Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering

Zheng Zhao, Toni Karvonen, Roland Hostettler, Simo Särkkä

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The note is concerned with Gaussian filtering in non-linear 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 linearisation 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 non-linear functions in the model. We analyse 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
Number of pages8
JournalIEEE Transactions on Automatic Control
Publication statusE-pub ahead of print - 25 Dec 2020
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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