SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Adaptive ODE Solvers in the Continuous-Discrete Extended Kalman Filtering Method I: Numerical Tests and Comparison

G. Kulikov and M. Kulikova

Abstract
This paper elaborates a new approach to nonlinear filtering based on an accurate implementation of the continuous-discrete extended Kalman filter (CD-EKF). It means that the arising moment differential equations for calculating the predicted state mean of the stochastic dynamic system and the corresponding error covariance matrix are solved accurately, i.e. with negligible error. The latter is achieved by using ODE solvers with global error control and allows the total error of the CD-EKF to be reduced, significantly. The new numerical scheme also retains the symmetry and the semi-positivity of the error covariance matrix, that is important for proper work of the CD-EKF. Eventually, our method results in a new Accurate Continuous-Discrete Extended Kalman Filter. The designed technique is compared numerically with other known implementations of the CD-EKF to confirm its outstanding performance on test problems.

Organized by         Universidad de Valladolid     IMUVA