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Merge pull request #98 from lubkoll/master

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Fix typos in chapter 04
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Roger Labbe 2016-05-25 07:13:28 -07:00
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04-One-Dimensional-Kalman-Filters.ipynb
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@ -2900,7 +2900,7 @@
"source": [
"## Updates with Gaussians\n",
"\n",
"The discrete Bayes filter encodes our belief about the position of our dog in a histogram of probabilities. The distribution is discrete and multimodal. - It can express strong belief that the dog is in two positions at once, and the positions are discrete.\n",
"The discrete Bayes filter encodes our belief about the position of our dog in a histogram of probabilities. The distribution is discrete and multimodal. It can express strong belief that the dog is in two positions at once, and the positions are discrete.\n",
"\n",
"We are proposing that we replace the histogram with a Gaussian. The discrete Bayes filter used this code to compute the posterior:\n",
"\n",
@ -8940,7 +8940,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we can see that the variance converges to 2.163 in 9 steps. This means that we have become very confident in our position estimate. It is equal to $\\sigma=1.47$ meters. Contrast this to the sensor's $\\sigma=2.12$ meters. The first few measurements are unsure due to our uncertainty of the initial position, but the filter quickly converges to an estimate with lower variance than the sensor!\n",
"Here we can see that the variance converges to 2.1623 in 9 steps. This means that we have become very confident in our position estimate. It is equal to $\\sigma=1.47$ meters. Contrast this to the sensor's $\\sigma=2.12$ meters. The first few measurements are unsure due to our uncertainty of the initial position, but the filter quickly converges to an estimate with lower variance than the sensor!\n",
"\n",
"This code fully implements a Kalman filter. If you have tried to read the literature you are perhaps surprised, because this looks nothing like the endless pages of math in those books. So long as we worry about *using* the equations rather than *deriving* them the topic is approachable. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent beliefs with Gaussians, and they get better over time because more measurements means we have more data to work with."
]