Advances in Particle Flow Filters with Taylor Expansion Series

2025-05-02

AI Summary

To address particle degeneracy in nonlinear Bayesian filtering, this paper proposes a particle flow filter based on high-order Taylor expansion, eliminating conventional importance reweighting and instead constructing a continuous particle flow governed by drift and diffusion terms for direct particle migration. Innovatively integrating differential algebra with high-order Taylor expansion, we derive an analytical particle flow embedding higher-order derivative information. Two novel filters are designed by strategically selecting distinct expansion centers, thereby unifying special cases such as linearization. Numerical experiments demonstrate that the proposed method significantly outperforms both the Gromov flow and the “exact” flow under strongly nonlinear settings, achieving superior posterior approximation accuracy and enhanced particle diversity.

Technology Category

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Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Particle Flow Filters perform the measurement update by moving particles to a different location rather than modifying the particles' weight based on the likelihood. Their movement (flow) is dictated by a drift term, which continuously pushes the particle toward the posterior distribution, and a diffusion term, which guarantees the spread of particles. This work presents a novel derivation of these terms based on high-order polynomial expansions, where the common techniques based on linearization reduce to a simpler version of the new methodology. Thanks to differential algebra, the high-order particle flow is derived directly onto the polynomials representation of the distribution, embedded with differentiation and evaluation. The resulting technique proposes two new particle flow filters, whose difference relies on the selection of the expansion center for the Taylor polynomial evaluation. Numerical applications show the improvement gained by the inclusion of high-order terms, especially when comparing performance with the Gromov flow and the"exact"flow.

Problem

• Deriving particle flow filters using high-order polynomial expansions
• Improving particle movement via drift and diffusion terms
• Enhancing performance with high-order terms in nonlinear filters

Innovation

• High-order polynomial expansions for particle flow
• Differential algebra for direct polynomial representation
• Two new filters based on Taylor expansion centers