Convergence of the auxiliary particle implementation of the PHD filter

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.

Auxiliary particle implementation of the probability hypothesis density filter

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), we present a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency. Numerical examples are presented for two scenarios, including a challenging nonlinear observation model.

Drag on an ellipsoid particle in free-molecular plasma flow

Based on the analysis of molecular gas dynamics, the drag and moment acting on an ellipsoid particle of revolution X-2/a(2) + Y-2/a(2) + Z(2)/c(2) = 1, as an example of nonspherical particles, are studied under the condition of free-molecular plasma flow with thin plasma sheaths. A nonzero moment which causes nonspherical particle self-oscillation and self-rotation around its own axis in the plasma flow-similar to the pitching moment in aerodynamics-is discovered for the first time. When the ratio of axis length c/a is unity, the moment is zero and the drag formula are reduced to the well-known results of spherical particles. The effects of the particle-plasma relative velocity, the plasma temperature, and the particle materials on the drag and moment are also investigated.