A plethora of open problems in particle flow research for nonlinear filters, Bayesian decisions, Bayesian learning, and transport

Daum, Fred; Huang, Jim

doi:10.1117/12.2217755

Cited by 8 publications

(10 citation statements)

References 52 publications

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“…There are multiple possibilities for future efforts. A comprehensive list of topics for future research is provided in [11,12]. Here we just point out a few directly relevant to the topic of this paper.…”

Section: Discussionmentioning

confidence: 99%

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A New Parameterized Family of Stochastic Particle Flow Filters

Dai,

Daum

2021

Preprint

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We derive a parameterized family of stochastic particle flows driven by a nonzero diffusion process for nonlinear filtering, Bayesian inference, or target tracking. This new family of stochastic flows takes the form of a linear combination of prior knowledge and measurement likelihood information. It is shown that several particle flows existing in the literature are special cases of this family. We prove that the particle flows are unbiased under the assumption of linear measurement and Gaussian distributions, and examine the consistency of estimates constructed from the stochastic flows. We further establish several finite time stability concepts for this new family of stochastic particle flows.

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Section: Discussionmentioning

confidence: 99%

“…It was derived again in [5,24]. We need to verify that when Q = 0, (12) and ( 13) become ( 21) and ( 22), respectively. When Q = 0, we know from (8) that…”

Section: Appendixmentioning

confidence: 98%

A New Parameterized Family of Stochastic Particle Flow Filters

Dai,

Daum

2021

Preprint

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“…The results guarantee that the particles do not diverge to infinity. As for future efforts, a comprehensive summary of open problems is available in [11].…”

Section: Discussionmentioning

confidence: 99%

Stability and Convergence of Stochastic Particle Flow Filters

Dai¹,

Daum²

2021

Preprint

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In this paper, we examine dynamic properties of particle flows for a recently derived parameterized family of stochastic particle flow filters for nonlinear filtering and Bayesian inference.In particular, we establish that particles maintain desired posterior distribution without the Gaussian assumption on measurement likelihood. Adopting the concept of Lyapunov stability, we further show that particles stay close but do not converge to the maximum likelihood estimate of the posterior distribution. The results demonstrate that stability of particle flows is maintained for this family of stochastic particle flow filters.

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“…This is called the "Nprinciple". Further research to exploit this powerful fact is outlined in [32] and [34].…”

Section: Particle Flow For Bayes' Rulementioning

confidence: 98%