## Abstract

The probability hypothesis density (PHD) filter is a first moment approximation to the evolution of a dynamic point process which can be used to approximate the optimal filtering equations of the multiple-object tracking problem. We show that, under reasonable assumptions, a sequential Monte Carlo (SMC) approximation of the PHD filter converges in mean of order , and hence almost surely, to the true PHD filter. We also present a central limit theorem for the SMC approximation, show that the variance is finite under similar assumptions and establish a recursion for the asymptotic variance. This provides a theoretical justification for this implementation of a tractable multiple-object filtering methodology and generalises some results from sequential Monte Carlo theory.

Translated title of the contribution | Convergence of the SMC implementation of the PHD filter |
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Original language | English |

Pages (from-to) | 265 - 291 |

Number of pages | 27 |

Journal | Methodology and Computing in Applied Probability |

Volume | 8 (2) |

DOIs | |

Publication status | Published - Jun 2006 |