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02psps-02 Question 6 Help

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    Now I want to talk about the H matrix.
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    This is a matrix that takes a state, and when it multiplies
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    by that state, spits out a measurement.
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    Remember, we can only directly measure position and velocity,
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    so that's all we want the H matrix to keep.
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    Again, I want to talk about the 2D lecture case and the 4D homework case.
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    Hopefully, by comparing them, we'll be able to build some intuition,
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    and you'll be able to answer the homework.
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    What was the goal of the H matrix?
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    The goal of the H matrix was to take some state--
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    in the 2D case, our state was represented as an x and an ẋ--
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    multiply some matrix by that state in such a way that we extract a measurement.
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    In the 2D case the measurement was just x--just the x coordinate.
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    We can think of this as a 1 x 1 vector or a 1 x 1 matrix.
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    The matrix we use to do that was this one.
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    That was our H matrix--1, 0--because 1 times x gives us the x,
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    and 0 times ẋ gives us the nothing--exactly what we want.
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    But now let's talk about the dimensionality of these matrices
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    and how this multiplication yielded just this number x.
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    So we can think of x here as a 1 x 1 matrix.
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    We got that matrix by multiplying this one, which is a 1 x 2--
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    one row by two columns--with this, which is two rows by one column.
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    What we see here is that this 1 actually came from right here,
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    and this 1 came from right here.
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    These 2s we can think of as canceling out, in a way,
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    giving us this 1 x 1 matrix.
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    Now, let's see if we can generalize that to the 4-dimensional case as presented in the homework.
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    In the 4-dimensional case our state is now given by x, y, ẋ, ẏ.
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    We're going to have some H matrix.
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    I don't know anything about it yet, but I'm just going to put this there for now as a placeholder.
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    We want to get a measurement from that. What should this measurement be?
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    It's not just going to be x, because now our position includes both x and y.
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    So it's going to be a column vector--x and y.
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    Again, let's think. What's going on with the dimensionality here?
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    Here we have a 2 x 1 matrix,
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    and that came from this matrix, which I said we don't know anything about yet--
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    I'll just say a question mark by question mark--
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    and this matrix, which is four rows by one column.
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    Now, can you use the intuition we built up here
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    for how the dimensionality of matrices works with this to fill in the question marks?
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    Once you figure out the number of rows and the number of columns in this H matrix,
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    figuring out where to put your 1s and 0s will be a little bit easier.
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    I wish you luck.
Title:
02psps-02 Question 6 Help
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Team:
Udacity
Project:
CS373 - Artificial Intelligence
Duration:
03:02
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