daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Added algorithm pseudocode to help link chapters.

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I don't think the commonality of the algorithms was made as
expllicit as it could be. More work needs to be done in this regard.
This commit is contained in:
Roger Labbe 2015-06-25 18:39:57 -07:00
parent 10a62649df
commit 960771b4c4
3 changed files with 66 additions and 26 deletions
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24
01_g-h_filter.ipynb
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@ -1026,7 +1026,27 @@
"\n",
"Now consider trying to track a child's balloon in a hurricane. We have no legitimate model that would allow us to predict the balloon's behavior except over very brief time scales (we know the balloon cannot go 10 miles in 1 second, for example). In this case we would design a filter that emphasized the measurements over the predictions.\n",
"\n",
"Most of this book is devoted to expressing the concerns in the last three paragraphs mathematically, which then allows us to find an optimal solution. In this chapter we will merely be assigning different values to *g* and *h* in a more intuitive, and thus less optimal way. But the fundamental idea is just to blend somewhat inaccurate measurements with somewhat inaccurate models of how the systems behaves to get a filtered estimate that is better than either information source by itself."
"Most of this book is devoted to expressing the concerns in the last three paragraphs mathematically, which then allows us to find an optimal solution. In this chapter we will merely be assigning different values to *g* and *h* in a more intuitive, and thus less optimal way. But the fundamental idea is just to blend somewhat inaccurate measurements with somewhat inaccurate models of how the systems behaves to get a filtered estimate that is better than either information source by itself.\n",
"\n",
"We can express this as an algorithm:\n",
"\n",
"**Initialization**\n",
"\n",
" 1. Initialize the state of the filter\n",
" 2. Initialize our belief in the state - how accurate do we think it is\n",
" \n",
"**Predict**\n",
"\n",
" 1. Based on the system behavior, predict state at the next time step\n",
" 2. Adjust belief in that state to account for the uncertainty in prediction\n",
" \n",
"**Update**\n",
"\n",
" 1. Get a measurement and associated belief about its accuracy\n",
" 2. Compute difference (residual) between our estimated state and measurement\n",
" 3. Update state based on predicted state plus some proportion of the residual\n",
" \n",
"We will use this same algorithm throughout the book, albeit with some modifications. "
]
},
{
@ -2322,7 +2342,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.4.3"
"version": "3.4.1"
}
},
"nbformat": 4,

64
02_Discrete_Bayes.ipynb
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4
04_One_Dimensional_Kalman_Filters.ipynb
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@ -1601,7 +1601,7 @@
" \n",
"**Predict**\n",
"\n",
" 1. Based on the system behaves, predict its state at the next time step\n",
" 1. Based on the system behavior, predict state at the next time step\n",
" 2. Adjust belief in that state to account for the uncertainty in prediction\n",
" \n",
"**Update**\n",
@ -2472,7 +2472,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.4.3"
"version": "3.4.1"
}
},
"nbformat": 4,