A Kernel Learning Method for Backward SDE Filter

• URL: http://arxiv.org/abs/2201.10600v1
• Date: Tue, 25 Jan 2022 19:49:19 GMT
• Title: A Kernel Learning Method for Backward SDE Filter
• Authors: Richard Archibald, Feng Bao
• Abstract summary: We develop a kernel learning backward SDE filter method to propagate the state of a dynamical system based on its partial noisy observations. We introduce a kernel learning method to learn a continuous global approximation for the conditional probability density function of the target state. Numerical experiments demonstrate that the kernel learning backward SDE is highly effective and highly efficient.
• Score: 1.7035011973665108
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we develop a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to propagate the state of the target dynamical model, and Bayesian inference is applied to incorporate the observational information. To characterize the dynamical model in the entire state space, we introduce a kernel learning method to learn a continuous global approximation for the conditional probability density function of the target state by using discrete approximated density values as training data. Numerical experiments demonstrate that the kernel learning backward SDE is highly effective and highly efficient.

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