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I am trying to understand particle filters and their application but i am not able to understand the underlying methodology. I have read a few sources but either the language is not clear or they dive into mathematics too quickly.

I know kalman filters and have wrote a basic implementation in R myself after little help.I would like to have a similar understanding of particle filter.

Edit : A reference to a very good paper/tutorial would also be fine.

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2 Answers 2

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I know kalman filters and have ...

If this knowledge extends to Unscented filters, UKF, you can think of the UKF being a sparse particle filter. With a UKF you have a few sigma points which are propagated forward via your model function and then after the measurement update these sigma points are updated via covariance estimation.

With a particle filter, instead of a few sigma points you have very many more randomly allocated particles which are propagated forward via the model function and after the measurement update these particles are weighted according to their closeness to the new measurement. A new set of particles is then generated by weighted sampling of the "old" particles, and then we're ready to start the next round of propagation and update. Hopefully, over time, the cloud of particles converges to the true underlying state.

A completely non mathematical explanation is given at https://www.youtube.com/watch?v=aUkBa1zMKv4. MATLAB/Octave code for this youtube video is available at http://www.it.uu.se/katalog/andsv164/Teaching/Material/PF.m

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  • $\begingroup$ The youtube link explained it very nicely and inutuitively.Is there a good explanation for the mathematical part.Mainly how to filter the states based on current observation and how to update the weights of the particles ,something with code would be excellent $\endgroup$
    – pppp_prs
    Jun 25, 2020 at 14:05
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Supposing you put random points over a surface, over which the Density function is a terrain(hills,valleys) i.e.,you objective is go to a place where some information about your target is in the form of a peak, the sampling gives you an intution of the location of the target. Then you want to reduce the area of your sampling space as you gather more information on the target. If you adopt rejection sampling, you may sometimes miss the target peak during sampling. So you adopt to a method called importance sampling. For this you choose an appropriate PDF(even uniform pdf) and use the ratio of the heights of your PDF with the new selected PDF covering your space of sampling. The process goes on as Predict based on information, and Update using this information. This is how Monte Carlo methods work.

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