Read:
http://www.fas.org/man/dod-101/navy/...P/snr_prop.htm
It provides a good basic overview of sonar modeling.
What you're interested in more or less is the figure of merit. This gives the probability of detecting the contact 50% of the time.
Classification is a bit tricky since it will depend on the contact and the environment. The best way to model whether or not an AI has successfully classified a target would probably be to figure out the FOM of a few sources on the target and then say that the AI has successfully classified the target if X number of sources have a high enough FOM.