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clean up localization docs (#570)
* clean up localization docs * clean up localization docs * clean up localization docs
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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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"collapsed": true,
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"pycharm": {
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"name": "#%% md\n"
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}
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},
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"source": [
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"# Particle Filter Localization\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"source": [
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"## How to calculate covariance matrix from particles\n",
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"\n",
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"The covariance matrix $\\Xi$ from particle information is calculated by the following equation: \n",
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"\n",
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"$\\Xi_{j,k}=\\frac{1}{1-\\sum^N_{i=1}(w^i)^2}\\sum^N_{i=1}w^i(x^i_j-\\mu_j)(x^i_k-\\mu_k)$\n",
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"\n",
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"- $\\Xi_{j,k}$ is covariance matrix element at row $i$ and column $k$.\n",
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"\n",
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"- $w^i$ is the weight of the $i$ th particle. \n",
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"\n",
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"- $x^i_j$ is the $j$ th state of the $i$ th particle. \n",
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"\n",
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"- $\\mu_j$ is the $j$ th mean state of particles.\n",
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"\n",
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"Ref:\n",
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"\n",
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"- [Improving the particle filter in high dimensions using conjugate artificial process noise](https://arxiv.org/pdf/1801.07000.pdf)\n"
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],
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"metadata": {
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"collapsed": false
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}
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 2
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython2",
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"version": "2.7.6"
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},
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"pycharm": {
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"stem_cell": {
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"cell_type": "raw",
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"source": [],
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"metadata": {
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"collapsed": false
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}
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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