Let me see if I remember that right - that is for a half barrel, right?

I don't know many submerged filters that are small enough to fit on the bottom of such a barrel pond, but you can try making a simple bucket filter yourself. Its basically a 3-5 gallon bucket (new), pea gravel and some sort of sponge to catch the bigger debris.
The bucket has a hole (or two) in the lower 1/3, with a net of some kind covering it up, so the pea gravel won't fall out and into the pond. Put pea gravel on the bottom of the bucket, you can use lots of it, half full is fine, that pea gravel is your basis for the beneficial bacteria. Put the sponge or filter floss material on top of it, that will catch any bigger debris and waste. Homedepot has some neat (although bright orange

) buckets with a lid - I usually drill a hole into the lid and put it on the bucket.
The way it works - a pump carries water from the barrel into the bucket through the hole in the lid, the water runs through the filter floss/sponge material and the pea gravel to the bottom of the bucket, where its relased back into the barrel via the hole(s) in the lower part of the bucket.
Now, the pump can't be too strong or too weak, otherwise the bucket either overflows, or not enough water will run through the filter media.
You can hide the bucket nicely behind the barrel on a raised platform, like an upside down terracotta pot, and put a few potted plants around it. Nobody will ever notice...