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Uncertainty Propagation on Unimodular Matrix Lie Groups
Jikai Ye, Amitesh S. Jayaraman, Gregory S. Chirikjian
This paper addresses uncertainty propagation on unimodular matrix Lie groups that have a surjective exponential map. We derive the exact formula for the propagation of mean and cov…
A Lie-Theoretic Approach to Propagating Uncertainty Jointly in Attitude and Angular Momentum
Amitesh S. Jayaraman, Jikai Ye, Gregory S. Chirikjian
Dynamic state estimation, as opposed to kinematic state estimation, seeks to estimate not only the orientation of a rigid body but also its angular velocity, through Euler's equati…
On the Inertial Rotational Brownian Motion of Arbitrarily Shaped Particles
Amitesh S. Jayaraman, Jikai Ye, Gregory S. Chirikjian
This article reports the modeling of inertial rotational Brownian motion as an Ornstein-Uhlenbeck process evolving on the cotangent bundle of the rotation group, SO(3). The benefit…