The continuous-discrete extended Kalman filter revisited

Russian Journal of Numerical Analysis and Mathematical Modelling, 32(1) (2017), 27-38
http://dx.doi.org/10.1515/rnam-2017-0003

This paper elaborates a new approach to nonlinear filtering grounded in an accurate implementation of the continuous–discrete extended Kalman filter for estimating stochastic dynamic systems. It implies that the moment differential equations for calculation of the predicted state mean and error covariance of propagated Gaussian density are solved accurately, i.e., with negligible errors. 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. In addition, this filter exploits the scaled local and global error controls to avoid any comparison of different physical units. The designed state estimator is compared numerically with continuous–discrete unscented and cubature Kalman filters to expose its practical efficiency. The problem of long waiting times (i.e., infrequent measurements) arisen in chemical and other engineering is also addressed.