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ICASSP
2008
IEEE

On nonlinear transformations of stochastic variables and its application to nonlinear filtering

13 years 10 months ago
On nonlinear transformations of stochastic variables and its application to nonlinear filtering
A class of nonlinear transformation-based filters (NLTF) for state estimation is proposed. The nonlinear transformations that can be used include first (TT1) and second (TT2) order Taylor expansions, the unscented transformation (UT), and the Monte Carlo transformation (MCT) approximation. The unscented Kalman filter (UKF) is by construction a special case, but also nonstandard implementations of the Kalman filter (KF) and the extended Kalman filter (EKF) are included, where there are no explicit Riccati equations. The theoretical properties of these mappings are important for the performance of the NLTF. TT2 does by definition take care of the bias and covariance of the second order term that is neglected in the TT1 based EKF. The UT computes this bias term accurately, but the covariance is correct only for scalar state vectors. This result is demonstrated with a simple example and a general theorem, which explicitly shows the difference between TT1, TT2, UT, and MCT.
Fredrik Gustafsson, Gustaf Hendeby
Added 30 May 2010
Updated 30 May 2010
Type Conference
Year 2008
Where ICASSP
Authors Fredrik Gustafsson, Gustaf Hendeby
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