Efficient numerical implementation of the continuous-discrete extended Kalman Filter |
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| 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 {\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. |
| Keywords | State estimation and prediction, extended Kalman filter |
| Type | Journal paper [With referee] |
| Journal | Computers and Chemical Engineering |
| Year | 2007 |
| BibTeX data | [bibtex] |
| IMM Group(s) | Mathematical Statistics |