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Merge pull request #116 from esvhd/nb05_typo_fix

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Fixed two typos in notebook 5 Multivariate Gaussians.
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Roger Labbe 2016-09-12 17:34:10 -07:00 committed by GitHub
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05-Multivariate-Gaussians.ipynb
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@ -21763,7 +21763,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"You can already see why a multivariate Kalman filter can perform better than a univariate one. Correlations between variables to significantly improve our estimates. We can take this much further. **This section contains the key insight to this chapter, so read carefully**.\n",
"You can already see why a multivariate Kalman filter can perform better than a univariate one. Correlations between variables can significantly improve our estimates. We can take this much further. **This section contains the key insight to this chapter, so read carefully**.\n",
"\n",
"Let's say we are tracking an aircraft and we get the following data for the $x$ and $y$ coordinates at time $t$=1, 2, and 3 seconds. What does your intuition tell you the value of $x$ will be at time $t$=4 seconds?"
]
@ -26568,7 +26568,7 @@
"source": [
"What makes this possible? Imagine for a moment that we superimposed the velocity from a different airplane over the position graph. Clearly the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the measurement of the position is not in the direction of the velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way. \n",
"\n",
"It is important to understand that we are taking advantage of the fact that velocity and position are correlated. We get a rough estimate of velocity from the distance and time between two measurement, and use Bayes theorem to and produce very accurate estimates after only a few observations. Please reread this section if you have any doubts. If you do not understand this you will quickly find it impossible to reason about what you will learn in the following chapters."
"It is important to understand that we are taking advantage of the fact that velocity and position are correlated. We get a rough estimate of velocity from the distance and time between two measurement, and use Bayes theorem to produce very accurate estimates after only a few observations. Please reread this section if you have any doubts. If you do not understand this you will quickly find it impossible to reason about what you will learn in the following chapters."
]
},
{
@ -26614,7 +26614,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.1"
"version": "3.5.2"
}
},
"nbformat": 4,