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[AMR] Notes on tasks, improved layouts
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@@ -2,8 +2,8 @@
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\bi{Meas. Model}: $\vec{z} = \vec{h}(\vec{x}) + \vec{v} + \vec{o}$, with $\vec{h}(\vec{x})$ determ. mean,
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$\vec{v}$ zero-mean noise, $\vec{o}$ unmodelled effects, $\vec{x}$ true state.
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$\vec{h}(\vec{x})$ describes how to compute $x$ from known values (e.g. Intercept-Theorem).
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Probabilistic M.M: use rand var in def, and s. \ref{sec:error-propagation}
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Probabilistic M.M: use random variable in definition, and s. \ref{sec:error-propagation}
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\bi{Motor encoders} Typ. 64-2048 incrm. per rev; Estim. rot
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\bi{Motor encoders} Typ. 64-2048 increments per rev; Estimate rot
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\bi{Rolling-Shutter} Most CMOS sensors don't take full image at once, need time stamp for each row
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@@ -40,7 +40,7 @@ If p. in diff frame, e.g. $W$-frame then $\vec{u} = \mat{K}[\mat{R}_{CW}\; {_C}\
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(Projection) $\vec{x'} = \vec{p}({_C}\vec{t}_P) = t_z^{-1} \cdot [t_x, t_y]^\top$
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(Distortion model) $r^2 = x'^2 + y'^2$, $\vec{x''} = \vec{d}(\vec{x'})$\\
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$\vec{x''} = \! \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} \vec{x'}
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$\vec{x''} = \! \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}; \vec{x'}
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+
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{\scriptsize
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\begin{bmatrix}
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