@ARTICLE\{IMM2007-04253,
    author       = "J. B. J{\o}rgensen and M. R. Kristensen and P. G. Thomsen and H. Madsen",
    title        = "Efficient numerical implementation of the continuous-discrete extended Kalman Filter",
    year         = "2007",
    keywords     = "State estimation and prediction, extended Kalman filter",
    journal      = "Computers and Chemical Engineering",
    volume       = "",
    editor       = "",
    number       = "",
    publisher    = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/4253-full.html",
    abstract     = "This paper presents the computational challenges of state
estimation in nonlinear stochastic continuous-discrete time
systems. The extended Kalman filter for continuous-discrete time
systems is introduced by \{\$\backslash\$em ad hoc\} extension of a probabilistic
approach, based on Kolmogorov's forward equation, to filtering in
linear stochastic continuous-discrete time systems. The resulting
differential equations for the mean-covariance evolution of the
nonlinear stochastic continuous-discrete time systems are solved
efficiently using an {ESDIRK} integrator with sensitivity analysis
capabilities. This {ESDIRK} integrator for the mean-covariance
evolution is implemented as part of an extended Kalman filter and
tested on several systems. For moderate to large sized systems,
the {ESDIRK} based extended Kalman filter for nonlinear stochastic
continuous-discrete time systems is more than two orders of
magnitude faster than a conventional implementation. This is of
significance in nonlinear model predictive control applications,
statistical process monitoring as well as grey-box modelling of
systems described by stochastic differential equations."
}