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Convergence of the auxiliary particle implementation of the PHD filter

Whiteley, N and Singh, SS and Godsill, SJ (2008) Convergence of the auxiliary particle implementation of the PHD filter. Technical Report. Cambridge University Engineering Department, Cambridge, UK.

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Optimal Bayesian multi-target filtering is in general computationally impractical owing to the high dimensionality of the multi-target state. The Probability Hypothesis Density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed Sequential Monte Carlo (SMC) implementations of the PHD filter. However, these implementations are the equivalent of the Bootstrap Particle Filter, and the latter is well known to be inefficient. Drawing on ideas from the Auxiliary Particle Filter (APF), a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency was proposed by Whiteley et. al. Numerical examples were presented for two scenarios, including a challenging nonlinear observation model, to support the claim. This paper studies the theoretical properties of this auxiliary particle implementation. $\mathbb{L}_p$ error bounds are established from which almost sure convergence follows.

Item Type: Monograph (Technical Report)
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:54
Last Modified: 07 Mar 2019 14:56