daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Elaborate how c_0=x_0

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Achmad Fathoni 2022-01-07 01:02:02 +07:00
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07-Kalman-Filter-Math.ipynb
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@ -294,6 +294,13 @@
"x = e^ce^{kt} \\\\\n",
"x = c_0e^{kt}\\end{gathered}$$\n",
"\n",
"When $t=0$, $x=x_0$. Substitute these to equation above.\n",
"\n",
"$$\\begin{gathered}x_0 = c_0e^{k(0)} \\\\\n",
"x_0 = c_01 \\\\\n",
"x_0 = c_0 \\\\\n",
"x = x_0e^{kt}\\end{gathered}$$\n",
"\n",
"Using similar math, the solution to the first-order equation \n",
"\n",
"$$\\dot{\\mathbf x} = \\mathbf{Ax} ,\\, \\, \\, \\mathbf x(0) = \\mathbf x_0$$\n",