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June10th 2015 GPS Smoothing Example Continued
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In the more general case, we use a parabolic curve with the following parametric form:
→c(t)=→a+→bt+→ct2
Minimizing the weighted distance to the 3D curve yields the following solution:
(axayazbxbybzcxcycz)=(∑iw2i00∑iw2iti00∑iw2it2i000∑iw2i00∑iw2iti00∑iw2it2i000∑iw2i00∑iw2iti00∑iw2it2i∑iw2iti00∑iw2it2i00∑iw2it3i000∑iw2iti00∑iw2it2i00∑iw2it3i000∑iw2iti00∑iw2it2i00∑iw2it3i∑iw2it2i00∑iw2it3i00∑iw2it4i000∑iw2it2i00∑iw2it3i00∑iw2it4i000∑iw2it2i00∑iw2it3i00∑iw2it4i)−1(∑iw2ipix∑iw2ipiy∑iw2ipiz∑iw2ipixti∑iw2ipiyti∑iw2ipizti∑iw2ipixt2i∑iw2ipiyt2i∑iw2ipizt2i)
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