Gaussian-Based Parametric Bijections for Automatic Projection Filters

Muhammad F. Emzir, Zheng Zhao, Lahouari Cheded, Simo Sarkka

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


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 paper, 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.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalIEEE Transactions on Automatic Control
Publication statusE-pub ahead of print - 2023
MoE publication typeA1 Journal article-refereed


  • Adaptive bijection
  • automatic differentiation
  • Hypercubes
  • Information filters
  • Manifolds
  • Mathematical models
  • numerical quadrature
  • projection filter
  • sparse-grid integration
  • Standards
  • Stochastic processes
  • Transforms


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