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... by linearization the Extended Kalman Filter (EKF) [5, p. 106] is obtained, the posterior density being still modeled as Gaussian. A recent alternative to the EKF is the Unscented Kalman Filter (UKF) =-=[42]-=- which uses a set of discretely sampled points to parameterize the mean and covariance of the posterior density. When the state space is discrete and consists of a finite number of states, Hidden Mark...

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...earities, Kalman filters approximate the robot motion model using a linear function obtained via Taylor series expansion. The resulting Kalman filter is known as extended Kalman filter [64] (see also =-=[47]-=-), and single motion commands are often approximated by a series of much smaller motion segments, to account for nonlinearities. For most robotic vehicles, such an approximation works well. The result...

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...a total of 15 variables. The design of this parameter space follows standard methodology �Farrell & Barth, 1999; van der Merwe & Wan, 2004�, as indicated in Table I. An unscented Kalman filter �UKF� �=-=Julier & Uhlmann, 1997-=-� estimates these quantities at an update rate of 100 Hz. The UKF incorporates observations from the GPS, the GPS compass, the IMU, and the wheel encoders. The GPS system provides both absolute positi...

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...t is similar to the arc reversal technique proposed for particle filters applied to Bayes networks [10] , and it is similar to recent work by van der Merwe [24] , who uses an unscented filtering step =-=[9]-=- for generating proposal distributions that accommodate the measurement. While this modification is conceptually simple, it has important ramifications. A key contribution of this paper is a convergen...

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...the EKFsalgorithm can, however, lead to poor representations of the nonlinear functions andsprobability distributions of interest. As as result, this filter can diverge.sRecently, Julier and Uhlmann (=-=Julier and Uhlmann 1997-=-) have introduced a filtersfounded on the intuition that it is easier to approximate a Gaussian distributionsthan it is to approximate arbitrary nonlinear functions. They named this filtersthe unscent...

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...h states and parameters are estimated simultaneously. This paper points out the flaws in using the EKF, and introduces an improvement, the Unscented Kalman Filter (UKF), proposed by Julier and Uhlman =-=[5]-=-. A central and vital operation performed in the Kalman Filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF, the state distribution is approximated by...

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... noise. Non-linearities are typically approximated by linearization at the current state, resulting in the extended Kalman filter (EKF). Recently, the unscented Kalman filter (UF) has been introduced =-=[45, 79]-=-. This approach deterministically generates samples (sigma-points) taken from the Gaussian state and passes these samples through the non-linear dynamics, followed by a Gaussian approximation of the p...

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...m variable that has undergone a transformation. When the system models are non-linear no general closed-form solutions exist [11] and many approximations have been proposed [1--3, 12, 13]. In [7] and =-=[9]-=- we introduced a new approximate method for propagating means and covariances through nonlinear transformations called the unscented transformation. A set of weighted sigma points are deterministicall...