Numerical Gaussian process Kalman filtering

Autor:	Küper, Armin, Waldherr, Steffen
Rok vydání:	2019
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning Electrical Engineering and Systems Science - Signal Processing Statistics - Computation
Druh dokumentu:	Working Paper
Popis:	In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian processes into the recursive Kalman filter equations. This embedding enables us to do Kalman filtering on infinite-dimensional systems using Gaussian processes. This is possible because i) we are obtaining a linear model from numerical Gaussian processes, and ii) the states of this model are by definition Gaussian distributed random variables. Convenient properties of the numerical GPKF are that no spatial discretization of the model is necessary, and manual setting up of the Kalman filter, that is fine-tuning the process and measurement noise levels by hand is not required, as they are learned online from the data stream. We showcase the capability of the numerical GPKF in a simulation study of the advection equation. Comment: 6 pages, 3 figures, this work has been accepted by IFAC for publication (\copyright 2020 IFAC)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1912.01234 Zobrazit plný text záznamu View this record from Arxiv