CDF-KF algorithm for conditionally linear Gaussian state space models

We propose a new algorithm, called the central difference filter - Kalman filter (CDF-KF) for conditionally linear Gaussian state space models. The linear state equation is firstly inserted into the measurement equation, and the CDF is applied to the new measurement and the nonlinear state equations to estimate the nonlinear states, where after the estimated means of the nonlinear states are substituted into the linear state equation and the original measurement equation to estimate the linear states using the Kalman filter (KF). Moreover, in order to improve the accuracy of the estimation, the estimated covariances of the nonlinear states are fed back to modify the estimations of the linear states. The simulation results of the proposed CDF-KF applying to target tracking show that it only consumes about 5% the computing time required by the Rao-Blackwellized particle filter (RBPF), while the consistent filtering performance is kept.