On the continuous-discrete nonlinear filters by using divided difference approximations

Abstract

This paper considers a continuous-discrete (CD) nonlinear filtering problem by using the divided difference method ([19, 16, 21]), and derives CD divided difference first-order (CD-DD1) and second-order (CD-DD2) filters. Numerical integration procedures for the time update differential equations for the conditional mean and covariance matrix are obtained by using both Euler and Heun schemes. By using two simple models, we have performed comparative simulation studies, together with the CD unscented Kalman filter ([18]), to show the feasibility of the CD-DD1 and CD-DD2 filters.