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Revision 37, 0.8 kB
(checked in by smidl, 17 years ago)
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Matrix in Cholesky decomposition, Square-root Kalman and many bug fixes
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| 1 | \form#0:$A=\frac{df}{dx}|_{x0,u0}$ |
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| 2 | \form#1:$A=\frac{d}{dx}f(x,u)|_{x0,u0}$ |
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| 3 | \form#2:$A=\frac{d}{du}f(x,u)|_{x0,u0}$ |
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| 4 | \form#3:$x \sim epdf(rv)$ |
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| 5 | \form#4:\[ f(x|a,b) = \prod f(x_i|a_i,b_i) \] |
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| 6 | \form#5:\[M = L'DL\] |
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| 7 | \form#6:\[ x_t = A x_{t-1} + B u_t + Q^{1/2} e_t \] |
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| 8 | \form#7:\[ y_t = C x_{t-1} + C u_t + Q^{1/2} w_t. \] |
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| 9 | \form#8:\[ f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) \] |
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| 10 | \form#9:$x^{(i)}, i=1..n$ |
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| 11 | \form#10:$x \sim epdf(rv|cond)$ |
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| 12 | \form#11:$\alpha=k$ |
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| 13 | \form#12:$\beta=k/\mu$ |
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| 14 | \form#13:$\mu/\sqrt(k)$ |
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| 15 | \form#14:$\mu$ |
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| 16 | \form#15:$\alpha$ |
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| 17 | \form#16:$\beta$ |
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| 18 | \form#17:\[ \left[\begin{array}{cc} R^{0.5}\\ P_{t|t-1}^{0.5}C' & P_{t|t-1}^{0.5}CA'\\ & Q^{0.5}\end{array}\right]<\mathrm{orth.oper.}>=\left[\begin{array}{cc} R_{y}^{0.5} & KA'\\ & P_{t+1|t}^{0.5}\\ \\\end{array}\right]\] |
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