Moved example notebooks to examples
Frank Dellaert
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# A Discrete Switching System\n",
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"\n",
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"A la multi-hypothesis-smoother (MHS), but all discrete.\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"tags": [
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"remove-cell"
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]
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},
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"source": [
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"GTSAM Copyright 2010-2022, Georgia Tech Research Corporation,\n",
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"Atlanta, Georgia 30332-0415\n",
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"All Rights Reserved\n",
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"\n",
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"Authors: Frank Dellaert, et al. (see THANKS for the full author list)\n",
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"\n",
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"See LICENSE for the license information"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<a href=\"https://colab.research.google.com/github/borglab/gtsam/blob/develop/python/gtsam/examples/DiscreteSwitching.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"tags": [
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"remove-cell"
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]
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},
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"outputs": [],
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"source": [
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"# This needs gtbook:\n",
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"% pip install --quiet gtbook"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"from gtsam import DiscreteBayesNet, DiscreteKeys, DiscreteFactorGraph, Ordering\n",
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"from gtsam.symbol_shorthand import S\n",
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"from gtsam.symbol_shorthand import M"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"def P(*args):\n",
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" \"\"\" Create a DiscreteKeys instances from a variable number of DiscreteKey pairs.\"\"\"\n",
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" # TODO: We can make life easier by providing variable argument functions in C++ itself.\n",
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" dks = DiscreteKeys()\n",
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" for key in args:\n",
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" dks.push_back(key)\n",
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" return dks\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"import graphviz\n",
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"\n",
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"\n",
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"class show(graphviz.Source):\n",
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" \"\"\" Display an object with a dot method as a graph.\"\"\"\n",
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"\n",
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" def __init__(self, obj):\n",
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" \"\"\"Construct from object with 'dot' method.\"\"\"\n",
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" # This small class takes an object, calls its dot function, and uses the\n",
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" # resulting string to initialize a graphviz.Source instance. This in turn\n",
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" # has a _repr_mimebundle_ method, which then renders it in the notebook.\n",
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" super().__init__(obj.dot())\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div><p><tt>DiscreteBayesNet</tt> of size 4</p><div>\n",
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"<p> <i>P(s2|m1,s1):</i></p>\n",
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"<table class='DiscreteConditional'>\n",
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" <thead>\n",
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" <tr><th><i>m1</i></th><th><i>s1</i></th><th>0</th><th>1</th><th>2</th></tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr><th>0</th><th>0</th><td>0.9</td><td>0.1</td><td>0</td></tr>\n",
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" <tr><th>0</th><th>1</th><td>0.1</td><td>0.8</td><td>0.1</td></tr>\n",
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" <tr><th>0</th><th>2</th><td>0</td><td>0.1</td><td>0.9</td></tr>\n",
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" <tr><th>1</th><th>0</th><td>0.1</td><td>0.9</td><td>0</td></tr>\n",
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" <tr><th>1</th><th>1</th><td>0</td><td>0.1</td><td>0.9</td></tr>\n",
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" <tr><th>1</th><th>2</th><td>0.9</td><td>0</td><td>0.1</td></tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>\n",
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"<div>\n",
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"<p> <i>P(s3|m2,s2):</i></p>\n",
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"<table class='DiscreteConditional'>\n",
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" <thead>\n",
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" <tr><th><i>m2</i></th><th><i>s2</i></th><th>0</th><th>1</th><th>2</th></tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr><th>0</th><th>0</th><td>0.9</td><td>0.1</td><td>0</td></tr>\n",
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" <tr><th>0</th><th>1</th><td>0.1</td><td>0.8</td><td>0.1</td></tr>\n",
