Author: Martin Brossard
Year: 2018
- Applied recently discovered UKF on Lie Group (UKF-LG)
- Composite manifold
$\chi \in SE_{2+p}(3)$ with pose, velocity and lmks: $$ \chi=\left[\begin{array}{cccccc} \mathbf{R} & \mathbf{v} & \mathbf{x} & \mathbf{p}1 & \cdots & \mathbf{p}p \ \mathbf{0}{2+p \times 3} & & \mathbf{I}{2+p \times 2+p} \end{array}\right] . $$ - UKF spares the user from jacobians computation
- compare left and right multiplication: right is better
$\dot{R} = R (\omega -b_{\omega})_{\times}$ - Random variable on LG with left multiplication by the mean: $$ \chi=\bar{\chi} \exp (\boldsymbol{\xi}), \boldsymbol{\xi} \sim \mathcal{N}(\mathbf{0}, \mathbf{P}) $$
- Can then define a left-UKF-LG and a right-UKF-LG
- Generates Sigma Points in the lie algebra and then map them into the group
- Propagation and update step
- Simulation + 5 trajectory of EUROC
- runtime pourri (matlab)