What web analytics system would be suitable for a small site with a SQLite database?

Question

Analytics

I know you want something weird.
There are a couple of sites on a small server. Sites are not public, used for the exchange of information by a very limited number of users.
I would like to have information from where, when and who went. I want to have information in a convenient interface.
Do not offer to look at the apache2 logs.
The only "but" - all sites use only sqlite (there are really few users, the server is really stunted) - I want the sqlite database to be used to store web analytics data.
Please tell me which web analytics system would fit these requirements?
Thank you.
PS I also don't want to store analytical information on "foreign" servers, so Google Analysis and its analogues are not suitable. It is necessary that the interface and the analytics database be on my server.