2 papers
math.NA2022
High-order symplectic Lie group methods on using the polar decomposition
Xuefeng Shen, Khoa Tran, Melvin Leok
A variational integrator of arbitrarily high-order on the special orthogonal group is constructed using the polar decomposition and the constrained Galerkin method. It has…
math.OC2019
Geometric Symmetry Reduction of the Unobservable Subspace for Kalman Filtering
Xuefeng Shen, Melvin Leok
In this article, we consider the implications of unobservable subspaces in the construction of a Kalman filter. In particular, we consider dynamical systems which are invariant wit…