Author: Zhang
Year: 2018
- Three solutions: fixing the unobservable states, setting a prior or let them free
- Accuracy similar but leads to different covariance estimation
- 4 DoF: Global position and yaw are unobservable (pitch and roll are provided by IMU)
- The objective function
$J$ is invariant to certain transformations$g$ of parameter$\boldsymbol{\theta}$ i.e. $$ J(\boldsymbol{\theta}) = J (g(\boldsymbol{\theta})) $$ - The orbit associated to
$\boldsymbol{\theta}$ is the 4D manifold: $$ \mathcal{M}_{\theta} = { g(\boldsymbol{\theta}) | g \in \mathcal{G} } $$ - Fixating the yaw in increment is not efficient as with propagation of updates, the yaw wrt the origin will change
- Gauge Fixation = fixing the position and yaw of the first pose = setting the jacobians of the corresponding columns to zero
- Gauge prior = let's add a penalty
- The prior weight needs to be properly tuned to not make too much iterations: 10^5 is great
- Covariance on free gauge is more distributed and has not meaningfull geometrical value