daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Mark Murnane 2022-05-12 10:36:04 -04:00 committed by GitHub
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03-Gaussians.ipynb
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@ -1287,7 +1287,7 @@
"\n",
"The discrete Bayes filter works by multiplying and adding arbitrary probability distributions. The Kalman filter uses Gaussians instead of arbitrary distributions, but the rest of the algorithm remains the same. This means we will need to multiply and add Gaussians. \n",
"\n",
"A remarkable property of Gaussians is that the sum of two independent independent normal variables (https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables) is also normally distributed! The product is not Gaussian, but proportional to a Gaussian. There we can say that the result of multipying two Gaussian distributions is a Gaussian function (recall function in this context means that the property that the values sum to one is not guaranteed).\n",
"A remarkable property of Gaussians is that the sum of two independent normal variables (https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables) is also normally distributed! The product is not Gaussian, but proportional to a Gaussian. There we can say that the result of multipying two Gaussian distributions is a Gaussian function (recall function in this context means that the property that the values sum to one is not guaranteed).\n",
"\n",
"Before we do the math, let's test this visually. "
]