TY - JOUR
T1 - A Backward Doubly Stochastic Differential Equation Approach for Nonlinear Filtering Problems
JO - Communications in Computational Physics
VL - 5
SP - 1573
EP - 1601
PY - 2018
DA - 2018/04
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2017-0084
UR - https://global-sci.org/intro/article_detail/cicp/11227.html
KW - Nonlinear filtering problems, backward doubly stochastic differential equation, first order algorithm, quasi Monte Carlo sequence.
AB - <p style="text-align: justify;">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 expectation of the state variable with respect to
the observation filtration, which solves the nonlinear filtering problem through the
Kallianpur formula. A first order finite difference algorithm is constructed to solve the
BSDES, which results in an accurate numerical method for nonlinear filtering problems.
Numerical experiments demonstrate that the BDSDE filter has the potential to
significantly outperform some of the well known nonlinear filtering methods such as
particle filter and Zakai filter in both numerical accuracy and computational complexity.</p>