daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Merge pull request #23 from enter-the-bot/first-chapter-typos-fix

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fixed some typos
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Roger Labbe 2015-04-06 08:55:49 -07:00
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01_g-h_filter.ipynb
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@ -4818,7 +4818,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"That is pretty good! There is a lot of data here, so let's talk about how to interpret it. The thick green line shows the estimate from the filter. It starts at day 0 with the inital guess of 160 lbs. The red line shows the prediction that is make from the previous day's weight. So, on day one the previous weight was 160 lbs, the weight gain is 1 lb, and so the first prediction is 161 lbs. The estimate on day one is then part way between the prediction and measurement at 159.8 lbs. Above the chart is a print out of the previous weight, predicted weight, and new estimate for each day. Finally, the thin black line shows the actual weight gain of the person being weighed. \n",
"That is pretty good! There is a lot of data here, so let's talk about how to interpret it. The thick green line shows the estimate from the filter. It starts at day 0 with the inital guess of 160 lbs. The red line shows the prediction that is made from the previous day's weight. So, on day one the previous weight was 160 lbs, the weight gain is 1 lb, and so the first prediction is 161 lbs. The estimate on day one is then part way between the prediction and measurement at 159.8 lbs. Above the chart is a print out of the previous weight, predicted weight, and new estimate for each day. Finally, the thin black line shows the actual weight gain of the person being weighed. \n",
"\n",
"The estimates are not a straight line, but they are straighter than the measurements and somewhat close to the trend line we created. Also, it seems to get better over time. \n",
"\n",
@ -15633,7 +15633,7 @@
"source": [
"Now let's try a practical example. Earlier in the chapter we talked about tracking a train. Trains are heavy and slow, thus they cannot change speed quickly. They are on a track, so they cannot change direction except by slowing to a stop and then reversing course. Hence, we can conclude that if we already know the train's approximate position and velocity then we can predict its position in the near future with a great deal of accuracy. A train just cannot change its velocity much in a second or two. \n",
"\n",
"So let's write a filter for a train. Its position is expressed as its position on the track in relation to some fixed point which we say is 0 km. I.e., a position of 1 means that the train is 1 km away from the fixed point. Velocity is expresses as meters per second. We perform measurement of position once per second, and the error is $\\pm$ 500 meters. How should we implement our filter?\n",
"So let's write a filter for a train. Its position is expressed as its position on the track in relation to some fixed point which we say is 0 km. I.e., a position of 1 means that the train is 1 km away from the fixed point. Velocity is expressed as meters per second. We perform measurement of position once per second, and the error is $\\pm$ 500 meters. How should we implement our filter?\n",
"\n",
"First, let's just simulate the situation without a filter. We will assume that the train is currently at kilometer 23, and moving at 15 m/s. We can code this as \n",
"\n",