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Particle Filters for Random Set Models

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Abstract

This chapter reviews the fundamentals of particle filtering with sensor control and introduces formally the most popular Bayes filters that emerged from the random set theoretical framework.

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Notes

  1. 1.

    A joint distribution function \(f_n(\mathbf{x }_1,\dots ,\mathbf{x }_n)\) is said to be symmetric if its value remains unchanged for all of the \(n!\) possible permutations of its variables.

  2. 2.

    While the FISST densities are not probability densities, they have been shown to be equivalent to probability densities on \({\fancyscript{F({ X})}}\) relative to some reference measure [29]. Subsequently, we do not distinguish between FISST densities and probability densities of random finite sets.

  3. 3.

    Some authors also call it the full Bayes multi-object filter.

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  1. DSTO, Lorimer Street 506, 3207, Port Melbourne, Australia

    Branko Ristic

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Ristic, B. (2013). Background. In: Particle Filters for Random Set Models. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6316-0_2

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  • DOI: https://doi.org/10.1007/978-1-4614-6316-0_2

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