 There are questions about that. So, what about the yaw component? So, for a yaw we use the magnetometer to correct yaw error. So, this is similar to the way we did tilt correction you have to um take a measurement estimate the amount of error in yaw and then apply corrections gradually again you can use a complementary filter um. So, similar process so similar to tilt correction um calculate estimated error estimated drift error and then gradually apply correction using a complementary filter. Well what problems do we have here? So, it may be very natural for us to think of a magnetometer as being a compass, but we have to really go back and think about what it is measuring just like the accelerometer is not an up sensor a magnetometer is not exactly a compass what it is measuring is a 3 dimensional magnetic field. So, the problem was such an approach is that the um the sensor that is a magnetometer measures the vector sum just like this vector sum, but is a vector sum of the earth's field that is the part that we are normally interested in right um the simplest assumption is that um perhaps if I have perhaps the magnetic field as I as I um grab a magnetometer for the earth is always arranged in such a way that the vector field lines just point north right that is something that I naively believed a long time ago. It turns out that in most places of the world there is a strong vertical component and so mostly for example, in um in the US um when I was in California doing oculus development it was about 60 degrees downward is where the vector mainly points. When I was doing development for oculus from Finland it was close to um like 75 degrees or so 70 degrees or so is very close to vertical. If the earth's magnetic vector field is pointing straight down then it is going to be aligned with gravity and it is not going to provide any additional useful information right um. So, so that is something interesting it varies dramatically based on where you are at on the earth and also the field lines do not exactly point north they could be off by a few degrees it could be off by 10 to 20 degrees there are few strange places in the earth where they are off by a lot they will not even point anywhere near north they will point maybe 90 degrees away um. So, so the um so the earth's field is first of all three dimensional and quite strange and you just want the horizontal component of it you do not want the vertical component. So, if most of the field is in the vertical component you are just essentially wasting that information you already know the vertical component reasonably well due to the accelerometer. You are trying to find this horizontal component that is parallel to the surface of the earth. So, you can correct which way you are facing. The next problem is that in addition to the earth's field there is a field inside of the building if you are indoors which most people are right. So, there is a building field which is generated by whatever ferrous materials there are indoors it is very interesting to grab a an expensive magnetometer and go around and just try to see what the fields are inside of a building as they they vary dramatically their entire um startup companies that just provide services for mapping out buildings just using the magnetic field inside of the building. So, it varies so much that you could build reasonable maps not down to millimeter level accuracy, but it varies quite a bit over on the scale of um meters let us say as you go through the building. Also on the circuit board itself there is there is a field. So, there may be ferrous materials on the circuit board. So, every time you install the magnetometer on the board it will behave differently than it would on some other board. Now, it may be consistent for the board that you have designed. So, that is good. So, you could do a calibration procedure to try to compensate for that. It may just add some constant offset um based on the materials around the board um. So, those are three main fields and what is very interesting is that you could get so unfortunate that when you are inside of the building in some location the buildings field might cancel off the earth's field. So, the two vectors may be in nearly opposite directions and you get a horizontal component that is very close to 0 in which case it is useless. So, these are some frustrations with dealing with magnetometers um. So, there are calibration challenges you may actually have to ask the user to perform calibrations you may have done this before with your smart phones or calibration programs for your magnetometer um field might vary over time and position. You would like to have it so that if you move your head a half meter to the side you do not get a completely different orientation of the field because that would cause great confusion. So, you need the field to be mostly constant it could be bending in some ways especially if you are unfortunate and there is also something called soft iron bias which I will not cover here, but which induces a kind of elliptical distortion on the magnetic field readings um based on Ferris materials in the vicinity of the sensor. So, all these end up being complicated challenges we found um we were able to get accuracy down to around 5 degrees or so which is not great, but most of the time things are working fine and down around 5 degrees or so is not too painful at least it keeps your cockpit from drifting away indefinitely. So, it more or less gives you a consistent sense of forward it is not as critical to get this right down as accurately as it was for tilt human beings can detect tilt errors down to about half of a degree. So, if the world is tilted we end up being not very comfortable if the world starts drifting a little bit to where we are facing a different direction um a couple of degrees of error and that is is not much of an issue it does not cause a sickness of any kind and usually we are kind of quickly fooled by small errors and and can compensate for that. Um if you want to read more on these things I have talked about here um there is a paper by Mahoney 2008 and it is all about complimentary filters on the space of transformations that arrives for rigid bodies. So, like SO 3 which is the space of 3D rotation. So, I think this is an excellent paper to look at that talks about how to combine measurements from multiple sources and perform drift corrections select the coefficients in such a way that everything globally converges that has mathematical analysis as well. So, I think it is both practical and mathematically sounds it is a very nice source um I have also co-authored a paper um at the um international conference on robotics and automation 2014 that covers Oculus Rift head tracking up to um up to this and the rest after that was um not public. So, um alright questions or comments on that? Yes. Oh the camera yeah that is great that is a part 2. So, so that is a very good question that is just leading into the next part of the lecture. So, um I am only talking about orientation tracking right.