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John B. Jørgensen, Morten R. Kristensen, Per G. Thomsen and Henrik
Madsen
Efficient Numerical
Implementation of the Continuous Discrete Extended Kalman Filter
Submitted to Computers and
Chemical Engineering, 2006
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 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 is 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 of stochastic differential equations.
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