As someone who has never used a sonar device at a depth other than the surface, i know there are concievable ways for a computer program to quickly give a bearing, speed and relative depth. Obviously the closer the contact is and the more sensitive your equipment is the quick and more accurate this becomes.
Think of it this way. Your course, speed, depth, and location are being fed into a computer so it takes all of these into account in its computations. When you "pick up" a contact at say bearing 095 with broad spectrum sonar. You then ping again but this time you narrow your listening scope from 180 to 125 degrees vertical +and - 3 degrees horizontal to accomodate his possible movements. You can quickly narrow down his location tightening your angular "net", while keeping him centered in your sonar bearing.when you tighten and dont recieve a response ping you know hes either at the top or bottom of the net, so you just check both the top and bottom and where you get your ping. Wala!.
Now with all these pings and points of data you should easily have his Speed, Course, relative depth(which gives you his true depth based on your depth) and gives you a nice solution to go from.
Now if hes an enemy sub pinging a ton is giving away your position, but no fear! Using directional hydrophones (only 2 needed) its possible to triangulate his position.
Each phone when sensitive down to 1/2 to 1 degree can give you a bearing and elevation. Leaving you to fill in the trigonometric details with computers (even an analogue comp could do this job!)
If we were talking ww2 tech then yes it would be near impossible, but all you need is an elevation capabilities on your hydrophones and you could do this with 1 hydrophone by taking multiple readings over time. Similar to the "hydrophone only" course speed and bearing solution for surface ships. Except in 3 dimensions.
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