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On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear Systems

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1 Author(s)
Sarkka, S. ; Helsinki Univ. of Technol., Helsinki

This paper considers the application of the unscented Kalman filter (UKF) to continuous-time filtering problems, where both the state and measurement processes are modeled as stochastic differential equations. The mean and covariance differential equations which result in the continuous-time limit of the UKF are derived. The continuous-discrete UKF is derived as a special case of the continuous-time filter, when the continuous-time prediction equations are combined with the update step of the discrete-time UKF. The filter equations are also transformed into sigma-point differential equations, which can be interpreted as matrix square root versions of the filter equations.

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Automatic Control, IEEE Transactions on  (Volume:52 ,  Issue: 9 )