filter is an amazing tool in order to estimate predicted values but it's sometimes very difficult to understand how the Kalman filter actually works so therefore I made some videos to describe what a Kalman filter actually is how to use it with some nice examples so follow this so what is a Kalman filter well it is an iterative mathematical process it's so you you follow a set of iterations it's a mathematical process that uses a set of equations those equations and consecutive data input so we get a data input we use the equation we calculate the new estimate we get another data input we calculate the new estimate we get another data input we calculate a new estimate again it's an iterative process and the reason for doing it like this is so that we can quickly estimate the true value so let's say that we have 50 or 100 data points that come in one at a time and you could you and yes we can do a for example a distribution of these values and find the average value and then say well the average value must be very close to the true value in order to do that we need to have a whole bunch of inputs already the Kalman filter doesn't wait for a whole bunch of inputs it very quickly starts to narrow in to the true value by taking a few of those inputs and beyond by understanding the variation or the uncertainty of those inputs of data inputs so it quickly estimates the true value position velocity whatever it is that we're trying to measure of the object that's being measured when the measured values contain unpredicted or random errors and certainties or variations as well so remember that the data coming in is not the true value it's somewhere around the true value with a certain amount of uncertainty and of course since that can bounce all over the place it would very difficult to any other system to try and very figure out what the true values are come very close to the true value so a very simple example here in the graphical sense can help you understand that let's say we're trying to the temperature with a certain thermometer that thermometer is not very accurate it has a certain amount of uncertainty in the data measurements let's say that the vertical axis here means temperature the horizontal axis means time or consecutive sample inputs the little crosses here are consecutive inputs so here the temperature is measured to be this high than to be this high to be this high to be this high than this so you can see that the temperature measured time and again always varies because there's certain amount of uncertainty in that temperature measurement technique for whatever reason it may be and so therefore it would take a very long time for us to average these values out the Kalman filter can do it a lot faster it starts out by taking an initial estimate it almost doesn't matter what the initial estimate is and of course in your estimate you have to predict a certain amount of error or uncertainty but very quickly as data points start coming in and we go through that iterative process the Kalman filter actually narrows down to somewhere close to the true value very quickly it doesn't take very many data points to get there and once you get there as more and more data points come in the variations will become very very small and the predicted value to the Kalman filter process will be very very close to the actual temperature in this case in this example so the estimated temperature using the Kalman filter will zero in and come very very close to the actual temperature very quickly now in this example here there's only one measured value or after the temperature however this can be used especially like in radar technology or GPS tracking satellites we need to know the target that we're tracking we need to know its position in the x-direction the position in the y direction the velocity x direction the velocity in the Y direction and yes the Kalman filter can very quickly again to the very same process narrow it down there are these intermediate values that come in which can be all over the place because as you're trying to track airplanes via radar or target via radar you're trying to track satellites that's not an exact science the data coming in will have certain amount of uncertainty in it and the Kalman filter can very easily handle that uncertainty and very quickly zero on the true position and the true philosophy of the of the object that you're tracking of course if we're looking for something like this where we have multiple data inputs that we have to converge at the same time it's a little different process than if we take a singular value like the temperature measured with a thermometer what that means is that when we track satellites or airplanes we'll have to use instead of using a single number system in a simple set of equations we'll have to use equations using of course matrices and we'll show you how to do that as well but to get the technique down first we're going to start with a very simple example like this just simply measuring the temperature and see how Kalman filters we can very quickly zoom in to that actual temperature that we're trying to figure out and then once we have that technique down that we'll expand it to the more complicated set of equations to be used to figure out how to track targets like using radar or how to use GPS tracking you know tracking of satellites all right hopefully that gives you kind of an idea what a Kalman filter is of course without showing examples you're still a long ways probably from saying oh okay I'm good with that I know what this is at least you have a conceptual idea of what a common filter is now let's go practice with some real examples of how to do that so you get a very strong feel for what Kalman filters is and how to use it yourself

Channel: Michel van Biezen

Views: 444,707

Keywords: ilectureonline, ilectureonline.com, Mike, Mike van Biezen, van Biezen, ilecture, ilecture online, Linear, Mathematics (Field Of Study), Kalman Filter, What is a Kalman Filter, Iteration

Id: CaCcOwJPytQ

Length: 5min 55sec (355 seconds)

Published: Sat Sep 12 2015