A Kernel Learning Method for Backward SDE Filter

TL;DR

This paper introduces a kernel learning-based backward SDE filter that estimates the state of stochastic systems from noisy observations, combining stochastic differential equations with kernel methods for efficient Bayesian inference.

Contribution

It presents a novel kernel learning approach integrated with backward SDEs to approximate the conditional density function across the entire state space.

Findings

The method effectively estimates system states from noisy data.

Numerical experiments show high efficiency and accuracy.

The approach outperforms traditional filtering techniques.

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.