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...en the dynamics and measurement model are nonlinear or the noise processes are non-Gaussian, the posterior distribution can be approximated using techniques such as linearization, unscented filtering =-=[38]-=-, interacting multiple models [39], particle filters [40], or other numerical methods. Authorized licensed use limited to: Univ of Calif Berkeley. Downloaded on June 17,2010 at 19:01:49 UTC from IEEE ...

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... degrades rapidly as the IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 41, NO. 1 JANUARY 2005 309snonlinearities become more severe. To alleviate this problem the unscented KF (UKF) [4], =-=[5]-=- maintains the second-order statistics of the target distribution by recursively propagating a set of carefully selected sigma points. This method requires no linearisation, and generally yields more ...

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...Filter (EKF)[1]. A more recent development is to use a deterministic sample based approximation to ensure that the models (1)-(2) are never approximated, only the distributions under examination[28], =-=[29]-=-, the so-called “unscented transform”. We will describe both of these in turn. An exemplar system which requires such an approximation is described as: Xt = ϕ(Xt−1, ɛt) (24) Yt = φ(Xt, νt) (25) with ɛ...

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...tion, and the sensor-to-sensor transform, from camera and IMU measurements. The algorithm is based on the unscented Kalman filter (UKF), an alternative to the well-known extended Kalman filter (EKF) (=-=Julier & Uhlmann 2004-=-). Our choice of the UKF is motivated by its superior performance compared to the EKF for many nonlinear problems. For Gaussian state distributions, the posterior estimate produced by the UKF is accur...

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...tion in a Kalman Filtering (KF) setup. While the discontinuous non-linearity precludes application of the extended (E) KF, it can be handled with more powerful techniques such as the unscented (U) KF =-=[14]-=-, or the particle filter (PF) [7], [16]—algorithms that have also been applied in the context of filtering [6], [29] and target tracking with a WSN [1], [8]. However, all these approaches are signific...

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...be used by replacing the non-linear model with a locally linearized model as in the extended Kalman filter (EKF) [2,6] or by using the unscented transformation as in the unscented Kalman filter (UKF) =-=[29]-=-. • Target dynamics are linear Gaussian p(xk,j | xk−1,j) = N(xk,j | Ak−1,jxk−1,j, Qk−1,j), (5) where the transition matrix Ak−1,j and process noise covariance matrix Qk−1,j may be different for differ...

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...x=m (j) k|k−1 ]T + H (j) k , U (j) k (j) P k|k−1 [H(j) k ]T , (50) (j) ∂hk(m k|k−1 = ∂ε , ε) ∣ ∣ ε=0 . (51) B. Unscented Kalman CPHD (UK-CPHD) Recursion Analogous to the unscented Kalman filter (UKF) =-=[41]-=-, a non-linear approximation to the Gaussian mixture CPHD recursion is proposed based on the unscented transform (UT). The strategy here is to use the UT to propagate the first and second moments of e...

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...[3,4]. This may work well but without any guarantees for mildly nonlinear systems where the true posterior is unimodal Gust one peak) and essenti ally symmetri c. 3) The unscented Kalman filter (UKF) =-=[5,6]-=- propagates a number of point s in the state space from which a Gaussian distribution is fit at each time step. UKF is known to accomodate also the quadratic term in nonlinear models, and is often mor...