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" <tr><th>0</th><th>2</th><td>0</td><td>0.1</td><td>0.9</td></tr>\n",
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" <tr><th>1</th><th>0</th><td>0.1</td><td>0.9</td><td>0</td></tr>\n",
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" <tr><th>1</th><th>1</th><td>0</td><td>0.1</td><td>0.9</td></tr>\n",
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" <tr><th>1</th><th>2</th><td>0.9</td><td>0</td><td>0.1</td></tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>\n",
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"<div>\n",
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"<p> <i>P(s4|m3,s3):</i></p>\n",
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"<table class='DiscreteConditional'>\n",
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" <thead>\n",
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" <tr><th><i>m3</i></th><th><i>s3</i></th><th>0</th><th>1</th><th>2</th></tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr><th>0</th><th>0</th><td>0.9</td><td>0.1</td><td>0</td></tr>\n",
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" <tr><th>0</th><th>1</th><td>0.1</td><td>0.8</td><td>0.1</td></tr>\n",
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" <tr><th>0</th><th>2</th><td>0</td><td>0.1</td><td>0.9</td></tr>\n",
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" <tr><th>1</th><th>0</th><td>0.1</td><td>0.9</td><td>0</td></tr>\n",
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" <tr><th>1</th><th>1</th><td>0</td><td>0.1</td><td>0.9</td></tr>\n",
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" <tr><th>1</th><th>2</th><td>0.9</td><td>0</td><td>0.1</td></tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>\n",
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"<div>\n",
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"<p> <i>P(s5|m4,s4):</i></p>\n",
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"<table class='DiscreteConditional'>\n",
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" <thead>\n",
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" <tr><th><i>m4</i></th><th><i>s4</i></th><th>0</th><th>1</th><th>2</th></tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr><th>0</th><th>0</th><td>0.9</td><td>0.1</td><td>0</td></tr>\n",
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" <tr><th>0</th><th>1</th><td>0.1</td><td>0.8</td><td>0.1</td></tr>\n",
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" <tr><th>0</th><th>2</th><td>0</td><td>0.1</td><td>0.9</td></tr>\n",
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" <tr><th>1</th><th>0</th><td>0.1</td><td>0.9</td><td>0</td></tr>\n",
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" <tr><th>1</th><th>1</th><td>0</td><td>0.1</td><td>0.9</td></tr>\n",
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" <tr><th>1</th><th>2</th><td>0.9</td><td>0</td><td>0.1</td></tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>\n"
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],
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"text/markdown": [
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"`DiscreteBayesNet` of size 4\n",
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"\n",
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" *P(s2|m1,s1):*\n",
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"\n",
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"|*m1*|*s1*|0|1|2|\n",
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"|:-:|:-:|:-:|:-:|:-:|\n",
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"|0|0|0.9|0.1|0|\n",
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"|0|1|0.1|0.8|0.1|\n",
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"|0|2|0|0.1|0.9|\n",
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"|1|0|0.1|0.9|0|\n",
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"|1|1|0|0.1|0.9|\n",
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"|1|2|0.9|0|0.1|\n",
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"\n",
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" *P(s3|m2,s2):*\n",
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"\n",
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"|*m2*|*s2*|0|1|2|\n",
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"|:-:|:-:|:-:|:-:|:-:|\n",
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"|0|0|0.9|0.1|0|\n",
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"|0|1|0.1|0.8|0.1|\n",
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"|0|2|0|0.1|0.9|\n",
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"|1|0|0.1|0.9|0|\n",
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"|1|1|0|0.1|0.9|\n",
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"|1|2|0.9|0|0.1|\n",
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"\n",
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" *P(s4|m3,s3):*\n",
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"\n",
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"|*m3*|*s3*|0|1|2|\n",
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"|:-:|:-:|:-:|:-:|:-:|\n",
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"|0|0|0.9|0.1|0|\n",
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"|0|1|0.1|0.8|0.1|\n",
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"|0|2|0|0.1|0.9|\n",
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"|1|0|0.1|0.9|0|\n",
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"|1|1|0|0.1|0.9|\n",
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"|1|2|0.9|0|0.1|\n",
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"\n",
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" *P(s5|m4,s4):*\n",
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"\n",
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"|*m4*|*s4*|0|1|2|\n",
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"|:-:|:-:|:-:|:-:|:-:|\n",
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"|0|0|0.9|0.1|0|\n",
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"|0|1|0.1|0.8|0.1|\n",
