Stochastic Models, Information Theory, and Lie Groups, Volume 2

By Gregory S. Chirikjian. 2012

290 citations recorded by the source corpus.

Subfields: Finance, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/34c4a93198e4abef83e749490f036be7bce2402d

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Citations in the corpus

A micro Lie theory for state estimation in robotics (2018, background): “They share the rotational part θ , but clearly ρ = p (see [11, pag.”
Legged Robot State-Estimation Through Combined Forward Kinematic and Preintegrated Contact Factors (2017, methodology): “We first establish the mathematical notation where we assume readers are already familiar with basics of Lie groups, Lie Algebra, and optimization on matrix Lie groups [19], [20], [21].”
SVO: Semidirect Visual Odometry for Monocular and Multicamera Systems (2017, background): “The term J−1 r is the inverse of the right Jacobian of SO(3) [70, 71]:”
Contact-aided invariant extended Kalman filtering for robot state estimation (2019, methodology): “We assume a matrix Lie group [39, 23] denoted G and its associated Lie Algebra denoted g.”
Torsional Diffusion for Molecular Conformer Generation (2022, background): “29 is trivial and yields the volume over SO (3) of 8 π 2 [Chirikjian, 2011], proving the proposition.”
Supplementary Material to: IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation (2015, unknown): “41) A closed-form expression of the right Jacobian is given in [3]: Jr( ) = I 1 cos(k k) k k2 ^ + k k sin(k k) k (3)k ( ^)2.”
Quaternion kinematics for the error-state Kalman filter (2015, unknown): “(182) The right Jacobian and its inverse can be computed in closed form (Chirikjian, 2012, page 40), Jr(θ) = I− 1− cos ‖θ‖ ‖θ‖2 [θ]× + ‖θ‖ − sin ‖θ‖ ‖θ‖3 [θ]2× (183) J−1r (θ) = I + 1 2 [θ]× + ( 1 ‖θ‖2 − 1 + cos ‖θ‖ 2‖θ‖ sin ‖θ‖ ) [θ]2× (184) The right Jacobian of SO(3) has the following properties,…”