Dual Representation of Gaussians
Moments parameterization with mean $\mu$ and covariance matrix $\Sigma$
Canonical parameterization with information vector $\xi$ and information matrix $\Omega$
Moments to canonical
Canonical to moments
Marginalization and conditioning
Marginalization is cheap for moment parameterization whereas conditioning is cheap for canonical parameterization; Contioning is expensive for moment parameterization whereas marginalization is expensive for canonical parameterization.
Extended Inofrmation Filter (EIF) SLAM
EIF vs. EKF
- Same expressiveness as the EKF
- Prediction step is more costly, Correction step is cheaper
Literature
Extended Information Filter, Thrun et al.: “Probabilistic Robotics”, Chapter 3.5