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Unscented Kalman Filter Tutorial

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Unscented Kalman Filter TutorialGabriel A. TerejanuDepartment of Computer Science and EngineeringUniversity at Buffalo, Buffalo, NY IntroductionThe Unscented Kalman Filter belongs to a bigger class of filters calledSigma-Point Kalman FiltersorLinear Regression Kalman Filters, which are using thestatistical linearizationtechnique[1,5]. This technique is used to linearize a nonlinear function of a random variable through a linearregression betweennpoints drawn from the prior distribution of the random variable. Since we areconsidering the spread of the random variable the techniquetends to be more accurate than Taylorseries linearization [7].In the same family of filters we have The Central Difference Kalman Filter , The Divided Differ-ence Filter , and also the Square-Root alternatives for UKF and CDKF [7].

The sigma points are chosen so that their mean and covariance to be exactly xa k−1 and P k−1. Each sigma point is then propagated through the nonlinearity yielding in the end a cloud of transformed points. The new estimated mean and covariance are then computed based on their statistics. This process is called unscented transfor-mation.

  Process, Sigma

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