Exact Theory of Tracking of Moving Underwater Object by Short‐Base Navigation System Attached to an Imperfectly Stabilized Moving Ship

The theory of locating a deep submersible by measurement of time delays in arrival of an acoustic pulse from the deep submersible to three hydrophones of a short‐base navigational system has been developed in detail. The theory incorporates all the relevant variables such as the translational and rotational positions and velocities of the tracking ship and the variation of acoustic speed with depth. No restrictions have been placed on the relative values of the horizontal and vertical coordinates of the submersible relative to the tracking ship. A numerical example is given to demonstrate the use of the theory and to show the effects of ignoring the motion of the tracking ship and the variation of acoustic speed with oceanic depth.