The paper and CN comments are interesting. Some cautionary thoughts:
Having a new focus algorithm in Ekos wouldn't necessarily hurt anything, but it may not help much either. The old saying "out of the pan, into the fire" comes to mind.
The paper acknowledges some new algorithm weaknesses, and these are different pains, but on par with existing algorithm weaknesses.
1. Any saturated stars in the image will cause an inverted fitting problem. Until this has been addressed, fast imaging systems (e.g < f/4?) will likely be particularly sensitive to the issue.
2. A quote from the author (CN post): "Starting from nothing is a problem for any algorithm. IMO, a rough focus position is needed to get autofocusing started". This is the same problem ekos currently has (all algorithms), and one of the primary reasons why temperature and altitude focus compensation was implemented (although never integrated).
3. Improperly set step size is a problem. The authors suggest 1/2 CFZ for a step size. I've previously stated that CFZ size is critical (the setting should have been automated). I concur with the 1/2 CFZ size suggestion.
4. The number of images needed is stated from 8-17. That probably excludes any use for guiding assistance (only noted because Jasem raised that question).
In the end, star detection becomes non-problematic, but avoiding star saturation becomes problematic. The same "avoid donuts" starting condition problem prevails, and setting step_size appropriately is equally important.
IMO, integration of temperature based focus compensation (even if using the current config file vs unimplemented GUI) would answer the donuts problem while seriously reducing time consuming focus runs (as focus is updated between exposures...thus tracking longer before another focus run is needed).
See:
indilib.org/forum/ekos/7626-temperature-...us-compensation.html
CS... Doug