This is identical to the process of positioning an artifact using baseline measurements from control points. There are differences between using tape measures and acoustics. Acoustic positioning systems can compute the position of a point many times a second. Many acoustic ranges can be measured at the same time for added redundancy. The diver unit can accurately measure its own depth.
Many divers can use the array of beacons at the same time with no loss in update rate or accuracy.
Systems are available which are accurate to 10mm or so over ranges of a few hundred metres. Systems are also available which are accurate to 50 mm which can cover kilometres. APS are expensive and currently quite complicated. Existing systems do not work well in confined spaces. The cost of most systems prohibits their use in a number of cases however compared to the expense of making tape measurements they are a viable alternative, especially in deep water.