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Merge pull request #280 from yoneken/fix-kalman_basic

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[Kalman Basics] Align some subscripts on the text to follow the code
This commit is contained in:
Atsushi Sakai
2020-02-02 14:03:39 +09:00
committed by GitHub
parent 81ddb1fc3e c6c0a61d49
commit 9898daf7ef
1 changed files with 4 additions and 4 deletions
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8
Localization/Kalmanfilter_basics.ipynb
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@@ -354,14 +354,14 @@
"\n",
"Here for the numerator, $P(Z \\mid X),P(X)$ both are gaussian.\n",
"\n",
"$N(\\bar\\mu, \\bar\\sigma^1)$ and $N(\\bar\\mu, \\bar\\sigma^2)$ are their mean and variances.\n",
"$N(\\mu_1, \\sigma_1^2)$ and $N(\\mu_2, \\sigma_2^2)$ are their mean and variances.\n",
"\n",
"New mean is \n",
"\n",
"$$\\mu_\\mathtt{new} = \\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2}$$\n",
"$$\\mu_\\mathtt{new} = \\frac{\\mu_1 \\sigma_2^2 + \\mu_2 \\sigma_1^2}{\\sigma_1^2+\\sigma_2^2}$$\n",
"New variance is\n",
"$$\n",
"\\sigma_\\mathtt{new} = \\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}\n",
"\\sigma_\\mathtt{new} = \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2}\n",
"$$"
]
},
@@ -759,4 +759,4 @@
},
"nbformat": 4,
"nbformat_minor": 2
}
}