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Fixed math for P = FPF^ #274

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Roger Labbe 2020-05-04 17:40:00 -07:00
parent 82f7dba206
commit 10203d3a42
1 changed files with 3 additions and 4 deletions
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06-Multivariate-Kalman-Filters.ipynb
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@ -1769,12 +1769,11 @@
"If you have some experience with linear algebra and statistics, this may help. The covariance due to the prediction can be modeled as the expected value of the error in the prediction step, given by this equation. \n",
"\n",
"$$\\begin{aligned}\n",
"\\bar{\\mathbf P} &= \\mathbb E[(\\mathbf{Fx})(\\mathbf{Fx})^\\mathsf T]\\\\\n",
" &= \\mathbb E[\\mathbf{Fxx}^\\mathsf T\\mathbf F^\\mathsf T] \\\\\n",
" &= \\mathbf F\\, \\mathbb E[\\mathbf{xx}^\\mathsf T]\\, \\mathbf F^\\mathsf T\n",
"\\bar{\\mathbf P} &= \\mathbb E[(\\mathbf{Fx - \\bar \\mu})(\\mathbf{Fx - \\bar\\mu})^\\mathsf T]\\\\\n",
" &= \\mathbf F\\, \\mathbb E[\\mathbf{(x- \\bar\\mu)(x- \\bar\\mu)}^\\mathsf T]\\, \\mathbf F^\\mathsf T\n",
"\\end{aligned}$$\n",
"\n",
"Of course, $\\mathbb E[\\mathbf{xx}^\\mathsf T]$ is just $\\mathbf P$, giving us\n",
"Of course, $\\mathbb E[\\mathbf{(x- \\bar\\mu)(x- \\bar\\mu)}^\\mathsf T]$ is just $\\mathbf P$, giving us\n",
"\n",
"$$\\bar{\\mathbf P} = \\mathbf{FPF}^\\mathsf T$$\n",
"\n",