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    2 Literature review on quadrature based nonlinear estimation (Cont'd...)

    2.2 Unscented Kalman filter (cont'd...)

    In [Julier 2002b] the generalization of the unscented transformation has been made which is known as scaled unscented transformation. It is claimed that the method calculates the mean and covariance with an accuracy of second order with out calculation of Jacobian or Hessian. In [Julier 2004] the advantage of UKF over EKF has been discussed. The motivation, development and implementation of unscented transformation have also been discussed.

    After UKF has been proposed, the filter is being extensively used in various field of application. In [Wan 2000], Wan et.al lucidly illustrated the concept of sigma points using attractive figures. The estimator has also been used in dual estimation problem. This work advocated the use of UKF as a better substitution of EKF at a comparable level of complexity.

    In [Merwe 2003, 2001] the square root unscented Kalman filter (SRUKF) has been proposed and the filter has been applied to a robot arm problem. The simulation results show that the SRUKF show better results than EKF and UKF. In the paper [Briers 2003] , Rao Blackwellisation technique has been introduced to calculate the tractable integrals found in the unscented Kalman filtering technique. The newly developed filter has been named as Rao Blackwellised UKF filter. The advantage of this new variant of UKF has been stated as (i) reduction in quasi Monte Carlo variance (ii) decrease in computational load.

    Wu [Wu 2005] discussed the augmented and non-augmented unscented transformation for nonlinear system with additive noise. Based on the two types of transformation, augmented and non-augmented UKF has been derived. It is shown that the basic difference between them is that the augmented UKF draws a sigma set only once while the non-augmented UKF has to redraw a new set of sigma points after the time update to incorporate the effect of additive process noise. An example has been provided and the performances of these two filters have been compared. In [Zhan 2007] , an iterated UKF algorithm has been introduced and was successfully applied to a passive target tracking problem. It alleviates the problem of standard UKF such as weakness in robustness, tracking accuracy and convergence speed.

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