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## Matrix Fill In

[Narrator] Hi class, this is homework assignment #6 on SLAM, and we're going to practice some more questions about the graph SLAM algorithm, and I will ask you something new about how to make graph SLAM more efficient towards the end of this homework assignment. There's 3 questions and 1 new thing, which comes with additional questions and a programming assignment. Let's dive in. In this example, picture a robot that starts at initial position 5. This robot which lives in 1D, even though I'm drawing this in 2D, sees a landmark with a relative measurement of 2. It then moves to coordinate X1 by taking a step of 7. It now sees a different landmark, L1, with a measurement value of 4. Finally, it moves again with a motion 2, and now it sees the same second landmark, not the original one,at a value of 2. Obviously, when I work it out and solve this, you find that the best coordinates over here are 12 and 14, with landmark coordinates of 7 and 16, but none of the numbers I just told you will be inserted in the question I'm about to ask. Picture the matrix omega and the vector C. I want you to add all these constraints into omega with a caveat that for the initial constraint I assume the strength is just 1, so enter it the way you're used to. Now let's assume the motion update has a sigma of 1, but the measurement update--the sigma for measurements has a value of 0.5, and remember we weigh those updates with 1 over sigma, which in the measurement case would therefore be 2. I want you to fill in the values for sigma and for C for this specific example. I gave you some of the sigma values and some of the C values, and I want you to fill in the missing values over here. You can check whether you got them correct by verifying that I got those numbers correct, and you can also solve for omega minus 1 times C, and out should come the right positions shown in the diagram over here.