27 April 2010 A study of nonlinear filters with particle flow induced by log-homotopy
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In this paper, a study of the particle flow filter proposed by Daum and Huang has been conducted. It is discovered that for certain initial conditions, the desired particle flow that brings one particle from a good location in the prior distribution to a good location in the posterior distribution with an equal value does not exist. This explains the phenomenon of outliers experienced by Daum and Huang. Several ways of dealing with the singularity of the gradient have been discussed, including (1) not moving the particles without a flow solution, (2) stopping the flow entirely when it approaches the singularity, and (3) stopping for one step and starting in the next. In each case the resulting set of particles are examined, and it is doubtful that they form a valid set of samples for the approximation of the desired posterior distribution. In the case of the last method (stop and go), the particles mostly concentrate on the mode of the desired distribution (but they fail to represent the whole distribution), which may explain the "success" reported in the literature so far. An established method of moving particles, the well known Population Monte Carlo method, is briefly presented in this paper for ease of reference.
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Lingji Chen, Lingji Chen, Raman K Mehra, Raman K Mehra, } "A study of nonlinear filters with particle flow induced by log-homotopy", Proc. SPIE 7697, Signal Processing, Sensor Fusion, and Target Recognition XIX, 769706 (27 April 2010); doi: 10.1117/12.853001; https://doi.org/10.1117/12.853001

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