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"|0|2|0|0.1|0.9|\n",
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"|1|0|0.1|0.9|0|\n",
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"|1|1|0|0.1|0.9|\n",
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"|1|2|0.9|0|0.1|\n",
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"\n"
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],
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"text/plain": [
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"DiscreteBayesNet\n",
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" \n",
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"size: 4\n",
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"conditional 0: P( s2 | m1 s1 ):\n",
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" Choice(s2) \n",
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" 0 Choice(s1) \n",
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" 0 0 Choice(m1) \n",
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" 0 0 0 Leaf 0.9\n",
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" 0 0 1 Leaf 0.1\n",
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" 0 1 Choice(m1) \n",
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" 0 1 0 Leaf 0.1\n",
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" 0 1 1 Leaf 0\n",
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" 0 2 Choice(m1) \n",
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" 0 2 0 Leaf 0\n",
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" 0 2 1 Leaf 0.9\n",
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" 1 Choice(s1) \n",
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" 1 0 Choice(m1) \n",
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" 1 0 0 Leaf 0.1\n",
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" 1 0 1 Leaf 0.9\n",
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" 1 1 Choice(m1) \n",
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" 1 1 0 Leaf 0.8\n",
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" 1 1 1 Leaf 0.1\n",
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" 1 2 Choice(m1) \n",
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" 1 2 0 Leaf 0.1\n",
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" 1 2 1 Leaf 0\n",
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" 2 Choice(s1) \n",
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" 2 0 Choice(m1) \n",
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" 2 0 0 Leaf 0\n",
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" 2 0 1 Leaf 0\n",
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" 2 1 Choice(m1) \n",
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" 2 1 0 Leaf 0.1\n",
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" 2 1 1 Leaf 0.9\n",
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" 2 2 Choice(m1) \n",
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" 2 2 0 Leaf 0.9\n",
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" 2 2 1 Leaf 0.1\n",
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"\n",
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"conditional 1: P( s3 | m2 s2 ):\n",
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" Choice(s3) \n",
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" 0 Choice(s2) \n",
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" 0 0 Choice(m2) \n",
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" 0 0 0 Leaf 0.9\n",
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" 0 0 1 Leaf 0.1\n",
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" 0 1 Choice(m2) \n",
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" 0 1 0 Leaf 0.1\n",
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" 0 1 1 Leaf 0\n",
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" 0 2 Choice(m2) \n",
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" 0 2 0 Leaf 0\n",
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" 0 2 1 Leaf 0.9\n",
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" 1 Choice(s2) \n",
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" 1 0 Choice(m2) \n",
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" 1 0 0 Leaf 0.1\n",
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" 1 0 1 Leaf 0.9\n",
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" 1 1 Choice(m2) \n",
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" 1 1 0 Leaf 0.8\n",
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" 1 1 1 Leaf 0.1\n",
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" 1 2 Choice(m2) \n",
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" 1 2 0 Leaf 0.1\n",
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" 1 2 1 Leaf 0\n",
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" 2 Choice(s2) \n",
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" 2 0 Choice(m2) \n",
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" 2 0 0 Leaf 0\n",
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" 2 0 1 Leaf 0\n",
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" 2 1 Choice(m2) \n",
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" 2 1 0 Leaf 0.1\n",
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" 2 1 1 Leaf 0.9\n",
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" 2 2 Choice(m2) \n",
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" 2 2 0 Leaf 0.9\n",
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" 2 2 1 Leaf 0.1\n",
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"\n",
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"conditional 2: P( s4 | m3 s3 ):\n",
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" Choice(s4) \n",
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" 0 Choice(s3) \n",
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" 0 0 Choice(m3) \n",
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" 0 0 0 Leaf 0.9\n",
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" 0 0 1 Leaf 0.1\n",
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" 0 1 Choice(m3) \n",
