A Kernel Learning Method for Backward SDE Filter

2022/01/25 by Richard Archibald, Archibald, Richard, Feng Bao +1
Computer Science · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.2201.10600

openalex publication_date 2022/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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