The accurate continuous-discrete extended Kalman filter for continuous-time stochastic systems

Russian Journal of Numerical Analysis and Mathematical Modelling, 30(4) (2015), 239-249
http://dx.doi.org/10.1515/rnam-2015-0021

This paper elaborates a new approach to nonlinear filtering based on an accurate implementation of the continuous-discrete extended Kalman filter. It implies that the moment differential equations for calculating the predicted state mean of stochastic dynamic system and the corresponding error covariance matrix are solved accurately, i.e. with negligible error. The latter allows the total error of the extended Kalman filter to be reduced significantly and results in a new Accurate Continuous-Discrete Extended Kalman Filtering method. The developed technique is compared theoretically and numerically with other implementations of the extended Kalman filter to confirm its outstanding performance on test examples.