Numerical Algorithms

Variational Unscented Kalman Filter (UKF-V) for Satellite Attitude Estimation

Description: The following animated simulation shows the estimated trajectory of a Cubic satellite. Using the proposed algorithm, the estimated error is significantly reduced to a low level.
Reference: Tianzhi Li and Jinzhi Wang, Variational unscented Kalman filter on matrix Lie groups, Automatica, 172: 111995, 2025.

Optimal Control of n-DOF Gaussian Distributions

Description: The following animated simulation shows the optimal trajectory of a controlled 3-DOF Gaussian distribution. The initial Gaussian distribution $mathcal{N}left(R_{0},m_{0}right)$ is controlled to the desired state $mathcal{N}left(R_{f},m_{f}right)$ while minimizing the energy cost $J=int_{t_{0}}^{t_{f}}frac{1}{2}|u|^{2}dt$ over the time window $[t_{0}, t_{f}]$ .
Reference: Tianzhi Li, Rui Fu, and Jinzhi Wang, Reduced dynamics and geometric optimal control of nonequilibrium thermodynamics: Gaussian case, Automatica, 164: 111626, 2024.