Author: Paul Chauchat
Year: 2018
- group affine observation system = class of estimation pb on Lie Groups
- independence linearization => no need to relinearize
- smoothing approach for SLAM takes advantage of the sparsity of the pb
- Here equations must have specific properties more than lying on manifold (group affine systems on Lie Groups)
- uncertainty on Lie-group with left or right multiplicative noise based on a gaussian noise vector projected through exponential map
- Extension to invariant KF to smoothing
Smoothing:
- filtering: consider only latest state of the system
- smoothing: recover the MAP of the full trajectory given a set of measurements
- MAP can be converted in least square pb under the assumption of additive gaussian noise
- The link between factor graph is straight forward -> each term of the sum are referred as factors
-
$\boxminus : M \times M \rightarrow TM$ &$\boxplus : M \times TM \rightarrow M$ BEWARE these can be defined for left or right operation
Invariant smoothing:
- a group affine observation system has specific properties on
$f$ (dynamic model) and$h$ (observation model) - After calculations, linearization of factors do not depend on current state
Experiments:
- A 2D wheeled robot with odometers and artificial observations that are noisy added groundtruth poses (~GNSS)
- All smoothing methods are more robust to wrong initialization than filtering