On the Continuous-Discrete Nonlinear Filters by Using Divided Difference Approximation

Abstract

This paper considers a continuous-discrete (C-D) nonlinear filtering problem by using the divided difference method, and develops C-D versions of the divided difference first-order (DD1) filter and the divided difference second-order (DD2) filter by extending the results due to Schei [6], Norgaard, et al [7] and Simandl, et al [8]. Since Jacobians are not needed in designing C-D DD1 and DD2 filters, these filters can be applied to the filtering problem for any C-D nonlinear systems, to which the C-D extended Kalman filter (EKF) is difficult to apply. Simulation results show that the performance of the proposed C-D DD2 algorithm is comparable to that of the C-D unscented Kalman filter (UKF), though the performance of the C-D DD1 filter is slightly inferior to them.