<p><strong>Particle Filter</strong> is what you are looking for to localize a robot. </p>

<p>To implement particle filter, you need an understanding of basic probability(mostly Bayes theorem), Gaussian distributions in 2D.</p>

<p><a href="http://ais.informatik.uni-freiburg.de/teaching/ws12/mapping/pdf/slam09-particle-filter-4.pdf" rel="nofollow noreferrer">slides</a>, <a href="https://www.youtube.com/watch?v=w0hH0bRF1zk" rel="nofollow noreferrer">video</a> </p>

<p>Watch these <a href="https://www.youtube.com/playlist?list=PLgnQpQtFTOGQrZ4O5QzbIHgl3b1JHimN_" rel="nofollow noreferrer">course videos</a>, which are really good.</p>

<blockquote>
  <p>for e.g. in one of the research paper it was written that Markov algorithm can be used in global indoor positioning system or when you have multi-modal gaussian distribution. whereas Kalman filter can not be used for the same reasons. Now, I completely didn't understand.</p>
</blockquote>

<p>Kalman filter or Extend Kalman filter is used for unimodal distribution and also the initial estimation must be good enough to track.</p>

<p>Particle filter is multi modal, doesn't need an initial guess, but need more particles (or samples) to converge to a better estimate.</p>

<blockquote>
  <p>second example, Markov Algorithm assume map is static and consider Markov assumption where measurements are independent and doesn't depend on previous measurements. but when environment is dynamic (objects are moving) , Markov assumption is not valid and we need to modify Markov algorithm to incorporate dynamic environment. Now, I don't understand why?</p>
</blockquote>

<p>If the objects are humans, it is not difficult to localize (unless the robot is completely covered by humans and robot is not able to see any part of the environment)even in a dynamic environment. A simple modification will be to consider laser rays which are in conformation with the map. Below paper explains this.</p>

<p>check this paper <a href="https://arxiv.org/pdf/1106.0222.pdf" rel="nofollow noreferrer">Markov Localization for Mobile Robots
in Dynami Environments</a></p>
How to understand Markov Localisation Algorithm?
<p>In my thesis project, I need to implement Monte Carlo Localisation algorithm (it's based on Markov Localisation). I have exactly one month of time to understand and implement the algorithm. I understand basics of probability and Bayes theorem. Now which topics I should get familiar with to understand Markov Algorithm? I have read couple of research papers 3-4 times, still I failed to understand everything. </p>

<p>I tried to do Google whichever terms I didn't understand but I couldn't get the essence of the algorithm. I want to understand systematically. I know what it does but I didn't fully understand how it does or why it does. </p>

<p>for e.g. in one of the research paper it was written that Markov algorithm can be used in global indoor positioning system or when you have multi-modal gaussian distribution. whereas Kalman filter can not be used for the same reasons. Now, I completely didn't understand. </p>

<p>second example, Markov Algorithm assume map is static and consider Markov assumption where measurements are independent and doesn't depend on previous measurements. but when environment is dynamic (objects are moving) , Markov assumption is not valid and we need to modify Markov algorithm to incorporate dynamic environment. Now, I don't understand why? </p>

<p>It would be great if someone point me out which topics should I learn to understand the algorithm. please keep in mind that I have only one month.</p>