The scaled unscented transformation

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

1,194 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Civil and Structural Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/23d320c56775693f7e0c63d11774375a0e4472ed

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Citations in the corpus

State estimation for legged robots on unstable and slippery terrain (2013, background): “For a more detailed discussion on the employed UKF please refer to [10].”
Unscented Filtering in a Unit Quaternion Space for Spacecraft Attitude Estimation (2007, neutral): “More details are found in [1][2][3][4].”
Cubature Kalman Filters (2009, background): “Instead, more secondary scaling parameters (apart from ) were introduced in an attempt to incorporate knowledge about the prior statistics in the unscented transformation [41].”
Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems (2011, background): “Some authors have proposed sigma-points which do not satisfy this distance property, in particular for star sigma-points for which increasing the weight of the center-point allows to preserve the unit covariance while moving the other points further away from the mean [11].”
An efficient image similarity measure based on approximations of KL-divergence between two gaussian mixtures (2003, background): “Scaling parameters can provide an extra degree of freedom to control the scaling of the sigma points further or towards μ [6].”
The unscented Kalman filter for nonlinear estimation (2000, background): “For non-Gaussian inputs, approximations are accurate to at least the second-order, with the accuracy of third and higher order moments determined by the choice of and (See [4] for a detailed discussion of the UT).”
Sigma-point kalman filters for probabilistic inference in dynamic state-space models (2004, methodology): “For a Gaussian prior the optimal choice is β = 2 [97].”
Visual-Inertial Sensor Fusion: Localization, Mapping and Sensor-to-Sensor Self-calibration (2011, methodology): “We employ the scaled form of the unscented transform Julier (2002), which requires a scaling term λ = α2( N + β) −N .”
Calibration of Strapdown Magnetometers in Magnetic Field Domain (2006, methodology): “While novel, nonlinear estimation techniques which combine the unscented transformation [11] with Kalman or Particle Filtering [12, 13] can be used to directly estimate the posterior covariance matrix, for the work reported in this paper, we will use the linearized estimate of P given by Equation 34”
Unscented filtering and nonlinear estimation (2004, methodology): “Assuming that and setting , it can be shown that [33]”
Approximate robust optimization of nonlinear systems under parametric uncertainty and process noise (2015, background): “An answer to the question how to choose the parameter κ and a thorough theoretical analysis of the approximation errors can be found in Julier and Uhlmann (1996). Note also that there is no unique way to choose these sigma points.”
Autonomous convoy driving by night: The vehicle tracking system (2015, methodology): “A detailed description of the Kalman filter innovation can be found in [24].”
Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations (2002, methodology): “However, this is not always the case and, in a related paper, we describe a method for minimising unwanted effects of higher order moments [16].”