Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering

• 成果类型: Article
• 署名作者: Zhao, Zheng; Karvonen, Toni; Hostettler, Roland; Sarkka, Simo
• 署名单位: Aalto University; Alan Turing Institute; Uppsala University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3047367
• 发表日期: 2021
• 页码: 4460-4467
• 关键词: Indium tin oxide; Taylor series; State-space methods; Numerical stability; Mathematical model; Time measurement; Thermal stability; Continuous-discrete state-space model; Gaussian filtering; Kalman filtering; stochastic differential equation (SDE); Taylor moment expansion (TME)

摘要

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.