Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations

By Simon Justin Julier, Jeffrey K. Uhlmann. Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002

403 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Civil and Structural Engineering, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/d2d89a61ac3f4671395bea6ffdbb1424166e820b

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Citations in the corpus

Which Is Better, an Ensemble of Positive–Negative Pairs or a Centered Spherical Simplex Ensemble? (2004, methodology): “Spherical Simplex Sigma Points The minimum number of sigma points required to have the same mean and covariance as an n-dimensional random variable is n 1 1 (Julier and Uhlmann 2002a; Julier 2003).”
Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems (2011, neutral): “These points can be constructed recursively with a procedure similar to that described in [10], namely, I = √ p Ĩ r , where the vectors Ĩ r are the columns of the matrix noted [Ĩ∗ r ] recursively defined by ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎩ [Ĩ∗ 1 ] = ( − 1 √ 2α 1 √ 2α ) , α = p p + 1”
A Numerical-Integration Perspective on Gaussian Filters (2006, methodology): “The UKF using a set of simplex sigma points [41], [42], [21, App.”
The spherical simplex unscented transformation (2003, background): “For space reasons it is not possible to analyse the full impact of the term, and we refer the reader to [ 9 ] and [8] for a fuller analysis.”
Ensemble Transform Kalman Filter-based ensemble perturbations in an operational global prediction system at NCEP (2006, methodology): “turbations about the analysis is the simplex transformation first proposed by Purser (1996) (see, also Julier and Uhlmann, 2002; Wang et al., 2004).”
Sparse Gauss-Hermite Quadrature Filter with Application to Spacecraft Attitude Estimation (2011, background): “The different sigma-point-set selection strategies include the symmetric points [6], the minimal-skew simplex points [23], the spherical simplex points [24,25], the Schmidt orthogonalizationbased simplex set [26], and thosewithmore than 2n 1 sigmapoints for accuracy enhancement [27–29], where n is t”
Unscented filtering and nonlinear estimation (2004, methodology): “In [49] we chose a set of points that minimize the skew (or third-order moments) of the distribution.”
Initial perturbations based on the ensemble transform (ET) technique in the NCEP global operational forecast system (2008, background): “2) is the simplex transformation (ST) (Purser, 1996; Julier and Uhlmann, 2002; Wang et al., 2004; W06).”