clean up localization docs (#570)

* clean up localization docs

* clean up localization docs

* clean up localization docs
This commit is contained in:
Atsushi Sakai
2021-11-18 22:35:10 +09:00
committed by GitHub
parent 137e372db1
commit 35984e8978
9 changed files with 28 additions and 1504 deletions

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"source": [
"# Particle Filter Localization\n",
"\n"
]
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"source": [
"## How to calculate covariance matrix from particles\n",
"\n",
"The covariance matrix $\\Xi$ from particle information is calculated by the following equation: \n",
"\n",
"$\\Xi_{j,k}=\\frac{1}{1-\\sum^N_{i=1}(w^i)^2}\\sum^N_{i=1}w^i(x^i_j-\\mu_j)(x^i_k-\\mu_k)$\n",
"\n",
"- $\\Xi_{j,k}$ is covariance matrix element at row $i$ and column $k$.\n",
"\n",
"- $w^i$ is the weight of the $i$ th particle. \n",
"\n",
"- $x^i_j$ is the $j$ th state of the $i$ th particle. \n",
"\n",
"- $\\mu_j$ is the $j$ th mean state of particles.\n",
"\n",
"Ref:\n",
"\n",
"- [Improving the particle filter in high dimensions using conjugate artificial process noise](https://arxiv.org/pdf/1801.07000.pdf)\n"
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