A Kernel Learning Method for Backward SDE Filter
This work addresses state estimation for stochastic systems, presenting an incremental improvement by integrating kernel learning with backward SDE methods.
The paper tackles state estimation in stochastic dynamical systems with partial noisy observations by developing a kernel learning backward SDE filter, which uses a kernel method to approximate conditional probability densities and shows high effectiveness and efficiency in numerical experiments.
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.