Accurate Numerical Implementation of the Continuous-Discrete Extended Kalman Filter. Kulikov, G., Y. & Kulikova, M., V. IEEE Transactions on Automatic Control, 59(1):273-279, 1, 2014.
Accurate Numerical Implementation of the Continuous-Discrete Extended Kalman Filter [link]Website  abstract   bibtex   
This paper addresses an accurate and effective implementation of the continuous-discrete extended Kalman filtering method. The technique under discussion is grounded in numerical solution of the moment differential equations to predict the state mean of the stochastic dynamical system and the corresponding error covariance matrix. Here, we apply an efficient embedded Runge-Kutta pair possessing superior stability and many other attractive features, including automatic global error control, in order to improve performance of the complex computational procedure consisting of the extended Kalman filter and the underlying adaptive ODE solver. Thus, we introduce a new continuous-discrete adaptive extended Kalman filter and show its advantage over the standard variant on two test examples. In practice, this technique allows for much longer sampling intervals without any loss of accuracy, and that improves the applied potential of the extended Kalman filtering method, significantly.
@article{
 title = {Accurate Numerical Implementation of the Continuous-Discrete Extended Kalman Filter},
 type = {article},
 year = {2014},
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 keywords = {Automatic global error control,Kalman filters,Runge-Kutta methods,adaptive ODE solver,automatic global error control,complex computational procedure,continuous systems,continuous-discrete extended Kalman filtering meth,continuous-discrete model,covariance matrices,differential equations,discrete systems,embedded Runge-Kutta pair possessing superior stab,embedded Runge–Kutta pair,error covariance matrix,extended Kalman filter,moment differential equations,nonlinear filters,numerical implementation,stochastic dynamical system state mean,stochastic systems},
 pages = {273-279},
 volume = {59},
 websites = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6553080},
 month = {1},
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 short_title = {Automatic Control, IEEE Transactions on},
 abstract = {This paper addresses an accurate and effective implementation of the continuous-discrete extended Kalman filtering method. The technique under discussion is grounded in numerical solution of the moment differential equations to predict the state mean of the stochastic dynamical system and the corresponding error covariance matrix. Here, we apply an efficient embedded Runge-Kutta pair possessing superior stability and many other attractive features, including automatic global error control, in order to improve performance of the complex computational procedure consisting of the extended Kalman filter and the underlying adaptive ODE solver. Thus, we introduce a new continuous-discrete adaptive extended Kalman filter and show its advantage over the standard variant on two test examples. In practice, this technique allows for much longer sampling intervals without any loss of accuracy, and that improves the applied potential of the extended Kalman filtering method, significantly.},
 bibtype = {article},
 author = {Kulikov, Gennady Yu. and Kulikova, Maria V.},
 journal = {IEEE Transactions on Automatic Control},
 number = {1}
}

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