Author: M.Kaess
Year: 2022
- Robusify iSAM to handle eroneous data association
- robust back end optimizer based on graduated non convexity (GNC)
- data association is NP-hard (?)
- Exact methods (JCBB) are not suitable for RT
- Other methods try to find the maximum consensus set (PCM, RRR)
- M-estimator: applying a robust kernel that applies a sub quadratic cost
- GNC proposes to optimize this kernel
- additionnal variables that calssifies costs as inliers or outliers
- GNC seems to be the best for SLAM scenarios
- convexifying the problem with a robust parametrized cost fct $\rho ( r, \mu ) $ with
$\mu$ controling the convexity degree: this is called "graduation" - infinite growth kernel lead to a single optimum skewed by outlier while asymptotically constant kernels lead to many local optima: a small
$\mu$ leads to a infinite growth kernel (convex) while big$\mu$ leads to a-constant kernel (non convex) - Efficient GNC algorithm to optimize the kernel
- propose the Scale Invariant Graduated (SIG) kernel: $$ \frac{1}{2} \frac{c^2 r^2} {c ^2 + (r)^{\mu}} $$
- it is convex for
$\mu < 0.5$ and non convex for$\mu > 0.5$ ,$c$ is the shape parameter - Adapt iSAM2 update to graduated solving
- GN leads to large update in the presence of outliers
- the only incrementalizable line search algorithm is Powell's Dogleg but it is incompatible with EGNC => developped an incremental Dog Leg line search suitable for EGNC
- Putting all this together => riSAM
- plus: quadratic cost for known inliers (like odom meas) and classify strong outliers and strong inliers to initialize better
$\mu$
- ATE wrt iSAM2 run with inliers only
- Manhattan dataset with outliers in lc meas