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" 0 1 0 Leaf 0.1\n",
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" 0 1 1 Leaf 0\n",
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" 0 2 Choice(m3) \n",
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" 0 2 0 Leaf 0\n",
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" 0 2 1 Leaf 0.9\n",
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" 1 Choice(s3) \n",
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" 1 0 Choice(m3) \n",
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" 1 0 0 Leaf 0.1\n",
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" 1 0 1 Leaf 0.9\n",
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" 1 1 Choice(m3) \n",
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" 1 1 0 Leaf 0.8\n",
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" 1 1 1 Leaf 0.1\n",
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" 1 2 Choice(m3) \n",
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" 1 2 0 Leaf 0.1\n",
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" 1 2 1 Leaf 0\n",
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" 2 Choice(s3) \n",
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" 2 0 Choice(m3) \n",
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" 2 0 0 Leaf 0\n",
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" 2 0 1 Leaf 0\n",
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" 2 1 Choice(m3) \n",
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" 2 1 0 Leaf 0.1\n",
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" 2 1 1 Leaf 0.9\n",
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" 2 2 Choice(m3) \n",
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" 2 2 0 Leaf 0.9\n",
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" 2 2 1 Leaf 0.1\n",
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"\n",
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"conditional 3: P( s5 | m4 s4 ):\n",
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" Choice(s5) \n",
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" 0 Choice(s4) \n",
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" 0 0 Choice(m4) \n",
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" 0 0 0 Leaf 0.9\n",
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" 0 0 1 Leaf 0.1\n",
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" 0 1 Choice(m4) \n",
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" 0 1 0 Leaf 0.1\n",
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" 0 1 1 Leaf 0\n",
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" 0 2 Choice(m4) \n",
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" 0 2 0 Leaf 0\n",
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" 0 2 1 Leaf 0.9\n",
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" 1 Choice(s4) \n",
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" 1 0 Choice(m4) \n",
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" 1 0 0 Leaf 0.1\n",
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" 1 0 1 Leaf 0.9\n",
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" 1 1 Choice(m4) \n",
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" 1 1 0 Leaf 0.8\n",
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" 1 1 1 Leaf 0.1\n",
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" 1 2 Choice(m4) \n",
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" 1 2 0 Leaf 0.1\n",
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" 1 2 1 Leaf 0\n",
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" 2 Choice(s4) \n",
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" 2 0 Choice(m4) \n",
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" 2 0 0 Leaf 0\n",
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" 2 0 1 Leaf 0\n",
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" 2 1 Choice(m4) \n",
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" 2 1 0 Leaf 0.1\n",
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" 2 1 1 Leaf 0.9\n",
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" 2 2 Choice(m4) \n",
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" 2 2 0 Leaf 0.9\n",
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" 2 2 1 Leaf 0.1\n"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"nrStates = 3\n",
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"K = 5\n",
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"\n",
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"bayesNet = DiscreteBayesNet()\n",
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"for k in range(1, K):\n",
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" key = S(k), nrStates\n",
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" key_plus = S(k+1), nrStates\n",
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" mode = M(k), 2\n",
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" bayesNet.add(key_plus, P(mode, key), \"9/1/0 1/8/1 0/1/9 1/9/0 0/1/9 9/0/1\")\n",
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"\n",
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"bayesNet"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/svg+xml": [
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"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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"</g>\n",
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"</svg>\n"
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],
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"text/plain": [
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]
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||||
},
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||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# Create a factor graph out of the Bayes net.\n",
|
||||
"factorGraph = DiscreteFactorGraph(bayesNet)\n",
|
||||
"show(factorGraph)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
