• Corpus ID: 246285493

A Kernel Learning Method for Backward SDE Filter

  title={A Kernel Learning Method for Backward SDE Filter},
  author={Richard Archibald and Feng Bao},
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… 
A PDE-based Adaptive Kernel Method for Solving Optimal Filtering Problems
An adaptive kernel method is introduced to adaptively construct Gaussian kernels to approximate the probability distribution of the target state of a target stochastic dynamical system based on partial noisy observational data.


A Backward Doubly Stochastic Differential Equation Approach for Nonlinear Filtering Problems
A backward doubly stochastic differential equation (BDSDE) based nonlinear filtering method is considered. The solution of the BDSDE is the unnormalized density function of the conditional
Adaptive Meshfree Backward SDE Filter
An adaptive meshfree approach to solve the nonlinear filtering problem based on forward backward stochastic differential equations and introduces a Markov chain Monte Carlo resampling method to address the degeneracy problem of the adaptive space points.
Novel approach to nonlinear/non-Gaussian Bayesian state estimation
An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters, represented as a set of random samples, which are updated and propagated by the algorithm.
New Results in Linear Filtering and Prediction Theory
The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results and properties of the variance equation are of great interest in the theory of adaptive systems.
Discretization and Simulation of the Zakai Equation
This paper accurately analyse the error caused by an Euler type scheme of time discretization of Zakai equation of nonlinear filtering problem and McKean-Vlasov type equations and proposes an approximation scheme based on the re\-pre\-sentation of the solutions as weighted conditional distributions.
Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications
We give a survey of the developments in the theory of Backward Stochastic Differential Equations during the last 20 years, including the solutions’ existence and uniqueness, comparison theorem,
Forward backward doubly stochastic differential equations and the optimal filtering of diffusion processes
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward
Unscented filtering and nonlinear estimation
The motivation, development, use, and implications of the UT are reviewed, which show it to be more accurate, easier to implement, and uses the same order of calculations as linearization.
A Hybrid Sparse-Grid Approach for Nonlinear Filtering Problems Based on Adaptive-Domain of the Zakai Equation Approximations
A hybrid finite difference algorithm for the Zakai equation is constructed that combines the splitting-up finite difference scheme and hierarchical sparse grid method to solve moderately high-dimensional nonlinear filtering problems.
Nonlinear stability and ergodicity of ensemble based Kalman filters
The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical models with observed data. Despite their