An Implicit Algorithm of Solving Nonlinear Filtering Problems

Nonlinear filter problems arise in many applications such as communications and signal processing.Commonly used numerical simulation methods include Kalman filter method,particle filter method,etc.In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly.Numerical experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.