This is a kind of difficult question.
I know about EKF-SLAM, which uses a state from previous time to estimate next state as an online filter, I also know about Graph-SLAM, which uses all states in past as full SLAM, and represents them as merely whole bunch of nodes and edges, and optimize structure of nodes and eges by minimizing error to estimate better states.
Now, I know that there is no meaning in running EKF-SLAM with odometry info only, since what EKF does is estimating future state by balancing weight between Odometry info AND Observation of landmark info. so both are needed.
My question is, is it possible to run Graph-SLAM with only Odometry info and no landmark observation info whatsoever? It seems like Graph-SLAM can run by gathering all Odometry info state upto current ones and converting them to nodes and edges just like it does when both Odo and obs are provided, and it can optimize the structure of nodes and edges. Is is possible? What does output mean? "Optimized" Odometry? Any thought to it? Thank you in advance. :)
preface: I am not 100% certain, these are just my assumptions/opinions
the point of SLAM is Simultaneous Localization And Mapping In order to do any mapping you need Observation of landmarks, or some other feature. Otherwise you are only performing localization.
Think if I dropped you a building you've never been in before and I said, create a map for me, BUT you can ONLY count your footsteps. You must not use any other senses (eyes closed, ears plugged, etc). You would quickly realize this is a nearly impossible task. If you use only odometry, something like a Kalman Filter, or EKF should work nicely, but again this is only doing localization, not mapping.
hope that helps