Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering

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.

Keywords

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

DOI

10.1109/TAC.2020.3047367

Citation

Zhao, Z, Karvonen, T, Hostettler, R & Särkkä, S 2021, ' Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering ', IEEE Transactions on Automatic Control, vol. 66, no. 9, pp. 4460-4467 . https://doi.org/10.1109/TAC.2020.3047367

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https://urn.fi/URN:NBN:fi:aalto-202101251543

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[article-cris] Sähkötekniikan korkeakoulu / ELEC

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Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering

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