Gaussian mixture PHD and CPHD filtering with partially uniform target birth
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The standard Gaussian Mixture Probability Hypothesis Density (GMPHD) filter and Cardinalised Probability Hypothesis Density (GMCPHD) filter require the target birth model to take the form of a Gaussian mixture. Although any density (including a uniform density), can be approximated using a sum of Gaussians, this can be inefficient in practice, especially when a large number of Gaussians is required to achieve the desired accuracy. A better alternative in the case of an uninformative birth model would be to directly use a uniform density instead of a Gaussian mixture approximation. In this paper we present new forms of the GMPHD and GMCPHD filtering equations, which allow part of the target birth model to take on a uniform distribution, thus obviating the need to use large Gaussian mixtures to approximate a uniform birth density.
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