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||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Position 0: s1, s2, s3, s4, s5, m1, m2, m3, m4\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# Create a BayesTree out of the factor graph.\n",
|
||||
"ordering = Ordering()\n",
|
||||
"# First eliminate \"continuous\" states in time order\n",
|
||||
"for k in range(1, K+1):\n",
|
||||
" ordering.push_back(S(k))\n",
|
||||
"for k in range(1, K):\n",
|
||||
" ordering.push_back(M(k))\n",
|
||||
"print(ordering)\n",
|
||||
"bayesTree = factorGraph.eliminateMultifrontal(ordering)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
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||||
"metadata": {},
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||||
"outputs": [
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{
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"data": {
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"<title>G</title>\n",
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"<title>0</title>\n",
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"<text text-anchor=\"middle\" x=\"102.02\" y=\"-228.95\" font-family=\"Times,serif\" font-size=\"14.00\">s4, s5, m1, m2, m3, m4</text>\n",
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"</g>\n",
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"<!-- 1 -->\n",
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"</g>\n",
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"<!-- 0->1 -->\n",
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"<g id=\"edge1\" class=\"edge\">\n",
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"<title>0->1</title>\n",
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"</g>\n",
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"<!-- 2 -->\n",
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"<g id=\"node3\" class=\"node\">\n",
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"<title>2</title>\n",
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|
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"<text text-anchor=\"middle\" x=\"102.02\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">s2 : m1, m2, s3</text>\n",
|
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"</g>\n",
|
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"<!-- 1->2 -->\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<title>1->2</title>\n",
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"<!-- 3 -->\n",
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"<text text-anchor=\"middle\" x=\"102.02\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">s1 : m1, s2</text>\n",
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"</g>\n",
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"<!-- 2->3 -->\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>2->3</title>\n",
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"</svg>\n"
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"text/plain": [
|
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"<__main__.show at 0x11775c3e0>"
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]
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},
|
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"execution_count": 8,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
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}
|
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],
|
||||
"source": [
|
||||
"show(bayesTree)"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "py312",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.12.6"
|
||||
},
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"orig_nbformat": 4
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},
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"nbformat": 4,
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"nbformat_minor": 2
|
||||
}
|
||||
|
|
@ -6,13 +6,19 @@
|
|||
"source": [
|
||||
"# Equivariant Filter Bias\n",
|
||||
"\n",
|
||||
"Implementing the example in [Fornasier et al, 2022, Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation with Online Calibration](https://arxiv.org/pdf/2209.12038).\n",
|
||||
"\n",
|
||||
"This notebook uses [Alessandro Fornasier's equivariant filter code](https://github.com/aau-cns/ABC-EqF) converted to use GTSAM's libraries.\n",
|
||||
"Implementing the example in the \"Overcoming Bias\" paper by {cite:t}`https://doi.org/10.1109/LRA.2022.3210867` ([arxiv version](https://arxiv.org/pdf/2209.12038)).\n",
|
||||
"This notebook was created by converting [Alessandro Fornasier's equivariant filter code](https://github.com/aau-cns/ABC-EqF) to use GTSAM's built-in data structures.\n",
|
||||
"\n",
|
||||
"Authors: Jennifer Oum & Darshan Rajasekaran"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<a href=\"https://colab.research.google.com/github/borglab/gtsam/blob/develop/python/gtsam/examples/EqF.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {
|
||||
|
|
|
|||
|
|
@ -1,24 +1,76 @@
|
|||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"\"\"\"\n",
|
||||
"# Extended Kalman Filter\n",
|
||||
"\n",
|
||||
"Extended Kalman filter on a moving 2D point, but done using factor graphs.\n",
|
||||
"This example uses the ExtendedKalmanFilter class to perform filtering\n",
|
||||
"on a linear system, demonstrating the same operations as in elaboratePoint2KalmanFilter.\n",
|
||||
"\"\"\"\n",
|
||||
"\n",
|
||||
"Author: Matt Kielo"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {
|
||||
"tags": [
|
||||
"remove-cell"
|
||||
]
|
||||
},
|
||||
"source": [
|
||||
"GTSAM Copyright 2010-2022, Georgia Tech Research Corporation,\n",
|
||||
"Atlanta, Georgia 30332-0415\n",
|
||||
"All Rights Reserved\n",
|
||||
"\n",
|
||||
"Authors: Frank Dellaert, et al. (see THANKS for the full author list)\n",
|
||||
"\n",
|
||||
"See LICENSE for the license information"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<a href=\"https://colab.research.google.com/github/borglab/gtsam/blob/develop/python/gtsam/examples/easyPoint2KalmanFilter.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {
