Gaussian-Based Parametric Bijections for Automatic Projection Filters

• 成果类型: Article
• 署名作者: Emzir, Muhammad F.; Zhao, Zheng; Cheded, Lahouari; Sarkka, Simo
• 署名单位: King Fahd University of Petroleum & Minerals; Uppsala University; Aalto University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3340979
• 发表日期: 2024
• 页码: 3449-3456
• 关键词: mathematical models; MANIFOLDS; Transforms; Hypercubes; Stochastic processes; STANDARDS; Information filters; Adaptive bijection; automatic differentiation; numerical quadrature; projection filter; sparse-grid integration

摘要

The automatic projection filter is a recently developed numerical method for projection filtering that leverages sparse-grid integration and automatic differentiation. However, its accuracy is highly sensitive to the accuracy of the cumulant-generating function computed via the sparse-grid integration, which in turn is also sensitive to the choice of the bijection from the canonical hypercube to the state space. In this article, we propose two new adaptive parametric bijections for the automatic projection filter. The first bijection relies on the minimization of Kullback-Leibler divergence, whereas the second method employs the sparse-grid Gauss-Hermite quadrature. The two new bijections allow the sparse-grid nodes to adaptively move within the high-density region of the state space, resulting in a substantially improved approximation while using only a small number of quadrature nodes. The practical applicability of the methodology is illustrated in three simulated nonlinear filtering problems.