daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Roger Labbe 2015-05-09 13:23:30 -07:00
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05_Kalman_Filters.ipynb
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@ -1467,8 +1467,8 @@
"We can incorporate that term into our equation above by observing that\n",
"$$ \n",
"\\begin{aligned}\n",
"\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n",
" &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n",
"\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a} \\\\\n",
" &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}} \\\\\n",
" &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n",
" &= \\frac{\\sigma^2_{x'}}{b}\n",
" \\end{aligned}\n",
@ -1478,9 +1478,9 @@
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n",
"\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x) \\\\\n",
"&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n",
"&= x + g_n(y-x)\\\\\n",
"&= x + g_n(y-x) \\\\\n",
"\\blacksquare\n",
"\\end{aligned}\n",
"$$\n",