Particle filter using second-order central difference

To improve the filtering precision when dealing with the state estimation problem of nonlinear systems, a new particle filter is proposed. The particle filter uses second-order central difference filter to generate the proposal distribution. The second-order central difference based on Stirling's interpolation formula is used to generate approximations to nonlinear dynamics, which avoids the evaluation of the Jacobian derivative matrix and is easy to implement. Cholesky factorization is employed to ensure the positive definiteness of the covariance matrix. The truncated errors of the local linearization are reduced in certain extent, and the latest measurements are integrated into the system state transition density so that the approximation to the system posterior density is improved. Simulation results indicate that the state estimation accuracy of new particle filter is improved more than 20% and the calculation cost is decreased, compared with the unscented particle filter.