The only filtering I've ever done has been through my kidneys. And I get extremely clear beer, usually forgetting even to add moss to my boil.
I get little if any sediment in my bottles, simply by opting for a long primary. This is my yeastcake for my Sri Lankin Stout that sat in primary for 5 weeks. Notice how tight the yeast cake is? None of that got racked over to my bottling bucket. And the beer is extremely clear.
That little bit of beer to the right is all of the 5 gallons that DIDN'T get vaccumed off the surface of the tight trub. Note how clear it is, there's little if any floaties in there.
When I put 5 gallons in my fermenter, I tend to get 5 gallons into bottles. The cake itself is like cement, it's about an inch thick and very, very dense, you can't just tilt your bucket and have it fall out. I had to use water pressure to get it to come out.
This is the last little bit of the same beer in the bottling bucket, this is the only sediment that made it though and that was done on purpose, when I rack I always make sure to rub the autosiphon across the bottom of the primary to make sure there's plenty of yeast in suspension to carb the beer, but my bottles are all crystal clear and have little sediment in them.
Half the time I forget to use moss, and you can't tell the difference in clarity.
Another thing is to leave your beer in the fridge for at least a week. The longer you chill the beer in the fridge, the tighter the yeast cake. I had a beer in the back of my fridge for 3 months, that I could completely upend and no yeast came out. Longer in the cold the tighter the yeast cake becomes. Even just chilling for a week (besides getting rid of chill haze) will go to great lengths to allow you to leave the yeast behind, but with only a minimum amount of beer.
I get the barest hint of sediment in my bottles....just enough for the yeast to have done the job of carbonating the beer.