FastKDE?
Well, afaik DrussGT is using 151 bins in his movement, iirc. And my old experimental anti-aliased VCS gun uses more than 1500 bins (where continuing increasing bins no longer increase performance).
In targeting, DrussGT and ScalarBot (inspired by DrussGT) is using max overlap to reconstruct firing angles, not kernel density estimation, and it's O(nlgn).
Anyway, fastKDE is not to accelerate existing computation — but to accelerate the process of getting the real probability density function (which includes computing bandwidth and shape function effectively), with way less samples. You know, in robocode, the sample amount is really restricted, and I think this method is exactly what modern bots needs.
I use max overlap in O(nlogn) in Monk in the swarm gun as well because of the great amount of data, and I see those subquadratic approaches as a very nice way to spend more time in other time-consuming tasks. Anyway, looking closer, fastKDE seems to be very useful at first glance, given that it could even be used on top of the existing kNN guns just to weight the queried data more carefully. The real question now is if that's worth understanding and implementing :P That's probably a topic for the future. Maybe you gonna be the first one to put your hands on that?
