How can I find out how many people are subscribed to an RSS feed i'm serving?

Question

We have a site that is serving some RSS feeds, and we'd like to know how many people is subscribed to each one, without using a system like FeedBurner to serve them.

The original approach to figuring this out was basically logging requests, and then getting the number of unique IP's that had requested each feed. However, if I get 1 million people subscribing through Google Reader, for example, then I'm only going to get 1 request from Google for all the subscribers, right?

Is there a way around this?

How does FeedBurner itself work around it?
Being Google's property now, it can surely find out how many people are subscribed to a certain feed in GReader specifically, but I'm sure there are other online RSS feeds that would pose the same problems.

Any ideas?

Answer 1

This doesn't answer your entire question, but when Google Reader crawls your feed, it will expose to you, in the User-Agent, the number of people subscribed via Google Reader:

http://www.google.com/support/reader/bin/answer.py?hl=en&answer=70001