|
||||
"tags": [
|
||||
"remove-cell"
|
||||
]
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Note: you may need to restart the kernel to use updated packages.\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%pip install --quiet gtsam gtbook"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import gtsam\n",
|
||||
"import numpy as np"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -49,7 +101,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -64,8 +116,8 @@
|
|||
"X3 Update: [3. 0.]\n",
|
||||
"\n",
|
||||
"Easy Final Covariance (after update):\n",
|
||||
" [[0.0193 0. ]\n",
|
||||
" [0. 0.0193]]\n"
|
||||
" [[0.01930567 0. ]\n",
|
||||
" [0. 0.01930567]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -100,7 +152,7 @@
|
|||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"display_name": "py312",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
|
|
@ -114,7 +166,7 @@
|
|||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.10.12"
|
||||
"version": "3.12.6"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
@ -1,34 +1,69 @@
|
|||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"\"\"\"\n",
|
||||
"\n",
|
||||
"# Elaborate EKF Example\n",
|
||||
"\n",
|
||||
"Simple linear Kalman filter on a moving 2D point using factor graphs in GTSAM.\n",
|
||||
"This example manually creates all of the needed data structures to show how\n",
|
||||
"the Kalman filter works under the hood using factor graphs, but uses a loop\n",
|
||||
"to handle the repetitive prediction and update steps.\n",
|
||||
"\n",
|
||||
"Based on the C++ example by Frank Dellaert and Stephen Williams\n",
|
||||
"\"\"\"\n",
|
||||
"Author: Matt Kielo. Based on the C++ example by Frank Dellaert and Stephen Williams"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {
|
||||
"tags": [
|
||||
"remove-cell"
|
||||
]
|
||||
},
|
||||
"source": [
|
||||
"GTSAM Copyright 2010-2022, Georgia Tech Research Corporation,\n",
|
||||
"Atlanta, Georgia 30332-0415\n",
|
||||
"All Rights Reserved\n",
|
||||
"\n",
|
||||
"Authors: Frank Dellaert, et al. (see THANKS for the full author list)\n",
|
||||
"\n",
|
||||
"See LICENSE for the license information"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<a href=\"https://colab.research.google.com/github/borglab/gtsam/blob/develop/python/gtsam/examples/elaboratePoint2KalmanFilter.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import gtsam\n",
|
||||
"import numpy as np\n",
|
||||
"from gtsam import Point2, noiseModel\n",
|
||||
"from gtsam.symbol_shorthand import X"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The code below basically implements the SRIF (Square-root Information filter version of the EKF) with Cholesky factorization."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# [code below basically does SRIF with Cholesky]\n",
|
||||
"\n",
|
||||
"# Setup containers for linearization points\n",
|
||||
"linearization_points = gtsam.Values()\n",
|
||||
"\n",
|
||||
File diff suppressed because one or more lines are too long
|
|
@ -1,155 +0,0 @@
|
|||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# A Discrete Switching System\n",
|
||||
"\n",
|
||||
"A la MHS, but all discrete.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from gtsam import DiscreteBayesNet, DiscreteKeys, DiscreteFactorGraph, Ordering\n",
|
||||
"from gtsam.symbol_shorthand import S\n",
|
||||
"from gtsam.symbol_shorthand import M\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def P(*args):\n",
|
||||
" \"\"\" Create a DiscreteKeys instances from a variable number of DiscreteKey pairs.\"\"\"\n",
|
||||
" # TODO: We can make life easier by providing variable argument functions in C++ itself.\n",
|
||||
" dks = DiscreteKeys()\n",
|
||||
" for key in args:\n",
|
||||
" dks.push_back(key)\n",
|
||||
" return dks\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import graphviz\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class show(graphviz.Source):\n",
|
||||
" \"\"\" Display an object with a dot method as a graph.\"\"\"\n",
|
||||
"\n",
|
||||
" def __init__(self, obj):\n",
|
||||
" \"\"\"Construct from object with 'dot' method.\"\"\"\n",
|
||||
" # This small class takes an object, calls its dot function, and uses the\n",
|
||||
" # resulting string to initialize a graphviz.Source instance. This in turn\n",
|
||||
" # has a _repr_mimebundle_ method, which then renders it in the notebook.\n",
|
||||
" super().__init__(obj.dot())\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"nrStates = 3\n",
|
||||
"K = 5\n",
|
||||
"\n",
|
||||
"bayesNet = DiscreteBayesNet()\n",
|
||||
"for k in range(1, K):\n",
|
||||
" key = S(k), nrStates\n",
|
||||
" key_plus = S(k+1), nrStates\n",
|
||||
" mode = M(k), 2\n",
|
||||
" bayesNet.add(key_plus, P(mode, key), \"9/1/0 1/8/1 0/1/9 1/9/0 0/1/9 9/0/1\")\n",
|
||||
"\n",
|
||||
"bayesNet"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"show(bayesNet)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# Create a factor graph out of the Bayes net.\n",
|
||||
"factorGraph = DiscreteFactorGraph(bayesNet)\n",
|
||||
"show(factorGraph)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# Create a BayesTree out of the factor graph.\n",
|
||||
"ordering = Ordering()\n",
|
||||
"# First eliminate \"continuous\" states in time order\n",
|
||||
"for k in range(1, K+1):\n",
|
||||
" ordering.push_back(S(k))\n",
|
||||
"for k in range(1, K):\n",
|
||||
" ordering.push_back(M(k))\n",
|
||||
"print(ordering)\n",
|
||||
"bayesTree = factorGraph.eliminateMultifrontal(ordering)\n",
|
||||
"bayesTree"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"show(bayesTree)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"interpreter": {
|
||||
"hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
|
||||
},
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3.8.9 64-bit",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.9.7"
|
||||
},
|
||||
"orig_nbformat": 4
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 2
|
||||
}
|
||||
Loading…
Reference in New Issue