I want to implement my own pose graph SLAM following . Since my vehicle is moving in 3D-space i represent my pose using a 3D-translation vector and a quaternion for orientation.  tells me that it's necessary to adapt their algorithm 1 by using manifolds to project the poses into euclidean space. I also studied the approach of . In section "IV.B. Nonlinear Systems" they write that their approach remains valid for nonlinear systems. I conclude that for their case it's not obligatory to make use of a manifold. But I don't understand how they avoid it. So my questions are:
- Is it correct that there is an alternative to manifolds?
- If yes, how does this alternative look like?
 Grisetti, G., Kummerle, R., Stachniss, C., & Burgard, W. (2010). A tutorial on graph-based SLAM. Intelligent Transportation Systems Magazine, IEEE, 2(4), 31-43.
 Kaess, M., Ranganathan, A., & Dellaert, F. (2008). iSAM: Incremental smoothing and mapping. Robotics, IEEE Transactions on, 24(6), 1365-1378.