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Merge pull request #99 from lubkoll/master

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Fix typos in chapter 08
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Roger Labbe 2016-05-25 08:39:15 -07:00
commit 4b17de67a9
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6
08-Designing-Kalman-Filters.ipynb
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{
{
"cells": [
{
"cell_type": "markdown",
@ -1375,7 +1375,7 @@
"source": [
"### Design the Measurement Noise Matrix\n",
"\n",
"Wee assume that the $x$ and $y$ variables are independent white Gaussian processes. That is, the noise in x is not in any way dependent on the noise in y, and the noise is normally distributed about the mean 0. For now let's set the variance for $x$ and $y$ to be 5 meters$^2$. They are independent, so there is no covariance, and our off diagonals will be 0. This gives us:\n",
"We assume that the $x$ and $y$ variables are independent white Gaussian processes. That is, the noise in x is not in any way dependent on the noise in y, and the noise is normally distributed about the mean 0. For now let's set the variance for $x$ and $y$ to be 5 meters$^2$. They are independent, so there is no covariance, and our off diagonals will be 0. This gives us:\n",
"\n",
"$$\\mathbf R = \\begin{bmatrix}\\sigma_x^2 & \\sigma_y\\sigma_x \\\\ \\sigma_x\\sigma_y & \\sigma_{y}^2\\end{bmatrix} \n",
"= \\begin{bmatrix}5&0\\\\0&5\\end{bmatrix}$$\n",
@ -2412,7 +2412,7 @@
"\n",
"This is also called a *constant velocity* model, because of the assumption of a constant velocity.\n",
"\n",
"A second order has a second derivative. The second derivative of position is acceleration, with the equation\n",
"A second order system has a second derivative. The second derivative of position is acceleration, with the equation\n",
"\n",
"$$a = \\frac{d^2x}{dt^2}$$\n",
"\n",