RandProcNotesPart2

RandProcNotesPart2 - Software problem. i will fix this next...

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Unformatted text preview: Software problem. i will fix this next lecture. This "p(x)" factor does not belong here it is incorporated into the definition of "E(...)" My conjecture here is incorrect. So overall, 50% of the time Xnew lies to the left of AXoldtrue + B, and 50% of the time it lies to the right. E(Xnew) = E(Xnewtrue) = AXoldtrue + B = E(AXold + B) = E(XKalman) Now we can update again, taking the true old value to be Xnewtrue. XKalman is an unbiased estimator of this number, with a known mean square error, so it can play the role of Xold. So overall, 50% of the time Xnew lies to the left of AXoldtrue + B, and 50% of the time it lies to the right. E(Xnew) = E(Xnewtrue) = AXoldtrue + B = E(AXold + B) = E(XKalman) So overall, 50% of the time Xnew lies to the left of AXoldtrue + B, and 50% of the time it lies to the right. E(Xnew) = E(Xnewtrue) = AXoldtrue + B = E(AXold + B) = E(XKalman) WRONG! Corrected Nov. 24 m2 I made an error in the lecture at this point. The limits on the sums are n1 and n2 the dummy variables inside the sums need to be named something else. Here you see my corrections "m1" and "m2". m1 If m1m2 , m2 m1 If m1=m2 , m2 We'll finish the algebra next time. The first part of today's lecture is drawn directly from the text. Note I pasted in the wrong matrix during the lecture. The vector IS correct, and the discussion. The above matrix is the one I meant to paste in. ...
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