A new method for the nonlinear transformation of means and covariances in filters and estimators

By Simon Justin Julier, Jeffrey K. Uhlmann, H. F. Durrant-Whyte. IEEE Transactions on Automatic Control, 2000

3,867 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/76c52206888eedef8d8dead3007992e53e3c4ae8

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Citations in the corpus

High-degree cubature Kalman filter (2013, neutral): “…ei−1 Wi = 1/ (2 (n + κ)) 2 ≤ i ≤ n + 1 γ i = − √ n + κ ei−n−1 Wi = 1/ (2 (n + κ)) n + 2 ≤ i ≤ 2n + 1 (15) where ei−1 is the unit vector in Rn with the (i−1)th element being 1 and κ is a scaling parameter with the suggested optimal value of κ = 3 − n for Gaussian distributions (Julier et al., 2000).”
Aerodynamic parameter estimation from flight data applying extended and unscented Kalman filter (2006, background): “It is claimed that the computational complexity of the UKF is comparable to the EKF [15] [24].”
Decentralized Environmental Modeling by Mobile Sensor Networks (2008, methodology): “These expected quantities can be calculated by means of the unscented transform, originally developed to achieve higher-order accuracy in the nonlinear transformation of pdfs, beyond the accuracy obtained by linearizing the transformation at the mean of the estimate [21]–[23].”
Unscented Kalman filtering for nonlinear structural dynamics (2007, methodology): “To ensure accuracy of the results, in the analyses we have always adopted ∆t < ∆t?, ∆t? being the threshold at which a further reduction of the time step size do not modify the computed system response.”
Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering (2011, methodology): “As with the UKF, DDF 255 uses a deterministic sampling approach to propagate Gaussian statistics through the nonlinear 256 function; e) the Gaussian sum filters (GSF) approximates both the predicted and posterior 257 densities as sum of Gaussian densities, where the mean and covariance of each Gauss”
Bayesian State Estimation Method for Nonlinear Systems and Its Application to Recorded Seismic Response (2006, methodology): “Although the EKF has been widely used, it is only reliable for systems that are almost linear on the time scale of the updating intervals Julier et al. 2000; Wan and van der Merwe 2000.”
Nonlinear Dynamical System Identification from Uncertain and Indirect Measurements (2004, background): “It is motivated by the fact that it is easier to approximate a distribution by a Gaussian than to approximate an arbitrary nonlinear function by linearization [Julier et al., 1995; Julier et al., 2000].”
Sparse Gauss-Hermite Quadrature Filter with Application to Spacecraft Attitude Estimation (2011, methodology): “Another important contribution of this paper is to prove that the UKF with the suggested optimal parameter [6] is a subset of the SGHQF.”
An Introduction to Inertial and Visual Sensing (2007, methodology): “This estimation problemhasbeen solvedusing offlinebatch optimzation by Strelow (2004), extended Kalman filter by Qian et al. (2001), iterated extended Kalman filter by Strelow (2004) and unscented Kalman filter by Julier et al. (2000) and Armesto et al. (2004).”