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kalandfam.html
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<!DOCTYPE html>
<html lang="en-us">
<html>
<head>
<title>Pruthvi Sanghavi</title>
<link rel="icon" type="image/png" href="images/logo.png"/>
</head>
<script type="text/javascript" src="https://platform.linkedin.com/badges/js/profile.js" async defer></script>
<link href="https://fonts.googleapis.com/css2?family=Caveat&display=swap" rel="stylesheet">
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<link href="https://fonts.googleapis.com/css2?family=Poiret+One&display=swap" rel="stylesheet">
<!-- <body background="images/chaotic_oscillator.png"> -->
<!-- <body background="images/davinciback3.gif"> -->
<center>
<h1 style="color:black; font-family: Reenie Beanie; font-size:40px"> Kalman Filter and Family</h1>
</center>
<style>
p
{
width:900px;
word-wrap:break-word;
}
</style>
<style>
hr{
width: 900px;
}
</style>
<section id="menu">
<center>
<button style="color:white"><a href="index.html" style="text-decoration: none; color:black; font-family: Poiret One;">Home </a></button>
</center>
</section>
<section id="body">
<center>
<p align="justify" style="color:black; font-family: Poiret One;"><b>Thought:</b> My girl friend hasn't texted since an hour, she must have died!</p>
<p align="justify" style="color:black; font-family: Poiret One;"><b>Hypothesis:</b> She is dead.</p>
<p align="justify" style="color:black; font-family: Poiret One;"><b>Evidence:</b> She hasn't texted since in an hour.</p>
</center>
</section>
<section id="mathtest">
<center>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
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extensions: ["tex2jax.js"],
"HTML-CSS": { preferredFont: "TeX", availableFonts: ["STIX","TeX"] },
tex2jax: { inlineMath: [ ["$", "$"], ["\\(","\\)"] ], displayMath: [ ["$$","$$"], ["\\[", "\\]"] ], processEscapes: true, ignoreClass: "tex2jax_ignore|dno" },
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<p align="justify" style="color:black; font-family: Poiret One;">$P(E) = $ Probability of her not texting given that she has died = 100%</p>
<p align="justify" style="color:black; font-family: Poiret One;">$P(H) = $ Probability of suddenly dying = 0.01%</p>
<p align="justify" style="color:black; font-family: Poiret One;">$P(E/-H) = $ Probability of her not texting (regardless of her well being) = 50%</p>
<p align="justify" style="color:black; font-family: Poiret One;">Here in order to find the posterior $P(H/E)$ (Probability of her dying given that she did not text) Bayes theorem is used which can be written as,</p>
<p align="justify" style="color:black; font-family: Poiret One;">$P(H/E) = \frac{P(E)P(H)}{(P(E)+P(H)) + (P(-H)P(E/-H))}$</p>
</center>
</section>
<section id ="references">
<center>
<h4 style="color:black; font-family: Poiret One;">References</h4>
<p align="justify" style="color:black; font-family: Poiret One;">[1] https://www.intechopen.com/books/kalman-filters-theory-for-advanced-applications/kalman-filter-for-moving-object-tracking-performance-analysis-and-filter-design</p>
<p align="justify" style="color:black; font-family: Poiret One;">[2] https://towardsdatascience.com/kalman-filter-interview-bdc39f3e6cf3</p>
<p align="justify" style="color:black; font-family: Poiret One;">[3] https://www.youtube.com/playlist?list=PLX2gX-ftPVXU3oUFNATxGXY90AULiqnWT</p>
<p align="justify" style="color:black; font-family: Poiret One;">[4] http://ais.informatik.uni-freiburg.de/teaching/ws13/mapping/</p>
<p align="justify" style="color:black; font-family: Poiret One;">[5] https://www.youtube.com/playlist?list=PLzCl0zqNaIBuo957MnuuDyNF2YqOYfaDP</p>
</center>
</section>