Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering

Zheng Zhao, Toni Karvonen, Roland Hostettler, Simo Särkkä

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
151 Downloads (Pure)


This article is concerned with Gaussian filtering in nonlinear continuous-discrete state-space models. We propose a novel Taylor moment expansion (TME) Gaussian filter, which approximates the moments of the stochastic differential equation with a temporal Taylor expansion. Differently from classical linearization or Ito-Taylor approaches, the Taylor expansion is formed for the moment functions directly and in time variable, not by using a Taylor expansion on the nonlinear functions in the model. We analyze the theoretical properties, including the positive definiteness of the covariance estimate and stability of the TME filter. By numerical experiments, we demonstrate that the proposed TME Gaussian filter significantly outperforms the state-of-the-art methods in terms of estimation accuracy and numerical stability.

Original languageEnglish
Pages (from-to)4460-4467
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number9
Early online date25 Dec 2020
Publication statusPublished - Sep 2021
MoE publication typeA1 Journal article-refereed


  • Continuous-discrete state-space model
  • Gaussian filtering
  • Indium tin oxide
  • Kalman filtering
  • Mathematical model
  • Numerical stability
  • State-space methods
  • stochastic differential equation
  • Taylor moment expansion
  • Taylor series
  • Thermal stability
  • Time measurement


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