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On the Comparison of Gauge Freedom Handling in Optimization-based Visual-Inertial State Estimation

Author: Zhang

Year: 2018

Notes:

  • 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