Design of discrete second order filters for continuous-discrete models

The paper deals with state estimation of nonlinear stochastic dynamic systems. In particular, the stress is laid on development of second-order discrete-time filters for nonlinear continuous-discrete models. Two different filters are derived based on different order of nonlinear function approximation and discretization of the continuous dynamics equation. For the approximation the Taylor expansion is used and for the discretization either exact method or approximate method based on the stochastic Taylor expansion are utilized. Performance of the filter algorithms is illustrated using an example of tracking a ship in deep water.