Numerical Gaussian Process Kalman Filtering for Spatiotemporal Systems

• 成果类型: Article
• 署名作者: Kuper, Armin; Waldherr, Steffen
• 署名单位: KU Leuven; University of Vienna
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3232058
• 发表日期: 2023
• 页码: 3131-3138
• 关键词: Kalman filters; Gaussian Processes; Noise measurement; Numerical models; mathematical models; Spatiotemporal phenomena; Probabilistic logic; Kalman filtering; Linear system observers; Machine Learning; spatiotemporal systems

摘要

We present a novel Kalman filter (KF) for spatiotemporal systems called the numerical Gaussian process Kalman filter (NGPKF). Numerical Gaussian processes have recently been introduced as a physics-informed machine-learning method for simulating time-dependent partial differential equations without the need for spatial discretization while also providing uncertainty quantification of the simulation resulting from noisy initial data. We formulate numerical Gaussian processes as linear Gaussian state space models. This allows us to derive the recursive KF algorithm under the numerical Gaussian process state space model. Using two case studies, we show that the NGPKF is more accurate and robust, given enough measurements, than a spatial discretization-based KF.