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How do you calculate the likelihood of making an observation ?

Does someone have a link to a book or article that explains the math that you need to do to implement a PF algorithm? Conceptually i understand the implementation but I'm having a hard time updating the particles after a measurement update. Any resource that goes over the math in details/ with examples would really help.

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Here you can find a really interesting video explanation on particle filters.

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"Probabilistic Robotics" by Sebastian Thrun, Wolfram Burgard, Dieter Fox is the book you are looking for.

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