daviddoji/Kalman-and-Bayesian-Filters-in-Python
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typo mu -> sigma github #276

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Roger Labbe 2020-04-26 21:50:28 -07:00
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04-One-Dimensional-Kalman-Filters.ipynb
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@ -294,7 +294,7 @@
"$$\\begin{aligned}\\bar x &= \\mu_x + \\mu_{f_x} = 10 + 15 &&= 25 \\\\\n",
"\\bar\\sigma^2 &= \\sigma_x^2 + \\sigma_{f_x}^2 = 0.2^2 + 0.7^2 &&= 0.53\\end{aligned}$$\n",
"\n",
"It makes sense that the predicted position is the previous position plus the movement. What about the variance? It is harder to form an intuition about this. However, recall that with the `predict()` function for the discrete Bayes filter we always lost information. We don't really know where the dog is moving, so the confidence should get smaller (variance gets larger). $\\mu_{f_x}^2$ is the amount of uncertainty added to the system due to the imperfect prediction about the movement, and so we would add that to the existing uncertainty. \n",
"It makes sense that the predicted position is the previous position plus the movement. What about the variance? It is harder to form an intuition about this. However, recall that with the `predict()` function for the discrete Bayes filter we always lost information. We don't really know where the dog is moving, so the confidence should get smaller (variance gets larger). $\\sigma_{f_x}^2$ is the amount of uncertainty added to the system due to the imperfect prediction about the movement, and so we would add that to the existing uncertainty. \n",
"\n",
"Let's take advantage of the `namedtuple` class in Python's `collection` module to implement a Gaussian object. We could implement a Gaussian using a tuple, where $\\mathcal N(10, 0.04)$ is implemented in Python as `g = (10., 0.04)`. We would access the mean with `g[0]` and the variance with `g[1]`.\n",
"\n",
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