13 – 16 Introducing Noise Solution RENDER V1

So, I’m trying it out and see what happens. So, before it was minus 3, 2, 5, 7. Now, the first position is completely unchanged, and I’ll explain to you in a second why. The third one, went from five to 5.5, and the landmark went down from seven to 6.8. So graphically, this guy becomes larger than five, and this landmark even shift a little bit to the left to make these two things closer together than they were before when they had a separation distance of two. Now, this picture doesn’t really explain it well because it’s a 2D picture, but in 1D that’s exactly what’s happening. Also interesting, the initial position is unchanged. So, these are the correct answers. Now, I will be blown away if you guess them correctly. The reason why the original position doesn’t change is, the only information we have about the absolute coordinates location is the very first initial position anchor that we said it has to be minus three. None of the relative rubber bands change the fact that we need this guy to be minus three. A relative strength changed in these two things over here means the rubber band is different, but it’s a relative thing. This is the only absolute constraint we put in. So, clearly, the absolute location of the first position doesn’t change. The reason why it becomes larger than five is, well, think about rubber bands. Our landmark is at around seven. We believe to be a position five in the noise-free case, we just put a tight rubber band between them. It’s not two anymore, it’s now one. That means we’re inclined to move the landmark and this position closer together, and that’s exactly what happens. If you go find a position, becomes 5.5, and the landmark becomes 6.875 instead of seven. Now, this is a case where the rubber bands don’t add up. This is one of the places where graph’s limit is just magical. So, before everything adds up, but we have cycles in these structures, and these cycles might not add up, because we have noise and motionless measurements. What our method does, by computing this thing, Omega to the minus one times c, we find the best solution to the relaxation of those rubber bands. That to me is sheer magic.

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