the above computations may be solved repeatedly for each transmitter receiver region unlike previously known methods apparatus and systems the inventive methods apparatus and systems reduce or eliminate irregularities of the computed trends due in part to the sparseness of the samples in previous attempts because of the relatively few receivers associated with each individual transmitter in conventional systems as well as irregularities reflecting local environmental influences on the point receivers the receiver coordinates are revised by multi lateration on the basis of the computed ranges whereupon a new polynomial regression is fitted to the newly computed acoustic propagation velocity as a function of x y r and optionally z and the process is repeated until the difference between the previously determined coordinates and the subsequently determined coordinates converges to a preselected limit such as 0 1 meter the radial error drms is derived for each revised receiver position by any well known means well known kalman filtering may be employed as desired the methods apparatus and systems of the invention may also be augmented with additional sensors for increased robustness of the system such devices are for instance but not limited to inclinometers pressure gauges compasses and inertial sensors integrated in or placed on streamers 8 and further acoustic measurements provided by transmitters located on buoys or other vessels two possible towed marine applications are so called over under surveys and surveys employing a positioning streamer in these towed marine applications acoustic ranging may occur between streamers at different depths z dimension and determining depth.